Multivariate Calculus - Bruce E. Shapiro

Contents
1 Cartesian Coordinates 1
2 Vectors in 3D 9
3 The Cross Product 21
4 Lines and Curves in 3D 29
5 Velocity, Acceleration, and Curvature 37
6 Surfaces in 3D 45
7 Cylindrical and Spherical Coordinates 47
8 Functions of Two Variables 51
9 The Partial Derivative 59
10 Limits and Continuity 67
11 Gradients and the Directional Derivative 73
12 The Chain Rule 81
13 Tangent Planes 93
14 Unconstrained Optimization 101
15 Constrained Optimization: Lagrange Multipliers 117
16 Double Integrals over Rectangles 127
17 Double Integrals over General Regions 135
18 Double Integrals in Polar Coordinates 145
19 Surface Area with Double Integrals 155
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