Calculus Revisited Part 2 Study Guide
The Game of Mathematics

The following text files correspond to the video presentations.  They offer problems and completely worked-out and explained solutions. In addition you will find supplementary topics included in both the problems and solutions material.

For Part 2 supplementary topics click here.

Block 1: Mathematical Structure and Vectors
 

The Game of Mathematics
 

Problems and Pretest

Solutions

Vectors Revisited - Arrow Arithmetic
 

Problems

Solutions

3-dimensional Vectors
 

Problems

Solutions

The Dot Product
 

Problems

Solutions

The Cross Product
 

Problems

Solutions

Lines And Planes
 

Problems and Quiz

Solutions

Block 2:  Functions
 

Vector Functions of Scalar Variables
 

Problems and Pretest

Solutions

Tangent and Normal Vectors
 

Problems

Solutions

Polar Coordinates
 

Problems

Solutions

Vectors and Polar Coordinates
 

Problems and Quiz

Solutions

Block 3: Real Valued Functions of Several Real Variables
 

n-dimensional Vector Spaces
 

Problems and Pretest

Solutions

Introduction to the Calculus of Several Variables
 

Problems

Solutions

The Directional Derivative
 

Problems

Solutions

The Chain Rule
 

Problems

Solutions

Integrals Involving Parameters
 

Problems

Solutions

Exact Differentials
 

Problems and Quiz

Solutions

Block 4: Matrix Algebra

Linearity Revisited
 

Problems and Pretest

Solutions

Matrix Algebra
 

Problems

Solutions

Inverting a Square Matrix
 

Problems

Solutions

Inverting General Systems of Equations
 

Problems

Solutions Part 1

Solutions Part 2

Max-min Problems in Several Variables
 

Problems and Quiz

Solutions

Block 5: Line Integrals along closed curves (Green's Theorem) 

Double (Multiple) Sums
 

Problems and Pretest

Solutions

The Fundamental Theorem
 

Problems

Solutions

Multiple Integrals and the Jacobian
 

Problems

Solutions

Line Integrals
 

Problems

Solutions

Green's Theorem
 

Problems and Quiz

Solutions

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