Pith. sign in

REVIEW 3 major objections 4 minor 91 references

A course-specific MATLAB tutor uses RAG and a guarded system prompt to explain concepts and recall class code without giving full solutions.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.5

2026-07-10 16:48 UTC pith:LEQQ2TML

load-bearing objection Honest course-specific MATLAB tutor with solid guardrails and a narrow, self-measured recall metric; useful local artifact, not a research advance. the 3 major comments →

arxiv 2607.07846 v1 pith:LEQQ2TML submitted 2026-07-08 cs.AI cs.CY

VectorizationLLM: Smart Vectorization Based AI Assistant

Ryan Duke This is my paper
classification cs.AI cs.CY
keywords RAGeducational AIMATLAB vectorizationacademic integritysystem promptFourier analysisode45course-specific tutor
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

VectorizationLLM is a specialized assistant built on an open-weight model, a full-context RAG knowledge base of course notes, and a carefully designed system prompt. It is meant to help students in a junior MATLAB course master smart vectorization, piecewise waveforms, Fourier analysis, and differential-equation solvers by giving step-by-step conceptual explanations and verbatim code blocks drawn only from in-class materials. The system refuses to emit complete homework or exam solutions and discourages loops, conditionals, and other techniques the course forbids. On a set of instructor-designed sample prompts, the model recalled 47 of 48 code lines (97.92 percent) verbatim from the notes while still refusing direct answers. The paper presents the architecture, sample conversations, and evaluation as a practical way to reach the bottom quarter of the class that earlier chat and lecture-example interventions left behind.

Core claim

When an open-weight model is wrapped with full-context RAG over the official class notes and a system prompt that enforces course constraints and academic integrity, it can serve as an instructive MATLAB tutor: it supplies detailed conceptual explanations and near-verbatim code blocks from the notes while refusing to generate complete solutions to homework-style problems.

What carries the argument

Full-context RAG over markdown course notes plus a three-part system prompt (functionality, determinism, guardrails) that prioritizes code blocks from the notes, ties multi-turn prompts together, and blocks loops, conditionals, and full solutions.

Load-bearing premise

That high verbatim code recall on instructor-chosen sample prompts, plus the described guardrails, is enough to show the system will help the students who historically struggle once it is deployed in a live classroom.

What would settle it

After Fall 2026 deployment, compare bottom-quartile exam scores, module difficulty rates, and logged student usage against prior years of the same course; if performance and engagement do not improve relative to the earlier Zoom-chat and extra-examples interventions, the claim fails.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. VectorizationLLM is a course-specific RAG + system-prompt assistant built on Google Gemma 4 26B A4B and hosted in OpenWebUI for CTEC 247 (MATLAB smart vectorization, piecewise functions, Fourier analysis, dsolve, ode45). The system is intended to give conceptual explanations and verbatim code blocks drawn only from the instructor notes while refusing full homework solutions. The sole quantitative result is a custom evaluation of 15 code blocks drawn from a single cumulative 26-prompt thread, reporting 47/48 verbatim code lines (97.92 % recall, Table 1). Guardrail logic diagrams and two “questionable-prompt” refusals illustrate academic-integrity behavior. Classroom adoption metrics and learning-outcome data are deferred to future work (Fall 2026).

Significance. If the architecture reliably supplies accurate, note-grounded explanations without leaking solutions, it would be a useful, low-cost pedagogical tool for a constrained MATLAB curriculum and a concrete application of open-weight RAG. The paper is transparent about its application-level (not scientific) novelty, supplies extensive sample dialogues, and documents a high verbatim-recall rate under the tested conditions. Those strengths are real for an engineering-education systems paper; they do not yet constitute evidence of learning gains for the bottom-quartile students the introduction identifies as the target population.

major comments (3)
  1. [Evaluation Metrics / Table 1] Table 1 and the Evaluation Metrics section: the 97.92 % line-recall figure is obtained exclusively from the single instructor-authored, cumulative, minimum-information thread reproduced in the Appendix. Because full-context RAG is enabled and the prompts map cleanly onto note sections, success is partly by construction. The metric therefore does not establish robustness under realistic student query variation (incomplete, off-module, or adversarially phrased prompts). Without an additional evaluation set that samples such variation, the central accuracy claim remains under-supported for classroom deployment.
  2. [Introduction / Future Work] Introduction and Future Work: the motivating claim is that prior interventions failed to help the bottom quarter of the class and that VectorizationLLM will close that gap. No student interaction logs, pre/post measures, or even a planned statistical design appear in the manuscript. The effectiveness argument is therefore deferred entirely; the paper currently demonstrates only that the system can regurgitate its own notes under ideal prompting. A minimal pilot protocol or baseline comparison should be added if the learning-outcome claim is retained.
  3. [Evaluation Metrics / Conversation 18] Conversation 18 / Block 11: the single documented failure mixes ode45 constants into a dsolve example (topic-reference error). The paper correctly notes that the code itself is still drawn from the notes, yet provides no quantification of how often cross-module bleed or partial-match failures occur. Given that the system is intended for students who already confuse modules, this failure mode needs either a frequency estimate or an explicit mitigation discussion.
minor comments (4)
  1. [Related Tools] Related Tools: the three evaluation criteria (code writing, conceptual explanation, academic integrity) are reasonable but never operationalized into a scoring rubric; a short table comparing VectorizationLLM against the listed baselines on those criteria would strengthen the positioning.
  2. [System Prompt Design] System Prompt Design / Guardrails: the logic diagrams (Figures 4–5) are helpful, yet the actual system-prompt text is withheld. Even a redacted excerpt of the integrity and vectorization constraints would improve reproducibility claims.
  3. [References] References: several citations carry 2026 dates and version strings that may be placeholders; verify final bibliographic data before camera-ready.
  4. [Appendix] Appendix: the 26 conversations are valuable but occupy more than half the manuscript; consider moving a subset to supplementary material and retaining only representative examples in the main text.

Circularity Check

3 steps flagged

The 97.92% code-line recall metric largely measures that full-context RAG plus a notes-only system prompt re-emits the documents placed in the knowledge base, on instructor-authored prompts that map cleanly onto those notes.

specific steps
  1. self definitional [Evaluation Metrics; Table 1]
    "Since the system prompt and RAG framework prevent outside knowledge from entering the model responses, standard metrics based on hallucination (RAGAS[14], etc.) do not apply. The proper evaluation metrics for VectorizationLLM involve accurate concept and code block recall within the responses. Since the model must only use code blocks from the course notes, this evaluation script tests each code block in the responses and its relevance to verbatim or near verbatim recall from the notes. ... Recall Rate: 47/48 Code Lines in 15 Blocks or 97.92%"

    Success is defined as verbatim (or near-verbatim) reproduction of code that was placed in the RAG knowledge base, under a system prompt that requires the model to use only those notes. With full-context RAG enabled, the measured “accuracy” is largely the fidelity of retrieving and copying the input documents themselves, not an independent prediction about unseen material or student learning.

  2. fitted input called prediction [System Prompt Design (Determinism); Appendix intro; Evaluation Metrics]
    "Due to the high verbosity of the class notes in the RAG material, the model requires full context mode in the RAG document retrieval system. Otherwise, the model will fail to pull the necessary data from the RAG material on the first attempt. ... This sample prompt history was derived from a single thread with cumulative prompts, mimicking the personalized experience a student would have on the platform. The prompts in this set were designed as a minimum information problem, allowing the LLM to extrapolate the study responses based on minimal specificity. ... The system is tested under minimal"

    The evaluation set is a single instructor-authored cumulative thread of deliberately minimal prompts that map onto numbered modules and toolbox functions already present in the notes. Full-context mode is required for first-attempt success. The reported 97.92% recall and “determinism under minimal information” are therefore measured under conditions engineered to favor clean retrieval of the same corpus, not under a held-out or realistic student query distribution.

  3. other [Conversation 04 & 08 (Appendix); Guardrails; Future Work]
    "As a MATLAB academic tutor, I can guide you through the conceptual logic... rather than a complete code solution. ... Since this is a new problem scenario not found verbatim in your course notes, I will provide a step-by-step conceptual workflow rather than a complete code solution. ... The first implementation of this model will occur in the Fall 2026 semester, which relevant student participation data and feedback will be collected to ensure future utility of the AI assistant."

    Academic-integrity enforcement—the second pillar of the paper’s contribution—is demonstrated only on two author-written homework-style “questionable prompts,” not on independent student attempts or external red-team sets. Combined with deferred classroom outcome data, the integrity and effectiveness claims rest on self-selected illustrations rather than independent evidence, reinforcing the circular evaluation burden around the central accuracy claim.

full rationale

VectorizationLLM is an application paper, not a first-principles derivation, so classical self-citation uniqueness chains do not appear. The load-bearing quantitative claim is Table 1’s 47/48 (97.92%) verbatim code-line recall. That metric is defined as matching code blocks drawn from the same course-note markdown files that constitute the RAG corpus, under full-context retrieval and a system prompt that explicitly prioritizes those blocks and forbids outside knowledge. High recall is therefore expected by construction once retrieval succeeds; the evaluation does not test an independent external benchmark, student query distribution, or learning outcome. The Appendix’s single cumulative thread of 26 minimum-information, instructor-written prompts further selects for clean note-section hits. Academic-integrity refusals are shown only on two author-written “questionable” homework-style prompts. The paper itself defers classroom effectiveness to future work. This is partial circularity of the evaluation design (score ~5), not a fully tautological derivation (score 8–10): the system still has to retrieve and format correctly, and one topic-reference error is honestly reported. No self-citation uniqueness theorem or renamed known result is load-bearing.

Axiom & Free-Parameter Ledger

1 free parameters · 3 axioms · 1 invented entities

The work rests on standard LLM/RAG engineering assumptions plus a handful of course-specific pedagogical choices. No free parameters are fitted to external scientific data; the only numeric settings are the vendor-recommended sampling hyperparameters. The principal invented entity is the named system itself. Domain assumptions about what constitutes “smart vectorization” and academic integrity are taken from the local curriculum.

free parameters (1)
  • temperature / top_p / top_k = 1.0 / 0.95 / 64
    Set to the Gemma-recommended values 1.0 / 0.95 / 64; not fitted to any student-performance objective.
axioms (3)
  • domain assumption Full-context RAG retrieval is required for reliable first-attempt recall of verbose lecture notes.
    Stated in the Determinism subsection; without it the authors report 2/3 failure rate.
  • domain assumption Students must never use loops, conditionals, or logical indexing; only smart indexing and the course toolbox functions are allowed.
    Core pedagogical constraint encoded in the system-prompt guardrails (Module 0–5 difficulty list).
  • ad hoc to paper Providing only code blocks that already appear in the notes plus conceptual explanations is sufficient to teach without violating academic integrity.
    Central design premise of the Guardrails section; not independently validated against learning outcomes.
invented entities (1)
  • VectorizationLLM no independent evidence
    purpose: Named specialized assistant that packages Gemma + course RAG + integrity system prompt for CTEC 247.
    The paper’s sole novel artifact; no independent existence outside this work.

pith-pipeline@v1.1.0-grok45 · 27955 in / 2349 out tokens · 35471 ms · 2026-07-10T16:48:41.076484+00:00 · methodology

0 comments
read the original abstract

VectorizationLLM is a specialized Large Language Model based on Google open-weight LLMs. The model is designed to assist students to learn smart vectorization, time/wave vector analysis, piecewise functions, Fourier analysis, and differential equations in MATLAB. The course application is CTEC 247: Applied Computational Analysis II by the Department of Electrical & Computer Engineering Technology at New York Institute of Technology Old Westbury. The LLM model is designed to be an instructive assistant, providing detailed explanations of concepts with examples from in-class notes without providing direct answers to questions. The model is designed with a RAG (Retrieval Augmented Generation) knowledge base and system prompt architecture. Examples in both code, text, and images are provided in the LLM responses.

Figures

Figures reproduced from arXiv: 2607.07846 by Ryan Duke.

Figure 1
Figure 1. Figure 1: RAG Architecture Google Gemma 4 26B[4] was chosen over other open weight LLM models like Qwen[12] due to the high amount of user-friendliness which is expressed through prompt responses. Models like Qwen3.6 35B A3B[12] provide more technical, stale responses which are less user friendly. Due to the implementation of the RAG and system prompt layers, the technical aspect of the model is preconfigured. There… view at source ↗
Figure 2
Figure 2. Figure 2: System Prompt Design Functionality Functionality is designed via two main pillars: code explanations and code blocks. Code explanations are meant to be highly conceptual, often step-by-step explanations of MATLAB script and concept functionality. In addition, explanations of the interface (such as chart formatting and chart markers) are supplemented with example images [PITH_FULL_IMAGE:figures/full_fig_p0… view at source ↗
Figure 3
Figure 3. Figure 3: Sample Code Block with Response Code blocks are verbatim code snippets, either inline or in groups, taken from the class notes. Inline code 6 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Logic Diagram for Deterministic Prompt Responses [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Logic Diagram for Guardrail Enforcement Academic integrity guardrails provide necessary justification for the purpose of VectorizationLLM. Students must not be allowed to generate full solutions for code, nor generate new code from non-class examples. Any non-constrained LLM will violate this boundary immediately. The system prompt design is tailored to provide only code from the notes, and explains that i… view at source ↗
Figure 6
Figure 6. Figure 6: Logic Diagram for RAG Knowledge Base The RAG documents input to the OpenWebUi[3] knowledge base consist of markdown versions of the class notes in both CTEC 243 and CTEC 247. All CTEC 243 prerequisite material is readily available to the model. For CTEC 247, all class notes and examples as well as a readme file for each of the toolboxes (piecewise continuous functions and Fourier analysis) are included in … view at source ↗
Figure 7
Figure 7. Figure 7: Percentage Overshoot Figure: Example of percentage overshoot chart markers. The calculation for the example shown in the documentation is: percentageOvershoot = ((3.02 - 2.9) / 2.9) * 100 37 [PITH_FULL_IMAGE:figures/full_fig_p037_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Percentage Undershoot Figure: Example of percentage undershoot chart markers. The percentage undershoot calculation for the example in the documentation (where the peak undershoot value is −0.03 and the original value is 0.037) resolves to: percentageUndershoot = ((-0.03 - 0.037) / 0.037) * 100 39 [PITH_FULL_IMAGE:figures/full_fig_p039_8.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

91 extracted references · 91 canonical work pages · 3 internal anchors

  1. [1]

    Matlab version: 9.13.0 (r2022b),

    T. M. Inc., “Matlab version: 9.13.0 (r2022b),” Natick, Massachusetts, United States, 2022. [Online]. Available: https://www.mathworks.com

    work page 2022

  2. [2]

    Zoom workplace,

    Zoom Video Communications, Inc., “Zoom workplace,” Computer software, 2026. [Online]. Available: https://www.zoom.com

    work page 2026

  3. [3]

    Open webui: An open, extensible, and usable interface for ai interaction,

    O. W. Team, “Open webui: An open, extensible, and usable interface for ai interaction,” 2025

    work page 2025

  4. [4]

    Gemma 4: Open models based on gemini research and technology,

    Google DeepMind, “Gemma 4: Open models based on gemini research and technology,” https://ai.googl e.dev/gemma/docs/core/model_card_4, 2026

    work page 2026

  5. [5]

    (2026) Chatgpt (version 4.0)

    OpenAI. (2026) Chatgpt (version 4.0). Large language model. Accessed: 23 June 2026. [Online]. Available: https://chat.openai.com

    work page 2026

  6. [6]

    Gemini 3.5 Flash,

    Google, “Gemini 3.5 Flash,” 2026, accessed: June 20, 2026. [Online]. Available: https: //deepmind.google/models/gemini/flash/

    work page 2026

  7. [7]

    (2026) Circlein: The student success system

    CircleIn. (2026) Circlein: The student success system. CircleIn. Mobile application and web study platform. [Online]. Available: https://www.circleinapp.com/

    work page 2026

  8. [8]

    Ai tutor: Learn anything, anytime, anywhere,

    AI Tutor, “Ai tutor: Learn anything, anytime, anywhere,” https://ai-tutor.ai/, 2026, accessed: June 22,

    work page 2026

  9. [9]

    Available: https://ai-tutor.ai/

    [Online]. Available: https://ai-tutor.ai/

    work page

  10. [10]

    Khanmigo: Ai-powered teaching assistant and tutor,

    Khan Academy, “Khanmigo: Ai-powered teaching assistant and tutor,” 2023. [Online]. Available: https://khanacademy.org

    work page 2023

  11. [11]

    Github copilot,

    GitHub, Inc., “Github copilot,” https://github.com, 2026, computer software. Version X.Y.Z, accessed June 2026

    work page 2026

  12. [12]

    Dive into Claude Code: The Design Space of Today's and Future AI Agent Systems

    J. Liu, X. Zhao, X. Shang, and Z. Shen, “Dive into claude code: The design space of today’s and future ai agent systems,” 2026. [Online]. Available: https://arxiv.org/abs/2604.14228

    work page internal anchor Pith review Pith/arXiv arXiv 2026

  13. [13]

    Qwen3.6-35B-A3B: Agentic coding power, now open to all,

    Qwen Team, “Qwen3.6-35B-A3B: Agentic coding power, now open to all,” April 2026. [Online]. Available: https://qwen.ai/blog?id=qwen3.6-35b-a3b

    work page 2026

  14. [14]

    "Do Anything Now": Characterizing and Evaluating In-The-Wild Jailbreak Prompts on Large Language Models

    X. Shen, Z. Chen, M. Backes, Y. Shen, and Y. Zhang, “"do anything now": Characterizing and evaluating in-the-wild jailbreak prompts on large language models,” 2024. [Online]. Available: https://arxiv.org/abs/2308.03825

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  15. [15]

    Ragas: Automated Evaluation of Retrieval Augmented Generation

    S. Es, J. James, L. Espinosa-Anke, and S. Schockaert, “Ragas: Automated evaluation of retrieval augmented generation,” 2025. [Online]. Available: https://arxiv.org/abs/2309.15217 12 Appendix: Sample Prompt History This sample prompt history was derived from a single thread with cumulative prompts, mimicking the personalized experience a student would have...

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  16. [16]

    *Basic Plotting Commands:Usingplot(x, y) with vector pairs, utilizinghold on/hold off to overlay multiple waveforms, and employingaxis, xlim, andylim to control chart limits

    Plotting and Engineering Units You should be comfortable with the following plotting mechanics: *Conversion Divisors:Knowing how to scale axes or table columns to display values in engineering notation (e.g., dividing a time vector by1e-03 to display in milliseconds). *Basic Plotting Commands:Usingplot(x, y) with vector pairs, utilizinghold on/hold off to...

    work page

  17. [17]

    *2D Matrix Indexing:Understanding row and column subscripts (row, col) and how the colon operator: can select entire rows or columns

    Indexing Techniques Proper indexing is critical for selecting specific data points or ranges within vectors: *Smart Indexing:Using single subscripts for scalars, ranges (e.g.,10001:30001) for segments, and theend operator to dynamically access the last element of a vector. *2D Matrix Indexing:Understanding row and column subscripts (row, col) and how the ...

    work page

  18. [18]

    *Scalar-Aggregating Functions:Understanding that functions likesum, prod, and length collapse a vector into a single value

    Functions and Vectorization You must understand the difference between how MATLAB handles scalars versus vectors: *Vector-Smart Functions:Recognizing functions like sin, exp, sqrt, andlog that apply an operation element-wise to every item in a vector. *Scalar-Aggregating Functions:Understanding that functions likesum, prod, and length collapse a vector in...

    work page

  19. [19]

    • The ones Function:Using K * ones(1, n) to create vectors of constant values for use in tables or signal generation

    Data Organization and Tables • Table Generation:Using fprintf to create formatted, readable tables of instantaneous values by applying conversion divisors and specific field-width formatting. • The ones Function:Using K * ones(1, n) to create vectors of constant values for use in tables or signal generation. 14 Conversation 03: Conceptual Explanation: fin...

    work page

  20. [20]

    A Boolean expression results in a vector of true/false (1/0) values

    The Criterion Before usingfind, you must define acriterion, which must be a Boolean expression. A Boolean expression results in a vector of true/false (1/0) values. To create this criterion, you must directly compare a matrix or vector variable to a value or another expression using operators such as: *Equality/Inequality:== (equal to), != (not equal to) ...

    work page

  21. [21]

    plugged back

    Function Syntax and Behavior The general workflow is: 1.Define the criterion:criterion = variable > value; 2.Apply the find function:indexes = find(criterion); Key rules for thefind function:*Returns Indices:It returns the specific position (index) of every element that satisfies the criterion. *Handling Empty Results:If no elements in the matrix satisfy ...

    work page

  22. [22]

    Word worthy

    Examples of Usage Range SelectionIf you want to find all values in a vectorwvLinear that fall between 2.5 and 3.5 inclusive, you would use: criterion = wvLinear >= 2.5 & wvLinear <= 3.5; indexes = find(criterion); values = wvLinear(indexes); Time Period SelectionTo find all time periods in atSpanvector between 10ms and 20ms (exclusive): criterion = tSpan ...

    work page

  23. [23]

    Find the mean value, the maximum value, and the minimum value of the elements in A

    work page

  24. [24]

    Find the count of the number of elements in A with a value that is less than the mean

    work page

  25. [25]

    Be sure that your script outputs this answer

    Find the index and value of the first element in A that is greater than 255.0 K. Be sure that your script outputs this answer

    work page

  26. [26]

    Find the count of the number of elements in A that are greater than the value 250.0 K

    work page

  27. [27]

    Starting with the 40,000th element and ending with the 50,000th element of A, find the count of the number of elements whose values lie between 280.0 K and 300.0 K

    work page

  28. [28]

    Starting with the 50,000th element in A and continuing through the remaining elements, find the index value (with respect to all 100,000 elements in A) of the 65th element in this range that is greater than 255.0 K

    work page

  29. [29]

    ASSISTANT As a MATLAB academic tutor, I can guide you through the conceptual logic, mathematical operations, and specific MATLAB syntax required to solve this problem

    Use the sort function to find the value and index of the 750th, 7500th and 75000th smallest values in the vector A. ASSISTANT As a MATLAB academic tutor, I can guide you through the conceptual logic, mathematical operations, and specific MATLAB syntax required to solve this problem. Since this is a new problem scenario not found verbatim in your course no...

    work page

  30. [30]

    collapse

    Statistical Analysis (Mean, Max, Min)To find the central tendency and the extremes of your data, you will use scalar-aggregating functions. *Logic:These functions take a vector and “collapse” it into a single representative value. *Functions:Usemean(),max(), andmin()on your vectorA

    work page

  31. [31]

    *Logic:Create a logical vector where each element is true (1) if it is less than the mean andfalse (0) otherwise

    Boolean Criterion & Counting (Elements < Mean)To find how many elements meet a specific condition, you must first create a Boolean criterion. *Logic:Create a logical vector where each element is true (1) if it is less than the mean andfalse (0) otherwise. *Counting:To get thecountof these elements, you can use thesum()function on your Boolean criterion ve...

    work page

  32. [32]

    *Logic:Create a criterion for values greater than 255.0 K

    Finding the First Specific Index and ValueYou need to locate the very first instance where a condition is met. *Logic:Create a criterion for values greater than 255.0 K. Use thefind function to generate a vector of all indices that satisfy this. *Syntax:Sincefind returns indices in ascending order, the first element of the resulting index vector will corr...

    work page

  33. [33]

    *Logic:Define a criterion (e.g.,A > 250.0)

    Counting Elements > 250.0 KThis is similar to step 2. *Logic:Define a criterion (e.g.,A > 250.0). Apply thesum() function to this criterion to determine the total count of elements that satisfy the condition. 16

    work page

  34. [34]

    *Logic:First, extract the specific segment of the vector using smart indexing (from the 40,000th to the 50,000th element)

    Range Selection and Nested CriteriaThis requires combining smart indexing with a specific range. *Logic:First, extract the specific segment of the vector using smart indexing (from the 40,000th to the 50,000th element). *Logic:Once you have this sub-vector, create a Boolean criterion to find values between 280.0 K and 300.0 K using the logical AND (&) ope...

    work page

  35. [35]

    *Logic:Extract the sub-vector starting from the 50,000th element to the end ofA

    Advanced Indexing (Finding the Nth Occurrence in a Range)This is a multi-step process involving range extraction and searching. *Logic:Extract the sub-vector starting from the 50,000th element to the end ofA. *Logic:Within this sub-vector, create a criterion for values > 255.0 K and usefind to get the indicesrelative to that sub-vector. *Logic:Select the ...

    work page

  36. [36]

    two-week syllabus

    Sorting and Specific Rank ExtractionTo find values at specific “ranks” (like the 750th smallest), you must reorder the data. *Logic:Use the sort() function to sort the vectorA in ascending order. *Syntax: Note thatsort() can return both the sorted values and their original indices. *Logic:Once sorted, you can use smart indexing to pick out the values and ...

    work page

  37. [37]

    building blocks

    Master the Core Toolbox Functions Before attempting to build complex waves, you must understand how to generate the fundamental “building blocks” using the piecewise toolbox. You should practice using: *makeRamp(A, B, tStart, tIncrement, tEnd): Creates a linear wave between starting valueA and ending valueB. * makeSinewave(amplitude, freq, phase, tStart, ...

    work page

  38. [38]

    Single Period

    Learn the “Single Period” Construction Methodology Once you can create individual segments, you must learn how to stitch them together into a single piecewise period. The documentation outlines a specific 6-step process: *Step A: Definition.Define separate time and function vectors (t1,f 1 and t2,f 2, etc.) for each continuous segment.Crucial Rule:All seg...

    work page

  39. [39]

    template

    Master Periodicity withmakeCycles A piecewise function is often only the “template” for a repeating signal. You must learn how to take your single-period composite vector and turn it into a multi-cycle waveform. *Function:Use[t, f] = makeCycles(t, f, periods)to replicate your template a specified number of times

    work page

  40. [40]

    *Handling Discontinuities:Learn how to use vertical lines or abrupt changes inmakeRampvalues to simulate instantaneous jumps in voltage or current

    Advanced Applications: Square Waves and Discontinuities To reach advanced proficiency, apply your knowledge to specific waveform types: *Square Waves:Practice creating square waves by combiningmakeRamp segments to control theduty cycle(the ratio of the high segment to the total period). *Handling Discontinuities:Learn how to use vertical lines or abrupt c...

    work page

  41. [41]

    To create a smooth transition, you must offset the subsequent time vectors

    Concatenating Time Vectors (t) When building a piecewise function, you cannot simply concatenate time vectors end-to-end using standard methods because the end of the first segment and the start of the second segment would create a duplicate point. To create a smooth transition, you must offset the subsequent time vectors. The standard sequence for time c...

    work page

  42. [42]

    You typically concatenate all segments in a single line

    Concatenating Function/Value Vectors (wv) Concatenating the waveform values (thewv or f vectors) is more straightforward because they are being joined to the already established time vector. You typically concatenate all segments in a single line. The standard sequence for value concatenation is:f = [f1 f2(2:end) f3(2:end)];. Important Note on Dimensions:...

    work page

  43. [43]

    6-Step Method

    Summary of the Single Period Methodology When implementing a piecewise function for a single period (the “6-Step Method”), the workflow follows this sequence : *Step 1:Set up the individual vectors for each segment (e.g.,f1(t1), f2(t2)). *Step 2: (Optional) Plot each segment individually to verify the time axis is correct. *Step 3:Concatenate the time vec...

    work page

  44. [44]

    Building Blocks

    Define the Segments (The “Building Blocks”) You first define the individual time and value segments that make up one single cycle of the square wave. A common way to do this is by using themakeRamp toolbox function to create the high and low portions of the wave. To control theduty cycle(the percentage of the period that the wave is “high”), you must spec...

    work page

  45. [45]

    The Concatenation Sequence:*Time Vectors (t):You cannot simply append them because you must avoid duplicating the timestamp where one segment ends and the next begins

    Concatenate into a Single Period Once you have your individualt (time) andwv (waveform) vectors for each segment, you must stitch them together into one composite vector pair that describes one full cycle. The Concatenation Sequence:*Time Vectors (t):You cannot simply append them because you must avoid duplicating the timestamp where one segment ends and ...

    work page

  46. [46]

    To create a continuous square wave for a longer duration, you must repeat that single period multiple times

    Create Multiple Cycles The concatenation method described above only creates a single period. To create a continuous square wave for a longer duration, you must repeat that single period multiple times. • Using makeCycles:Once you have your single-periodt,wv vector pair, you can use themakeCycles toolbox function to generate a specified number of periods....

    work page

  47. [47]

    4.Verifythe single period by plotting with proper conversion divisors

    Concatenatethe time vectors using the offset method and the value vectors by skipping the first element. 4.Verifythe single period by plotting with proper conversion divisors. 5.Expandthe waveform to multiple cycles usingmakeCycles. 21 Conversation 08: Questionable Prompt: Piecewise Wave Problem USER a) Consider a base sinusoid waveform with amplitude A=2...

    work page

  48. [48]

    •Step 8: Phase and Shift Analysis 24 –Understand how time-shifting a waveform affects its components

    The Algorithm Method:Using a loop and conditional statements to find the specific harmonic where the power exceeds the 95% threshold. •Step 8: Phase and Shift Analysis 24 –Understand how time-shifting a waveform affects its components. A time shift will leave the power spectrum (amplitudes) unchanged but will cause the phase components (angles) to change....

    work page

  49. [49]

    Time Vector Generation:The function calculates the periodT from the fundamental frequency (T= 1/f(1)) and determines a time step (dt=T/N) to create the time vectort

    work page

  50. [50]

    Initialization:The waveform vector w is initialized as a vector of constant values equal to thedc component

    work page

  51. [51]

    Safety Check:The function includes a conditional check to ensure that the requested number of harmonics (F) does not exceed the maximum available harmonics (N/2−1)

    work page

  52. [52]

    Summation Loop:It uses a loop to iterate from 1 toF, adding the contribution of each successive harmonic to thew vector.(Note: Per course directives, while loops are generally discouraged, they are explicitly allowed for this specific algorithm in Fourier analysis). 26 Conversation 11: Conceptual Explanation: 95% Power Harmonic USER Explain how to calcula...

    work page

  53. [53]

    *Logic:You use thesumPowers toolbox function to calculate the power of the DC component and the accumulated power of the harmonics

    The Trial and Error Method This method involves manually testing different numbers of harmonics until you find the point where the accumulated power meets the threshold. *Logic:You use thesumPowers toolbox function to calculate the power of the DC component and the accumulated power of the harmonics. *Procedure:You check the power sum for increasing value...

    work page

  54. [54]

    trial and error

    The Algorithm Method This method uses programming structures to automate the search for the 95% threshold. *Logic:You utilize afor loop and a conditionalif statement to iterate through the harmonics and stop once the criteria are met. *Procedure:1. Define your target power aspower95 = 0.95 * (newRMSˆ2). 2. Initialize a loop (e.g., for count=1:100000). 3. ...

    work page

  55. [55]

    This is represented as:power95 = 0.95 * (newRMSˆ2)

    Define the Target Power:First, you must calculate the threshold, which is 95% of the total RMS power. This is represented as:power95 = 0.95 * (newRMSˆ2)

    work page

  56. [56]

    3.Iterative Search (Looping):You use aforloop to cycle through the available harmonics

    Initialize a Counter:You start with a counter representing the first harmonic (e.g.,harmonic = 1). 3.Iterative Search (Looping):You use aforloop to cycle through the available harmonics

    work page

  57. [57]

    5.Store and Terminate:Once the condition is met, you store that specific harmonic number and use thebreakcommand to exit the loop immediately

    Conditional Check:Inside the loop, you use anif statement to check the current accumulated power using thesumPowerstoolbox function: • If the sum of the power of the current harmonics is greater than yourpower95 target, the condition is met. 5.Store and Terminate:Once the condition is met, you store that specific harmonic number and use thebreakcommand to...

    work page

  58. [58]

    Solving a single differential equation:You define the derivative using thediff function

    Basic Syntax and Setup To usedsolve, you must first define your variables as symbolic using thesymscommand. Solving a single differential equation:You define the derivative using thediff function. For example, to solve a second-order equation: syms y(t) D2y = diff(y, 2);% Represents the 2nd derivative of y Dy = diff(y, 1);% Represents the 1st derivative o...

    work page

  59. [59]

    Complexity of Equations dsolve can solve various types of equations: *Constant forcing functions:Eqny2 = D2y + 4*Dy + 3*y == 6; *Sinusoidal forcing functions: Eqny3 = D2y + 4*Dy + 3*y == 3*cos(3*t); *Exponential forcing functions:Eqny4 = Dy + 4*y == 4*exp(-2*t)

    work page

  60. [60]

    This is common when analyzing the transient response of a circuit

    Plotting and Analysis Once you have obtained a solution withdsolve, you can usefplot to visualize the results. This is common when analyzing the transient response of a circuit. • Visualizing the solution:fplot(y1, [0 50]) plots the solution over the time interval from 0 to 50. • Transient Analysis:You can use the solutions to calculatepercentage overshoo...

    work page

  61. [61]

    *Charge (q):You solve the equation involving the second derivative of charge (L·d2q/dt2 +R·dq/dt+q/C = forcing function)

    Application in RLC Reactive Circuits In circuit analysis,dsolve is used to solve for charge (q) or current (i) in RLC circuits. *Charge (q):You solve the equation involving the second derivative of charge (L·d2q/dt2 +R·dq/dt+q/C = forcing function). *Current (i):You can solve for current using an equation likeL*Di + i*R == vS - q/C. Linkage of terms for c...

    work page

  62. [62]

    Define the Differential Equation:Usesyms q(t) to define charge as a symbolic variable and set up the differential equation for the circuit (e.g.,Ld2q dt2 +R dq dt + q C =v s(t))

    work page

  63. [63]

    3.Calculatev C:Perform the division of the symbolic variableqby the capacitor constantC

    Solve forq:Use the dsolve function, providing the differential equation and any necessary initial conditions (such as initial chargeq(0)), to find the symbolic expression forq. 3.Calculatev C:Perform the division of the symbolic variableqby the capacitor constantC. 4.Visualize:Use thefplotfunction to plot the resulting expressionq/Cover a specified time i...

    work page

  64. [64]

    Therefore, your first step is to usedsolve to find the symbolic expression for the current

    Solve for the Current (i) In most circuit models presented in the notes, the voltage across a resistor is directly proportional to the current flowing through it (vR = i·R). Therefore, your first step is to usedsolve to find the symbolic expression for the current. For an RL circuit, you would define a differential equation for the current, such as:eqnI =...

    work page

  65. [65]

    Implementation Logic:*Define the Resistor:Identify the resistance value R

    Apply the Ohm’s Law Relationship Once dsolve has provided you with the symbolic solution for current (i), you use the relationshipvR =i·R to derive the voltage. Implementation Logic:*Define the Resistor:Identify the resistance value R. *Perform Mul- tiplication:Multiply the symbolic current vector i by the scalarR. *Example Syntax: vR = i * R

    work page

  66. [66]

    Example Workflow (from RLC Analysis): % 1

    Visualization After calculating the expression forvR, you can usefplot to visualize the voltage profile over a specific time interval. Example Workflow (from RLC Analysis): % 1. Solve for current i using dsolve eqnI = L*Di + i*R == vP*sin(2*pi*f*t) - q/C; ICI = i(0) == 0; i = dsolve(eqnI, ICI); % 2. Calculate voltage across resistor vR = i * R; % 3. Plot ...

    work page

  67. [67]

    syms i(t)

    Set up the Symbolic Variables First, you must define your time variable and your current variable as symbolic. syms i(t)

    work page

  68. [68]

    The current is determined by the sum of voltages or the derivative of charge

    Define the Differential Equation The equation you provide todsolve depends on the circuit being analyzed. The current is determined by the sum of voltages or the derivative of charge. • For an RL Circuit:The relationship is defined by the inductor (L), the resistor (R), and the source voltage (vS). The differential equation is represented as: di dt = vS −...

    work page

  69. [69]

    *Syntax: i = dsolve(eqnI, IC); where IC is a vector containing your initial condition, such asi(0) == 0

    Solve with Initial Conditions To find a particular solution rather than a general one, you must provide initial conditions (e.g., the current at timet = 0). *Syntax: i = dsolve(eqnI, IC); where IC is a vector containing your initial condition, such asi(0) == 0

    work page

  70. [70]

    Example Workflow According to theRLSinForceexample, the calculation follows this logic: % Define constants A = 20; f = 2e03; T = 1/f; R = 500; L = 39.8e-03; syms i(t) % Define the derivative and the differential equation Di = diff(i, 1); vS = A*sin(2*pi*f*t); eqnI = L*Di + i*R == vS - q/C;% Note: q must be previously solved via dsolve % Solve for current ...

    work page

  71. [71]

    Original Value

    Identify the “Original Value”:In a transient response model, the original value is defined as the first chronological minimum valueat the start of the chart (the baseline from which the overshoot occurs). 2.Identify the “Peak Value”:This is the new maximum value reached during the overshoot

    work page

  72. [72]

    Apply the Formula:Subtract the original value from the peak value, divide by the original value, and multiply by 100. Practical Example In the provided RLC circuit analysis documentation, an example is given where: *Peak overshoot value =3.02*Original value=2.9 The calculation is executed in MATLAB as follows: percentageOvershoot = ((3.02 - 2.9) / 2.9) * ...

    work page

  73. [73]

    It is frequently applied to analyze the transient responses of various circuit types, such as: *RL and RC circuitswith sinusoidal inputs

    Core Purpose and Functionality ode45 is used to solve differential equations by stepping through time. It is frequently applied to analyze the transient responses of various circuit types, such as: *RL and RC circuitswith sinusoidal inputs. *RLC circuits(including more complex or high-frequency scenarios). *Discharging/Chargingbehaviors (e.g., a capacitor...

    work page

  74. [74]

    This tells MATLAB how the derivative of your variable (like currenti or voltagevC) changes with respect to time

    The Use of Function Handles To useode45, you must provide the differential equation in the form of afunction handleusing the@ operator. This tells MATLAB how the derivative of your variable (like currenti or voltagevC) changes with respect to time. The solver expects a function that defines the derivative (e.g.,di dt or dvC dt ). An example of a function ...

    work page

  75. [75]

    Typical Workflow in Circuit Analysis The process for usingode45in this course generally follows these steps:

    work page

  76. [76]

    Define the Time Span (tSpan):Create a vector of time points over which you want the solver to calculate the response (e.g.,tSpan = 0:1e-06:10*T)

    work page

  77. [77]

    3.Call the Solver:Pass the function handle, the time span, and the initial conditions toode45

    Define Initial Conditions:Specify the starting value of the variable att = 0(e.g., i(0) = 0 or vC(0) = 10). 3.Call the Solver:Pass the function handle, the time span, and the initial conditions toode45. •Syntax:[t, solution] = ode45(function_handle, tSpan, initial_condition)

    work page

  78. [78]

    Analyze the Output:The solver returns a time vectort and the calculated values (like current or voltage) which can then be plotted to observe the transient or steady-state response

    work page

  79. [79]

    Practical Applications The course utilizesode45 for several specific analytical tasks: *Transient Response:Observing how a system settles into a steady state after a change (e.g., an inductor current settling after a step change in frequency). *Frequency Sweeps:Running the solver at different frequencies (f1,f 2,f 3, etc.) to observe how the system’s resp...

    work page

  80. [80]

    Define the Differential Equation:For a discharging RC circuit, the derivative of the capacitor voltage is defined by the relationship: dvC dt = −vC RC In the provided documentation, this is implemented as a functionRCDischargeF

    work page

Showing first 80 references.