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Concept Tests for Calculus: Multivariable 8th Edition, Hughes-Hallett et al.

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Chapter 12 ConceptTests - Functions of Several Variables

• Sec.12-1 Functions of Two Variables (and solutions)
• Sec.12-2 Graphs and Surfaces (and solutions)
• Sec.12-3 Contour Diagrams (and solutions)
• Sec.12-4 Linear Functions (and solutions)
• Sec.12-5 Functions of Three Variables (and solutions)
• Sec.12-6 Limits and Continuity (and solutions)

Chapter 13 ConceptTests - A Fundamental Tool: Vectors

• Sec.13-1 Displacement Vectors (and solutions)
• Sec.13-2 Vectors in General (and solutions)
• Sec.13-3 The Dot Product (and solutions)
• Sec.13-4 The Cross Product (and solutions)

Chapter 14 ConceptTests - Differentiating Functions of Several Variables

• Sec.14-1 The Partial Derivative (and solutions)
• Sec.14-2 Computing Partial Derivatives Algebraically (and solutions)
• Sec.14-3 Local Linearity and the Differential (and solutions)
• Sec.14-4 Gradients and Directional Derivatives in the Plane (and solutions)
• Sec.14-5 Gradients and Directional Derivatives in Space (and solutions)
• Sec.14-6 The Chain Rule (and solutions)
• Sec.14-7 Second-Order Partial Derivatives (and solutions)
• Sec.14-8 Differentiability (and solutions)

Chapter 15 ConceptTests - Optimization: Local and Global Extrema

• Sec.15-1 Critical Points: Local Extrema and Saddle Points (and solutions)
• Sec.15-2 Optimization (and solutions)
• Sec.15-3 Constrained Optimization: Lagrange Multipliers (and solutions)

Chapter 16 ConceptTests - Integrating Functions of Several Variables

• Sec.16-1 The Definite Integral of a Function of Two Variables (and solutions)
• Sec.16-2 Iterated Integrals (and solutions)
• Sec.16-3 Triple Integrals (and solutions)
• Sec.16-4 Double Integrals in Polar Coordinates (and solutions)
• Sec.16-5 Integrals in Cylindrical and Spherical Coordinates (and solutions)
• Sec.16-6 Applications of Integration to Probability (and solutions)

Chapter 17 ConceptTests - Parameterization and Vector Fields

• Sec.17-1 Parameterized Curves (and solutions)
• Sec.17-2 Motion, Velocity, and Acceleration (and solutions)
• Sec.17-3 Vector Fields (and solutions)
• Sec.17-4 The Flow of a Vector Field (and solutions)

Chapter 18 ConceptTests - Line Integrals

• Sec.18-1 The Idea of a Line Integral (and solutions)
• Sec.18-2 Computing Line Integrals Over Parameterized Curves (and solutions)
• Sec.18-3 Gradient Fields and Path-Independent Fields (and solutions)
• Sec.18-4 Path-Dependent Vector Fields and Green’s Theorem (and solutions)

Chapter 19 ConceptTests - Flux Integrals and Divergence

• Sec.19-1 The Idea of a Flux Integral (and solutions)
• Sec.19-2 Flux Integrals for Graphs, Cylinders, and Spheres (and solutions)
• Sec.19-3 The Divergence of a Vector Field (and solutions)
• Sec.19-4 The Divergence Theorem (and solutions)

Chapter 20 ConceptTests - The Curl And Stokes’ Theorem

• Sec.20-1 The Curl of a Vector Field (and solutions)
• Sec.20-2 Stokes’ Theorem (and solutions)
• Sec.20-3 The Three Fundamental Theorems (and solutions)

Chapter 21 ConceptTests - Parameters, Coordinates, and Integrals

• Sec.21-1 Coordinates and Parameterized Surfaces (and solutions)
• Sec.21-2 Change of Coordinates in a Multiple Integral (and solutions)
• Sec.21-3 Flux Integrals over Parameterized Surfaces (and solutions)

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