CLP-4 Vector Calculus (Feldman, Rechnitzer, and Yeager)

This textbook covers Vector Calculus. There are chapters on curves, vector fields, surface integrals and integral theorems (such as the divergence theorem).

Calculus Mathematics

Tác giả: Joel Feldman, Andrew Rechnitzer and Elyse Yeager
Nhà xuất bản: University of British Columbia
Nguồn: LibreTexts
Giấy phép: CC BY-NC-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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Mục lục· 49 mục

01: Curves
1.01: Derivatives Velocity Etc.
1.02: Reparametrization
1.03: Curvature
1.04: Curves in Three Dimensions
1.05: A Compendium of Curve Formula
1.06: Integrating Along a Curve
1.07: Sliding on a Curve
1.08: Optional Polar Coordinates
1.09: Optional Central Forces
1.10: Optional Planetary Motion
1.11: Optional The Astroid
1.12: Optional Parametrizing Circles
02: Vector Fields
2.01: Definitions and First Examples
2.02: Optional Field Lines
2.03: Conservative Vector Fields
2.04: Line Integrals
2.05: Optional The Pendulum
03: Surface Integrals
3.01: Parametrized Surfaces
3.02: Tangent Planes
3.03: Surface Integrals
3.04: Interpretation of Flux Integrals
3.05: Orientation of Surfaces
04: Integral Theorems
4.01: Gradient Divergence and Curl
4.02: The Divergence Theorem
4.03: Green's Theorem
4.04: Stokes' Theorem
4.05: Optional Which Vector Fields Obey F 0
4.06: Really Optional More Interpretation of Div and Curl
4.07: Optional A Generalized Stokes' Theorem
05: True False and Other Short Questions
5.02: Exercises
06: Appendices
6.01: A Appendices
6.1.01: A.1 Trigonometry
6.1.02: A.2 Powers and Logarithms
6.1.03: A.3 Table of Derivatives
6.1.04: A.4 Table of Integrals
6.1.05: A.5 Table of Taylor Expansions
6.1.06: A.6 3d Coordinate Systems
6.1.07: A.7 ISO Coordinate System Notation
6.1.08: A.8 Conic Sections and Quadric Surfaces
6.1.09: A.9 Review of Linear Ordinary Differential Equations
6.02: B Hints for Exercises
6.03: C Answers to Exercises
6.04: D Solutions to Exercises