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rudin-real-complex-analysis
by parcadei
rudin-real-complex-analysisは、システム間の統合と連携を実現するスキルです。APIとデータの統合により、シームレスな情報フローと業務効率の向上をサポートします。
⭐ 3,352🍴 252📅 2026年1月23日
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Manusで実行ユースケース
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MCPサーバー連携
Model Context Protocolを活用したAIツール連携。rudin-real-complex-analysisを活用。
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API連携構築
外部サービスとのAPI連携を簡単に構築。
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データ同期
複数システム間のデータを自動同期。
SKILL.md
name: rudin-real-complex-analysis description: Problem-solving with Rudin's Real and Complex Analysis textbook allowed-tools: [Bash, Read]
Rudin's Real and Complex Analysis
Reference skill for Walter Rudin's "Real and Complex Analysis" (3rd Edition) - a graduate-level text covering measure theory, integration, functional analysis, and complex analysis.
When to Use
Use this skill when working on:
- Measure theory and Lebesgue integration
- Lp spaces and functional analysis
- Complex analysis (analytic functions, contour integration, residues)
- Connections between real and complex analysis
Topics Covered
Real Analysis
- Limits and continuity in metric spaces
- Convergence of sequences and series
- Differentiation and integration techniques
- Metric spaces and topology
Complex Analysis
- Analytic functions and Cauchy-Riemann equations
- Contour integration and Cauchy's theorem
- Residue theorem and applications
- Conformal mappings
- Power series representations
Topology
- Topological spaces
- Compactness and connectedness
- Metric space topology
Algebra
- Rings and ideals (in context of function spaces)
Decision Tree
-
Measure/Integration Problem?
- Use Lebesgue dominated convergence
- Check Fatou's lemma for liminf/limsup
- Apply Fubini-Tonelli for iterated integrals
-
Complex Analysis Problem?
- Check analyticity via Cauchy-Riemann
- For integrals: residue theorem
- For mappings: Schwarz lemma, conformal properties
-
Functional Analysis?
- Riesz representation for duals
- Hahn-Banach for extensions
- Open mapping/closed graph theorems
Tool Commands
Query Rudin Content
uv run python scripts/ragie_query.py --query "YOUR_TOPIC measure integration" --partition math-textbooks --top-k 5
SymPy for Symbolic Computation
uv run python scripts/sympy_compute.py integrate "exp(-x**2)" --var x --bounds "0,oo"
Z3 for Verification
uv run python scripts/z3_solve.py prove "forall x, |f(x)| <= M implies bounded"
Key Theorems Reference
| Theorem | Chapter | Use Case |
|---|---|---|
| Dominated Convergence | Ch 1 | Interchange limit and integral |
| Riesz Representation | Ch 2 | Identify dual spaces |
| Cauchy's Theorem | Ch 10 | Contour integrals = 0 for analytic |
| Residue Theorem | Ch 10 | Evaluate real integrals |
| Open Mapping | Ch 5 | Surjective bounded linear maps |
Cognitive Tools Reference
See .claude/skills/math-mode/SKILL.md for full tool documentation.
スコア
総合スコア
95/100
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ライセンスが設定されている
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100文字以上の説明がある
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GitHub Stars 1000以上
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3ヶ月以内に更新
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1つ以上のタグが設定されている
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