This textbook covers Vector Calculus. There are chapters on curves, vector fields, surface integrals and integral theorems (such as the divergence theorem).
Conditions of Use
This book is licensed under a Creative Commons License (CC BY-NC-SA). You can download the ebook CLP-4 Vector Calculus for free.
- Title
- CLP-4 Vector Calculus
- Author(s)
- Andrew Rechnitzer, Elyse Yeager, Joel Feldman
- Published
- 2023-05-14
- Edition
- 1
- Format
- eBook (pdf, epub, mobi)
- Pages
- 304
- Language
- English
- License
- CC BY-NC-SA
- Book Homepage
- Free eBook, Errata, Code, Solutions, etc.
Curves Derivatives, Velocity, Etc. Reparametrization Curvature Curves in Three Dimensions A Compendium of Curve Formula Integrating Along a Curve Sliding on a Curve Optional — Polar Coordinates Optional — Central Forces Optional — Planetary Motion Optional — The Astroid Optional — Parametrizing Circles Vector Fields Definitions and First Examples Optional — Field Lines More about r'(t)v(to.r(t))to.=0 Conservative Vector Fields Line Integrals Path Independence Optional — The Pendulum Surface Integrals Parametrized Surfaces Tangent Planes Surface Integrals Parametrized Surfaces Graphs Surfaces Given by Implicit Equations Examples of S dS Optional — Dropping Higher Order Terms in du,dv Interpretation of Flux Integrals Examples of Flux Integrals Orientation of Surfaces Integral Theorems Gradient, Divergence and Curl Vector Identities Vector Potentials Interpretation of the Gradient Interpretation of the Divergence Interpretation of the Curl The Divergence Theorem Optional — An Application of the Divergence Theorem — the Heat Equation Variations of the Divergence Theorem An Application of the Divergence Theorem — Buoyancy Optional — Torque Optional — Solving Poisson's Equation Green's Theorem Stokes' Theorem The Interpretation of Div and Curl Revisited Optional — An Application of Stokes' Theorem — Faraday's Law Optional — Which Vector Fields Obey -.4 -.4 -.4 -.4 F=0 Optional — More Interpretation of Div and Curl Optional — A Generalized Stokes' Theorem Trigonometry Trigonometry — Graphs Trigonometry — Special Triangles Trigonometry — Simple Identities Trigonometry — Add and Subtract Angles Inverse Trigonometric Functions Powers and Logarithms Powers Logarithms Table of Derivatives Table of Integrals Table of Taylor Expansions 3d Coordinate Systems Cartesian Coordinates Cylindrical Coordinates Spherical Coordinates ISO Coordinate System Notation Polar Coordinates Cylindrical Coordinates Spherical Coordinates Conic Sections and Quadric Surfaces Review of Linear Ordinary Differential Equations
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