Chapter 15: Multiple Integrals
Course
MATH241 (Calculus IV)
Overview
This chapter covers Multiple Integrals 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 15.1: Double Integrals over Rectangles
| Skill | Description | Difficulty |
|---|---|---|
| Double Integrals over Rectangles | Multiple Integrals | Intermediate |
| Iterated Integrals | Multiple Integrals | Intermediate |
Section 15.2: Double Integrals over General Regions
| Skill | Description | Difficulty |
|---|---|---|
| Double Integrals over General Regions | Multiple Integrals | Intermediate |
| Type I and Type II Regions | Multiple Integrals | Intermediate |
Section 15.3: Double Integrals in Polar Coordinates
| Skill | Description | Difficulty |
|---|---|---|
| Double Integrals in Polar | Multiple Integrals | Intermediate |
Section 15.4: Applications of Double Integrals
| Skill | Description | Difficulty |
|---|---|---|
| Mass and Density (2D) | Multiple Integrals | Intermediate |
| Moment of Inertia | Multiple Integrals | Intermediate |
| Moments and Center of Mass (2D) | Multiple Integrals | Intermediate |
Section 15.5: Surface Area
| Skill | Description | Difficulty |
|---|---|---|
| Surface Area | Multiple Integrals | Intermediate |
Section 15.6: Triple Integrals
| Skill | Description | Difficulty |
|---|---|---|
| Triple Integrals over Boxes | Multiple Integrals | Intermediate |
| Triple Integrals over General Regions | Multiple Integrals | Intermediate |
Section 15.7: Triple Integrals in Cylindrical Coordinates
| Skill | Description | Difficulty |
|---|---|---|
| Cylindrical Coordinates | Multiple Integrals | Intermediate |
| Triple Integrals in Cylindrical | Multiple Integrals | Intermediate |
Section 15.8: Triple Integrals in Spherical Coordinates
| Skill | Description | Difficulty |
|---|---|---|
| Spherical Coordinates | Multiple Integrals | Intermediate |
| Triple Integrals in Spherical | Multiple Integrals | Intermediate |
Section 15.9: Change of Variables in Multiple Integrals
| Skill | Description | Difficulty |
|---|---|---|
| General Change of Variables | Multiple Integrals | Advanced |
| The Jacobian | Multiple Integrals | Advanced |
Prerequisites
Before starting Chapter 15, review relevant prerequisite skills from earlier chapters.
| Previous | Up | Next |
|---|---|---|
| Chapter 14 | Home | Chapter 16 |