      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