On this webpage you will find my solutions to the sixth edition of "Vector Calculus" by Susan J. Colley. Here is a link to the book's page on amazon.com. If you find my work useful, please consider making a donation. Thank you.
- Chapter 1: Vectors
- Section 1.1: Vectors in Two and Three Dimensions
- Section 1.2: More About Vectors
- Section 1.3: The Dot Product
- Section 1.4: The Cross Product
- Section 1.5: Equations for Planes; Distance Problems
- Section 1.6: Some n-dimensional Geometry
- Section 1.7: New Coordinate Systems
- Chapter 2: Differentiation in Several Variables
- Section 2.1: Functions of Several Variables; Graphing Surfaces
- Section 2.2: Limits
- Section 2.3: The Derivative
- Section 2.4: Properties; Higher-order Partial Derivatives
- Section 2.5: The Chain Rule
- Section 2.6: Directional Derivatives and the Gradient
- Section 2.7: Newton's Method (Optional)
- Chapter 3: Vector-Valued Functions
- Section 3.1: Parametrized Curves and Kepler's Laws
- Section 3.2: Arclength and Differential Geometry
- Section 3.3: Vector Fields: An Introduction
- Section 3.4: Gradient, Divergence, Curl, and the Del Operator
- Chapter 4: Maxima and Minima in Several Variables
- Section 4.1: Differentials and Taylor's Theorem
- Section 4.2: Extrema of Functions
- Section 4.3: Lagrange Multipliers
- Section 4.4: Some Applications of Extrema
- Chapter 5: Multiple Integrals
- Section 5.1: Introduction: Areas and Volume
- Section 5.2: Double Integrals
- Section 5.3: Changing the Order of Integration
- Section 5.4: Triple Integrals
- Section 5.5: Change of Variables
- Section 5.6: Applications of Integration
- Section 5.7: Numerical Approximations of Multiple Integrals (optional)
- Chapter 6: Line Integrals
- Section 6.1: Scalar and Vector Line Integrals
- Section 6.2: Green's Theorem
- Section 6.3: Conservative Vector Fields
- Chapter 7: Surface Integrals and Vector Analysis
- Section 7.1: Parametrized Surfaces
- Section 7.2: Surface Integrals
- Section 7.3: Stokes's and Gauss's Theorems
- Section 7.4: Further Vector Analysis; Maxwell's Equations
- Chapter 8: Vector Analysis in Higher Dimensions
- Section 8.1: An Introduction to Differential Forms
- Section 8.2: Manifolds and Integrals of k-forms
- Section 8.3: The Generalized Stokes's Theorem
| Section 1.1 |
Section 1.2 |
Section 1.3 |
| Exercise 1 |
Exercise 19 |
Exercise 1 |
Exercise 19 |
Exercise 37 |
Exercise 1 |
Exercise 19 |
| Exercise 2 |
Exercise 20 |
Exercise 2 |
Exercise 20 |
Exercise 38 |
Exercise 2 |
Exercise 20 |
| Exercise 3 |
Exercise 21 |
Exercise 3 |
Exercise 21 |
Exercise 39 |
Exercise 3 |
Exercise 21 |
| Exercise 4 |
Exercise 22 |
Exercise 4 |
Exercise 22 |
Exercise 40 |
Exercise 4 |
Exercise 22 |
| Exercise 5 |
Exercise 23 |
Exercise 5 |
Exercise 23 |
Exercise 41 |
Exercise 5 |
Exercise 23 |
| Exercise 6 |
Exercise 24 |
Exercise 6 |
Exercise 24 |
Exercise 42 |
Exercise 6 |
Exercise 24 |
| Exercise 7 |
Exercise 25 |
Exercise 7 |
Exercise 25 |
Exercise 43 |
Exercise 7 |
Exercise 25 |
| Exercise 8 |
Exercise 26 |
Exercise 8 |
Exercise 26 |
Exercise 44 |
Exercise 8 |
Exercise 26 |
| Exercise 9 |
Exercise 27 |
Exercise 9 |
Exercise 27 |
Exercise 45 |
Exercise 9 |
Exercise 27 |
| Exercise 10 |
|
Exercise 10 |
Exercise 28 |
Exercise 46 |
Exercise 10 |
Exercise 28 |
| Exercise 11 |
|
Exercise 11 |
Exercise 29 |
Exercise 47 |
Exercise 11 |
Exercise 29 |
| Exercise 12 |
|
Exercise 12 |
Exercise 30 |
|
Exercise 12 |
Exercise 30 |
| Exercise 13 |
|
Exercise 13 |
Exercise 31 |
|
Exercise 13 |
Exercise 31 |
| Exercise 14 |
|
Exercise 14 |
Exercise 32 |
|
Exercise 14 |
Exercise 32 |
| Exercise 15 |
|
Exercise 15 |
Exercise 33 |
|
Exercise 15 |
Exercise 33 |
| Exercise 16 |
|
Exercise 16 |
Exercise 34 |
|
Exercise 16 |
Exercise 34 |
| Exercise 17 |
|
Exercise 17 |
Exercise 35 |
|
Exercise 17 |
Exercise 35 |
| Exercise 18 |
|
Exercise 18 |
Exercise 36 |
|
Exercise 18 |
Exercise 36 |