Math 4A Course Topics
Multivariable Calculus (7th ed.) by Howard Anton (Wiley)
Categories: 1. Must be covered.
2. Must be covered at least briefly.
3. Do not cover unless you have extra time after doing 1 and 2.
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Category
Section |
Section |
Topic |
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1 |
12.1 |
Rectangular Coordinates in 3-Space |
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1 |
12.2 |
Vectors |
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1 |
12.3 |
Dot Products; Projections |
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1 |
12.4 |
Cross Products |
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1 |
12.5 |
Parametric Equations of Lines |
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1 |
12.6 |
Planes in 3-Space |
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1 |
12.7 |
Quadric Surfaces |
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2 |
12.8 |
Cylindrical and Spherical Coordinates |
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1 |
13.1 |
Introductions to Vector-Valued Functions |
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1 |
13.2 |
Calculus of Vector-Valued Functions |
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1 |
13.3 |
Change of Parameters; Arc Length |
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1 |
13.4 |
Unit Tangent and Normal Vectors |
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1 |
13.5 |
Curvature |
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1 |
13.6 |
Motion Along a Curve |
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3 |
13.7 |
Kepler’s Laws of Planetary Motion |
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1 |
14.1 |
Functions of Two or More Variables |
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1 |
14.2 |
Limits and Continuity |
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1 |
14.3 |
Partial Derivatives |
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1 |
14.4 |
Differentiability, Local Linearity, and Differentials |
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1 |
14.5 |
The Chain Rule |
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1 |
14.6 |
Directional Derivatives and Gradients |
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1 |
14.7 |
Tangent Planes and Normal Vectors |
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1 |
14.8 |
Maxima and Minima of Functions of Two Variables |
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1 |
14.9 |
Lagrange Multipliers |
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1 |
15.1 |
Double Integrals |
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1 |
15.2 |
Double Integrals over Nonrectangular Regions |
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1 |
15.3 |
Double Integrals for Polar Coordinates |
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1 |
15.4 |
Parametric Surfaces; Surface Areas |
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1 |
15.5 |
Triple Integrals |
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1 |
15.6 |
Centroid, Center of Gravity, Theorem of Pappas |
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1 |
15.7 |
Triple Integrals in Cylindrical and Spherical |
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3 |
15.8 |
Change of Variables in Multiple Integrals |
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1 |
16.1 |
Vector Fields |
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1 |
16.2 |
Line Integrals |
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1 |
16.3 |
Independence of Path; Conservative Vector Fields |
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1 |
16.4 |
Green's Theorem |
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1 |
16.5 |
Introduction to Surface Integrals |
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1 |
16.6 |
Application of Surface Integrals; Flux |
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1 |
16.7 |
The Divergence Theorem |
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1 |
16.8 |
Stoke's Theorem |
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