Math 240 - Calculus III

Credits: 4

Course Description: This course is an introduction to the calculus of functions of several variables. It begins with studying the basic objects of multidimensional geometry: vectors and vector operations, lines, planes, cylinders, quadric surfaces, and various coordinate systems. It continues with the elementary differential geometry of vector functions and space curves. After this, it extends the basic tools of differential calculus - limits, continuity, derivatives, linearization, and optimization - to multidimensional problems. The course will conclude with a study of integration in higher dimensions, culminating in a multidimensional version of the substitution rule.

Pre-Requisites: MATH 141.

Note: Because MATH 240 is the final part of a three-semester calculus sequence, it should be taken as soon as possible after MATH 141.

Frequency:

Current Textbook: Multivariable Calculus, 6th Edition, by James Stewart, published by Brooks/Cole, 2007. ISBN: 0495011630. Check with your instructor to make sure this is the textbook used for your section.

Chapter 13:

13.1 Three-Dimensional Coordinate Systems.
13.2 Vectors.
13.3 The Dot Product.
13.4 The Cross Product.
13.5 Equations of Lines and Planes.
13.6 Cylinders and Quadric Surfaces.

Chapter 14:

14.1 Vector Functions and Space Curves.
14.2 Derivatives and Integrals of Vector Functions.
14.3 Arc Length and Curvature.
14.4 Motion in Space.

Chapter 15:

15.1 Functions of Several Variables.
15.2 Limits and Continuity.
15.3 Partial Derivatives.
15.4 Tangent Planes and Linear Approximations.
15.5 The Chain Rule.
15.6 Directional Derivatives and the Gradient Vector.
15.7 Maximum and Minimum Values.
15.8 Lagrange Multipliers.

Chapter 16:

16.1 Double Integrals over Rectangles.
16.2 Iterated Integrals.
16.3 Double Integrals over General Regions.
16.4 Double Integrals in Polar Coordinates.
16.5 Applications of Double Integrals.
16.6 Triple Integrals.
16.7 Triple Integrals in Cylindrical Coordinates.
16.8 Triple Integrals in Spherical Coordinates.
16.9 Change of Variables in Multiple Integrals.

Chapter 17:

17.1 Vector Fields.
17.2 Line Integrals.
17.3 The Fundamental Theorem for Line Integrals.
17.4 Green's Theorem.
17.5 Curl and Divergence.
17.6 Parametric Surfaces.
17.7 Surface Integrals.
17.8 Stoke's Theorem.
17.9 The Divergence Theorem.