Table of Contents

Multivariable Calculus

Course Overview

  • Coordinate systems
  • Vectors
  • Partial differentation
  • Multiple integration

Course Goals

  • For students to develop the ability to compute basic vector quantities, including the dot and cross products, and derivatives of vector functions;
  • For students to develop a geometric understanding of vectors (without components), including the dot and cross products, and motion in space.
  • For students to develop the ability to visualize curves and surfaces in space;
  • For students to develop the ability to relate multiple representations of functions of several variables, such as the relationship between graphs and level sets.
  • For students to develop the ability to evaluate partial derivatives;
  • For students to develop the ability to set up optimization problems involving several variables;
  • For students to develop the ability to evaluate the gradient of a function;
  • For students to develop a geometric understanding of the gradient, including its relationship to level sets.
  • For students to develop the ability to evaluate multiple integrals;
  • For students to develop the ability to set up multiple integrals in standard coordinate systems;

Sample Syllabus

Course Contents

(old version)

Introduction

Warmup
Representations of Multivariable Functions

Multiple Integrals

Review of Single Variable Integration
Double Integrals
Polar and Curvilinear Coordinates

Partial Derivatives I

Review of Differentiation
Differentials and Derivatives
Partial Derivatives
Chain Rule

Vectors I

Introduction
Dot Product

Partial Derivatives II

Gradient and Directional Derivatives
Optimization

Vectors II

Applications

Extra

Activities Included


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