Calculus III
Calculus of functions of more than one independent variable. Topics include the analytic geometry of the graphs of either scalar or vector-valued functions, limits, continuity, partial derivatives and their applications, including optimization, multiple integrals, including line and surface integrals, and the big three theorems of Green, Stokes, and Gauss. Includes handwritten lecture notes and typed notes from Stewart's Multivariable Calculus.
Johns Hopkins · AS.110.202 · Fall 2021
Lecture Notes
Calculus III Lecture Notes (PDF)
Handwritten notes from the whole course.
Textbook Notes
Notes from Multivariable Calculus 8th Edition by James Stewart.
Three Dimensional Coordinate System
- What is the formula for distance in 3D?
- What is the equation of a sphere?
Vectors
- How do you combine vectors algebraically?
- What are components of a vector?
- What are the properties of a vector?
- What is the unit vector?
The Dot Product
- What are its uses and properties?
- What is vector projetion and scalar projection?
- How does the dot product relate to work in physics?
Cross Product
- How do you calculate determinants?
- How do you calcuate the cross product?
- What are its properties?
- What are triple products?
- How does cross product relate to torque in physics?
Equations of Lines and Planes
- What are the vector and parametric equations of a line?
- How do you form the vector, scalar, or linear equation of the plane.
- When two planes intersect, how do you find the angle between the planes and the line of inersection?
- How do you find the distance between a point and plane?
Cylinder and Quadratic Surfaces
- What are cylinders?
- What are quadratic surfaces?