PENN STATE UNIVERSITY
MATH 230: CALCULUS AND VECTOR ANALYSIS
Text: Calculus: Early Transcendental Functions, 3rd ed, 2003
Author: Larson/Hostetler/Edwards
Publisher: Houghton Mifflin, ISBN 0-618-22307-X
Course Outline
-
Chapter 10:
- VECTORS AND THE GEOMETRY OF SPACE
- 10.1
- Vectors in the Plane
- 10.2
- Space Coordinates and Vectors in Space
- 10.3
- The Dot Product of Two Vectors
- 10.4
- The Cross Product of Two Vectors in Space
- 10.5
- Lines and Planes in Space
- 10.6
- Surfaces in Space
- 10.7
- Cylindrical and Spherical Coordinates
-
Chapter 11:
- VECTOR-VALUED FUNCTIONS
- 11.1
- Vector-Valued Functions
- 11.2
- Differentiation and Integration of Vector Valued Functions
- 11.3
- Velocity and Acceleration
- 11.4
- Tangent Vectors and Normal Vectors
- 11.5
- Arc Length and Curvature
-
Chapter 12:
- FUNCTIONS OF SEVERAL VARIABLES
- 12.1
- Introduction to Functions of Several Variables
- 12.2
- Limits and Continuity
- 12.3
- Partial Derivatives
- 12.4
- Differentials
- 12.5
- Chain Rules for Functions of Several Variables
- 12.6
- Directional Derivatives and Gradients
- 12.7
- Tangent Planes and Normal Lines
- 12.8
- Extrema of Functions of Two Variables
- 12.9
- Applications of Extrema of Functions of Two Variables
- 12.10
- Lagrange Multipliers **
-
Chapter 13:
- MULTIPLE INTEGRATION
- 13.1
- Iterated Integrals and Area in the Plane
- 13.2
- Double Integrals and Volume
- 13.3
- Change of Variables: Polar Coordinates
- 13.4
- Center of Mass and Moments of Inertia **
- 13.5
- Surface Area
- 13.6
- Triple Integrals and Applications
- 13.7
- Triple Integrals in Cylindrical and Spherical Coordinates
- 13.8
- Change of Variables: Jacobians **
-
Chapter 14:
- VECTOR ANALYSIS
- 14.1
- Vector Fields
- 14.2
- Line Integrals
- 14.3
- Conservative Vector Fields and Independence of Path
- 14.4
- Green's Theorem
- 14.5
- Parametric Surfaces
- 14.6
- Surface Integrals
- 14.7
- Divergence Theorem
- 14.8
- Stokes' Theorem
NOTES:
- INSTRUCTORS OF COURSES THAT HAVE MULTIPLE SECTIONS MUST CONSULT WITH EACH OTHER TO DESIGN FINAL EXAMS THAT TEST THE SAME TOPICS
- Calculators that perform symbolic manipulations (TI-89, TI-92, etc.)
are not permitted for exams and/or quizzes.
- Items in boldface MUST be covered; others are optional.