Chapter 16: Vector Calculus
Course
MATH241 (Calculus IV)
Overview
This chapter covers Vector Calculus from Stewart Calculus 9th Edition.
Each section contains:
- Skill breakdowns with learning objectives
- Practice problems at multiple difficulty levels
- Links to related skills and prerequisites
Sections
Section 16.1: Vector Fields
| Skill | Description | Difficulty |
|---|---|---|
| Gradient Fields | Vector Calculus | Intermediate |
| Vector Fields | Vector Calculus | Intermediate |
Section 16.2: Line Integrals
| Skill | Description | Difficulty |
|---|---|---|
| Line Integrals of Scalar Functions | Vector Calculus | Intermediate |
| Line Integrals of Vector Fields | Vector Calculus | Intermediate |
Section 16.3: The Fundamental Theorem for Line Integrals
| Skill | Description | Difficulty |
|---|---|---|
| Conservative Vector Fields | Vector Calculus | Intermediate |
| Fundamental Theorem for Line Integrals | Vector Calculus | Intermediate |
Section 16.4: Green’s Theorem
| Skill | Description | Difficulty |
|---|---|---|
| Applications of Green’s Theorem | Vector Calculus | Intermediate |
| Green’s Theorem | Vector Calculus | Intermediate |
Section 16.5: Curl and Divergence
| Skill | Description | Difficulty |
|---|---|---|
| Curl | Vector Calculus | Intermediate |
| Divergence | Vector Calculus | Intermediate |
| Properties of Curl and Divergence | Vector Calculus | Intermediate |
Section 16.6: Parametric Surfaces and Their Areas
| Skill | Description | Difficulty |
|---|---|---|
| Parametric Surfaces | Vector Calculus | Intermediate |
| Surface Area of Parametric Surfaces | Vector Calculus | Intermediate |
Section 16.7: Surface Integrals
| Skill | Description | Difficulty |
|---|---|---|
| Surface Integrals of Scalar Functions | Vector Calculus | Intermediate |
| Surface Integrals of Vector Fields | Vector Calculus | Intermediate |
Section 16.8: Stokes’ Theorem
| Skill | Description | Difficulty |
|---|---|---|
| Applications of Stokes’ Theorem | Vector Calculus | Advanced |
| Stokes’ Theorem | Vector Calculus | Advanced |
Section 16.9: The Divergence Theorem
| Skill | Description | Difficulty |
|---|---|---|
| Applications of Divergence Theorem | Vector Calculus | Advanced |
| The Divergence Theorem | Vector Calculus | Advanced |
Section 16.10: Summary
| Skill | Description | Difficulty |
|---|---|---|
| Summary of Vector Calculus | Vector Calculus | Intermediate |
Prerequisites
Before starting Chapter 16, review relevant prerequisite skills from earlier chapters.
| Previous | Up | Next |
|---|---|---|
| Chapter 15 | Home | Chapter 17 |