1 Vectors and the Geometry of 3D Space
45 practice problems
- 1.1 Vectors, Dot Products and Cross Products15 problems
- 1.2 Lines and Planes in Space15 problems
- 1.3 Vector-Valued Functions and Space Curves15 problems
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Lines and Planes in Space · Sample question
Calculus III practice problems
300 practice problems, organized by chapter and topic.
A multivariable and vector calculus course covering functions of several variables, partial derivatives, multiple integrals, and the theorems of Green, Stokes, and Gauss.
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Section 1.2: Lines and Planes in Space.
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2 Functions of Several Variables and Surfaces
30 practice problems
- 2.1 Domains, Level Curves and Surfaces15 problems
- 2.2 Multivariable Limits and Continuity15 problems
3 Partial Derivatives and the Gradient
62 practice problems
- 3.1 Partial and Higher-Order Derivatives16 problems
- 3.2 The Multivariable Chain Rule15 problems
- 3.3 Gradients and Directional Derivatives16 problems
- 3.4 Tangent Planes and Differentials15 problems
4 Optimization and Lagrange Multipliers
45 practice problems
- 4.1 Critical Points and the Second Derivative Test16 problems
- 4.2 Lagrange Multipliers15 problems
- 4.3 Absolute Extrema on Closed Regions14 problems
5 Multiple Integrals
60 practice problems
- 5.1 Double Integrals over Rectangles15 problems
- 5.2 General Regions and Polar Coordinates15 problems
- 5.3 Triple Integrals and Cylindrical and Spherical Coordinates16 problems
- 5.4 Change of Variables and Jacobians14 problems
6 Vector Calculus
58 practice problems
- 6.1 Line Integrals15 problems
- 6.2 Green's Theorem14 problems
- 6.3 Surface Integrals15 problems
- 6.4 Flux14 problems
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