Lecture Notes Enhancement

Lecture Notes Enhancement

Shared narrative rules

Load the writer skill's references/common/writing.md module. Keep process notes and defensive source disclaimers out of the lecture notes; state source limitations only when they affect the explained concept.

Overview

Systematic process for cross-referencing recordings, PPTs, and existing notes to identify gaps and enhance lecture notes with narrative-first writing. Uses parallel subagents for efficiency.

When to Use

Use when:

• Enhancing existing lecture notes (讲义.md) with course recordings and PPTs
• Course has multiple source materials (records/, extracted/, existing notes)
• Need systematic gap identification and content supplementation
• Following the writer Markdown narrative route (narrative flow before technical content)

Don't use when:

• Creating lecture notes from scratch (use brainstorming + writing-plans instead)
• Simple formatting or proofreading (use simplify skill instead)
• Single source material only (direct editing is sufficient)

Nature of Source Materials

Each source type has distinct role and limitations:

Slides (PPT extracted/) — Simplified outline only. Contain key formulas and section outlines — the final results, not the path to them. No detailed derivations, intermediate steps, or physical intuition. Treat slides as a what checklist, not the full content.

Recordings (records/) — Full content with caveats. Contain detailed derivations, step-by-step reasoning, and additional formulas not on slides. However: (a) teachers may not read every formula aloud — extract keywords to identify which formulas are being discussed; (b) ASR transcriptions introduce errors, especially for technical terms — always cross-reference with slides for precise formulas.

Existing notes — Baseline. Provide current structure and coverage level to supplement, not replace.

Core Pattern

The enhancement process follows four phases:

Phase 1: Parallel Analysis - Dispatch subagents to analyze each source material independently Phase 2: Gap Synthesis - Identify missing content, inconsistencies, and improvement opportunities Phase 3: Systematic Enhancement - Edit lecture notes section-by-section with narrative-first style Phase 4: Verification - Ensure all improvements follow the writer Markdown narrative route

Phase 1: Parallel Analysis Dispatch

For each course record or PPT file, dispatch a subagent with specific analysis scope:

Analyze records/week03.md:
- Focus: Numerical methods for PDE solving
- Extract: Discretization schemes, boundary conditions, solver algorithms
- Output: Structured summary with key formulas and implementation details

Why parallel? Each source is independent. Processing concurrently saves time and prevents context overflow.

Phase 2: Gap Identification Matrix

Create structured gap analysis organized by priority:

Phase 3: Narrative-First Enhancement

Apply the writer common narrative and Markdown principles:

✅ DO:

• Start sections with explanatory narrative
• Use bold for emphasis (never italics)
• Write complete, grammatical sentences
• Embed code snippets to support claims
• Weave narrative through content (narrative → content → narrative)

❌ DON'T:

• Start sections abruptly with lists/formulas
• Use bullet points for main narrative explanations
• Use conversational filler ("we will explore", "as we can see")
• Use vague emphasis words ("核心", "关键", "重要", "主要", "本质", "显著") as a substitute for evidence — state the role, input/output, or measured effect instead
• Write multi-paragraph docstrings or comment blocks
• Add meta-commentary about the editing process, source fidelity, or why a sentence was written a certain way
• Explain that an unsupported detail cannot be inferred unless that limitation changes the lecture content

Segment Length Principle

Break complex explanations into focused segments, giving the user a chance to respond after each. If answering 3+ distinct questions, deliver them as separate segments. Avoid massive single responses.

Phase 4: Section-by-Section Editing

Edit the lecture notes systematically by section:

1. Read current section in existing lecture notes
2. Read relevant analysis from supplement reports
3. Identify specific improvement needed
4. Apply narrative-first edit using Edit tool
5. Update todo list to track progress

Quick Reference

Common Enhancement Categories

Theoretical Foundations: Missing derivations, physical intuition, intermediate steps between slide formulas.

Numerical Methods: Solver details, algorithm choices, convergence analysis not shown on slides.

Implementation Details: Practical considerations, edge cases, boundary conditions discussed orally.

Writing Style: Narrative-first structure, symbol definitions at first use, bold for key terms, complete sentences.

Implementation

## Example Enhancement: Adding Cauchy Momentum Equation

**Before** (abrupt start):
### 1.1 Navier-Stokes方程
流体运动的数学描述建立在连续介质力学假设之上。Navier-Stokes方程是...

**After** (narrative-first):
### 1.1 连续介质力学基础
流体仿真的理论基础建立在**连续介质假设**之上：将流体视为连续分布的物质，而非离散的分子集合。在这一假设下，我们关注流体中每个**小体积元**的受力与运动。对于连续介质中的小体积元，它受到的力可以分为两大类。**体力**（body force）作用于整个体积，如重力场和磁场。**表面力**（surface force）通过表面接触传递，如流体内部的摩擦和压力。柯西动量方程（Cauchy Momentum Equation）是适用于所有连续介质的普适方程...

Common Mistakes

Real-World Impact

Before: Lecture notes missing key theoretical foundations, numerical details, and implementation context that only existed in recordings.

After: Enhanced notes with full derivations, physical intuition, and practical implementation details — all following narrative-first style. Each section now explains why before what.

Red Flags - STOP and Re-Read

• About to Edit without Reading current section first
• About to answer a question without editing the notes
• Starting a section with a list or formula (no narrative intro)
• Using italics instead of bold for emphasis
• Writing "we will explore" or "as we can see"
• Processing course records sequentially instead of in parallel
• Editing entire document at once without todo tracking
• About to use a symbol ($w_i$, $\mathbf{u}_i$, etc.) without defining it first
• Assuming slide content is the complete lecture — slides are outlines, not full content
• Copying transcription text into notes without cross-referencing slides for accuracy
• Expecting every formula to be read aloud in the recording — extract keywords instead

All of these mean: Stop, re-read the skill, and follow the correct approach.