Multivariate Calculus - Bruce E. Shapiro

CONTENTS
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The order in which the material is covered is more-or-less the same order as it is
presented in the textbook. The following table provides a cross-reference between
the notes and the textbook.
Lecture Topic Text Reference
1 Cartesian Coordinates 14.1
2 Vectors 14.2
3 Cross Products 14.3
4 Lines and Curves 14.4
5 Velocity, Acceleration, and Curvature 14.5
6 Surfaces 14.6
7 Cylindrical and Spherical Coordinates 14.7
8 Functions of 2 Variables 15.1
9 Partial Derivatives 15.2
10 Limits and Continuity 15.3
11 Gradients 15.4, 15.5
12 Chain Rule 15.6
13 Tangent Planes 15.7
14 Unconstrained Optimization 15.8
15 Constrained Optimization 15.9
16 Double Integrals: Rectangles 16.1, 16.2
17 Double Integrals: General 16.3
18 Double Integrals: Polar 16.4
19 Surface Area 16.6
20 Triple Integrals 16.7, 16.8
21 Vector Fields 17.1
22 Line Integrals 17.2, 17.3
23 Green’s Theorem 17.4
24 Flux Integrals 17.5, 17.6
25 Stokes’ Theorem 17.7
Math 250, Fall 2006 Revised December 6, 2006.