Calculus: The Mathematics of Change
The Mathematics of Change
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40 chapters
~51 hours total
308 sections
1
Front Matter
5 chapters2
Part I — Limits and Continuity
6 chapters- Part I — Limits and Continuity
- Why Calculus: The Tangent and Area Problems
- Chapter 2 — Functions and Models: The Language Calculus Speaks
- Chapter 3 — The Limit: What Happens When You Get Infinitely Close
- Continuity: Where Functions Behave and Where They Don't
- Rates of Change: The Idea That Started Everything
3
Part II — Differentiation
8 chapters- Part II — Differentiation
- The Derivative: Definition, Notation, and What It Means
- Chapter 7 — Differentiation Rules
- Chapter 8 — Implicit Differentiation and Related Rates
- Chapter 9 — Applications of Derivatives
- Chapter 10 — Optimization: Finding the Best Answer
- Chapter 11 — Linear Approximation, Differentials, and Newton's Method
- Chapter 12 — Antiderivatives and the Idea of Integration
4
Part III — Integration
8 chapters- Part III — Integration
- Chapter 13 — The Definite Integral
- Chapter 14 — The Fundamental Theorem of Calculus
- Integration Techniques I: Substitution and Integration by Parts
- Integration Techniques II: Trigonometric, Partial Fractions, and Numerical Methods
- Improper Integrals: When the Limits Stretch to Infinity
- Chapter 18 — Applications of Integration
- Chapter 19 — Differential Equations
5
Part IV — Sequences and Series
6 chapters6
Part V — Parametric, Polar, and Conic Coordinate Systems
4 chapters7
Part VI — Multivariable Calculus
7 chapters- Part VI — Multivariable Calculus
- Chapter 28 — Vector-Valued Functions and Space Curves
- Chapter 29 — Functions of Several Variables
- Chapter 30 — Multivariable Chain Rule and Gradient
- Chapter 31 — Optimization in Several Variables
- Chapter 32 — Multiple Integrals
- Chapter 33 — Change of Variables and Jacobians
8
Part VII — Vector Calculus
6 chapters9
Part VIII — Capstone and Synthesis
3 chapters10
Appendices
14 chapters- Index
- Answers to Selected Exercises
- Appendix A — Precalculus Review
- Appendix B — Formula Reference
- Appendix C — Python Setup Guide
- Appendix D — NumPy / SciPy / SymPy Cheatsheet
- Appendix E — Proof Techniques
- Appendix F — Notation Reference
- Appendix G — Historical Notes
- Appendix H — Stewart Chapter-to-Chapter Mapping
- Appendix I — OpenStax Chapter-to-Chapter Mapping
- Appendix J — Applications Catalog by Field
- Bibliography
- Glossary
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