Course Details - Mathematics and Statistics - Penn State Altoona

Math 230

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)