Outline
calc 3 - summer 2019
- Author:
- Brian Abbott
- Topic:
- Calculus
resources to go along with online calc 3 course using openstax and apex calculus as primary texts.
Table of Contents
Unit 1: Vectors and Vector-Valued Functions
- Vectors in Space - f(x,y) = 1/a(x^2+y^2)
- Cross Product: Demo
- calc 3 - openstax - ex 3.2
- calc 3 - openstax - parametric curves in space
- calc 3 - openstax - some helices
- calc 3 - openstax - derivatives of vector valued functions - tangent vector
- calc 3 - openstax - ex 3.7
- calc 3 - vector functions of constant length
- calc 3 - Tangent Velocity Vectors
- calc 3 - TNB Frame
- calc 3 - openstax - projectile motion ex. 3.16
Unit 2: Differentiation of Functions of Several Variables
- Intro to Functions in Several Variables
- Domains of Functions in Two Variables
- Limits of Multivariable Functions
- Limits that Do Not Exist at Origin
- Level Curves (Braxton Carrigan)
- Level Curves
- Level Curves
- Directional Derivative
- Directional derivatives and Gradient
- calc 3 - constrained min max problem
- calc 3 - lagrange multiplier example 1
- calc 3 - level sets review example
- calc 3 - level sets review question part 2
Unit 3: Multiple Integration
- Riemann Sums of a Double Integral
- Iterated Double Integrals
- Double Integrals
- Double integral over a rectangle
- Double Integral over Type I Region
- Double Integral on Rectangular Region
- General Region Double Integral
- double integration - polar coordinates - r dθ dr
- Triple Integrals - an example to start
- Triple Integral in rectangula…
- Triple Integral Cylindrical C…
- Triple Integral Spherical Coordinates
- Geometric interpretation of the Jacobian
- Jacobian Animation
- Jacobian Locus
Unit 4: Vector Calculus