Math 241. Calculus III
Lecture Syllabus

Textbook: Stewart, Calculus: Early Transcendentals,
8th edition, with Enhanced Webassign, Thomson Brooks/Cole.

Chapter 12. Vectors and Geometry of Space (4-5 lectures)
12.1 Three-Dimensional Coordinate Systems
12.2 Vectors
12.3 The Dot Product
12.4 The Cross Product
12.5 Equations of Lines and Planes
12.6 Cylinders and Quadratic Surfaces

Chapter 13. Vectors Functions (4 lectures)
13.1 Vector Functions and Space Curves
13.2 Derivatives and Integrals of Vector Functions
13.3 Arc Length and Curvature
13.4 Motion in Space: Velocity and Acceleration

Chapter 14. Partial Derivatives (8-9 lectures)
14.1 Functions of Several Variables
14.2 Limits and Continuity
14.3 Partial Derivatives
14.4 Tangent Planes and Linear Approximation
14.5 The Chain Rule
14.6 Directional Derivatives and the Gradient Vector
14.7 Maximum and Minimum Values
14.8 Lagrange Multipliers

Chapter 15. Multiple Integrals (9-11 lectures)
15.1 Double Integrals over Rectangles
15.2 Iterated Integrals
15.3 Double Integrals over General Regions
15.4 Double Integrals in Polar Coordinates
15.5 Applications of Double Integrals
15.6 Skip this section, material covered in Chapter 16.
15.7 Triple Integrals
15.8 Triple Integrals in Cylindrical Coordinates
15.9 Triple Integrals in Spherical Coordinates
15.10 Change of Variables in Multiple Integrals

Chapter 16. Vector Calculus (10-12 lectures)
16.1 Vector Fields
16.2 Line Integrals
16.3 The Fundamental Theorem for Line Integrals
16.4 Green's Theorem
16.5 Curl and Divergence
16.6 Parametric Surfaces and Their Areas
16.7 Surface Integrals
16.8 Stokes' Theorem
16.9 The Divergence Theorem

Course Prerequisite: Math 231. A minimum grade of C is recommended in Math 231.

Revised 10/26/17