# Calculus lll

Presents a study of differentiation and integration of functions of several variables, parametric curves and surfaces, and the calculus of vector fields. Topics are inclusive of, but not limited to, multivariable vector functions, partial derivatives, directional derivatives, surfaces and hyper surfaces, parametric equations, multiple integrals using several different coordinate systems, line integrals, Green's Theorem, the Divergence Theorem and Stokes Theorem.
Prerequisite: Calculus ll with a grade of C or better.

## Chapter 12

Vectors and The Geometry of Space

Lessons Homework HW Quiz
12.1 Three-Dimensional Coordinate System 12.1 12.1
12.2 Vectors 12.2 12.2
12.3 The Dot Product 12.3 12.3
12.4 The Cross Product 12.4 12.4
12.5 Lines and Planes in Space 12.5 12.5
12.6 Cylinders and Quadric Surfaces 12.6 12.6
Chapter 12 Test

## Chapter 13

Vector-Valued Functions and Motion in Space

Lessons Homework HW Quiz
13.1 Curves in Space and Their Tangents 13.1 13.1
13.2 Integrals of Vector Functions; Projectile Motion 13.2 13.2
13.3 Arc Length in Space 13.3 13.3
13.4 Curvature and Normal Vectors of a Curve 13.4 13.4
13.5 Tangential and Normal Components of Acceleration 13.5 13.5
13.6 Velocity and Acceleration in Polar Coordinates 13.6 13.6
Chapter 13 Test

## Chapter 14

Partial Derivatives

Lessons Homework HW Quiz
14.1 Functions of Several Variables 14.1 14.1
14.2 Limits and Continuity in Higher Dimensions 14.2 14.2
14.3 Partial Derivatives 14.3 14.3
14.4 The Chain Rule 14.4 14.4
14.5 Directional Derivatives and Gradient Vectors 14.5 14.5
14.6 Tangent Planes and Differentials 14.6 14.6
14.7 Extreme Values and Saddle Points 14.7 14.7
14.8 Lagrange Multipliers 14.8 14.8
14.9 Taylor's Formula for Two Variables 14.9 14.9
14.10 Partial Derivatives with Constrained Variables 14.10 14.10
Chapter 14 Test

## Chapter 15

Multiple Integrals

Lessons Homework HW Quiz
15.1 Double and Iterated Integrals over Rectangular Regions 15.1 15.1
15.2 Double Integrals over General Regions 15.2 15.2
15.3 Area by Double Integration 15.3 15.3
15.4 Double Integrals in Polar Form 15.4 15.4
15.5 Triple Integrals in Rectangular Coordinates 15.5 15.5
15.6 Moments and Center of Mass 15.6 15.6
15.7 Triple Integrals in Cylindrical and Spherical Coordinates 15.7 15.7
15.8 Substitutions in Multiple Integrals 15.8 15.8
Chapter 15 Test

## Chapter 16

Integration in Vector Fields

Lessons Homework HW Quiz
16.1 Line Integrals 16.1 16.1
16.2 Vector Fields and Linea Integrals: Work, Circulation, and Flux 16.2 16.2
16.3 Path Independence, Conservative Fields, and Potential Functions 16.3 16.3
16.4 Green's Theorem in the Plane 16.4 16.4
16.5 Surfaces and Area 16.5 16.5
16.6 Surface Integrals 16.6 16.6
16.7 Stoke's Theorem 16.7 16.7
16.8 The Divergence Theorem and a Unified Theory 16.8 16.8
Chapter 16 Test

## Chapter 17

Second-Order Differential Equations

Lessons Homework HW Quiz
17.1 Second-Order Linear Equations 17.1 17.1
17.2 Nonhomogeneous Linear Equations 17.2 17.2
17.3 Applications 17.3 17.3
Chapter 17 Test
 Final for Calculus lll