PENN STATE UNIVERSITY MATH 231 CALCULUS AND VECTOR ANALYSIS Text Calculus Early Transcendental Functions 5th Edition 2011 Author Larson Hostetler Edwards Publisher Houghton Mifflin ISBN 13 978 0 538 73550 6 Course Outline CHAPTER 11 VECTORS AND THE GEOMETRY OF SPACE 11 1 Vectors in the Plane 11 2 Space Coordinates and Vectors in Space 11 3 The Dot Product of Two Vectors 11 4 The Cross Product of Two Vectors in Space 11 5 Lines and Planes in Space 11 6 Surfaces in Space 11 7 Cylindrical and Spherical Coordinates CHAPTER 12 VECTOR VALUED FUNCTIONS 12 1 Vector Valued Functions 12 2 Differentiation and Integration of Vector Valued Functions 12 3 Velocity and Acceleration 12 4 Tangent Vectors and Normal Vectors 12 5 Arc Length and Curvature CHAPTER 13 FUNCTIONS OF SEVERAL VARIABLES 13 1 Introduction to Functions of Several Variables 13 2 Limits and Continuity 13 3 Partial Derivatives 13 4 Differentials 13 5 Chain Rules for Functions of Several Variables 13 6 Directional Derivatives and Gradients 13 7 Tangent Planes and Normal Lines 13 8 Extrema of Functions of Two Variables 13 9 Applications of Extrema of Functions of Two Variables 13 10 Lagrange Multipliers 1 NOTES 1 INSTRUCTORS OF COURSES THAT HAVE MULTIPLE SECTIONS MUST CONSULT WITH EACH OTHER TO DESIGN FINAL EXAMS THAT TEST THE SAME TOPICS 2 Calculators that perform symbolic manipulations TI 89 TI 92 etc are not permitted for exams and or quizzes 3 All items must be covered and items with are optional Edited 08 2011 by Amos Ong 2