## Calculus and Vector Analysis

**4 credits**

**Blue Book Description:** Three-dimensional analytic geometry; vectors in space; partial differentiation; double and triple integrals; integral vector calculus. Students who have passed either MATH 231 or 232 may not schedule MATH 230 for credit.

**Pre-requisites:** MATH 141

**Pre-requisite for:** MATH 412, MATH 414, MATH 416, MATH 419, MATH 421, MATH 451

**Suggested Textbook:**

Multivariate calculus: Early Transcendentals, by James Stewart, published by Brookes Cole Thomson.*Check with your instructor to make sure this is the textbook used for your section.*

**Topics:**

Chapter 12: Vectors and the Geometry of Space

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 Quadric Surfaces

12.7 Cylindrical and Spherical Coordinates

Chapter 13: Vector Functions

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

14.1 Functions of Several Variables

14.2 Limits and Continuity

14.3 Partial Derivatives

14.4 Tangent Planes and Linear Approximations

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

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 Surface Area

15.7 Triple Integrals

15.8 Triple Integrals in Cylindrical and Spherical Coordinates

15.9 Change of Variables in Multiple Integrals

Chapter 16: Vector Calculus

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 (Optional)

16.10 Summary (Optional)