Author(s): Joel Feldman, Andrew Rechnitzer and Elyse Yeager
Series: CLP Calculus 04
Edition: Text
Publisher: University of British Columbia
Year: 2021
Language: English
Tags: mathematics; maths; math; calc; calculus; single variable; limits; differentiation; differential; integration; integral; continuity; differentiability; analysis; real; complex; multiple variables; multivariable; multivariate; several variables; many variables
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
