Need to Review Calculus 1 & 2 (1131/1132)?
A Few Useful Links:
Paul’s Online Math Notes, Calculus III
3D Function Grapher (also does Parametric Surfaces!)
Learning Activities, By Week:
| Week | Section | Topic | Learning Activities | Assessments |
| 1 | 12.1 | Three-Dimensional Coordinate Systems | Visualizing the Octants | |
| 12.6 | Cylinders and Quadric Surfaces | Quadric Surfaces | Understanding Surfaces Worksheet (Week 2) | |
| 12.2 | Vectors | Visualizing Vectors in 3D | Notes on Vectors (Week 1, not collected) | |
| 12.3 | The Dot Product | Dot Products in 3D
Direction Angles (*useful application) Projections (*useful application) |
Notes on the Dot and Cross Product (Week 1, not collected) | |
| 12.4 | The Cross Product | Cross Products
Volume of a Parallelepiped (*useful application) |
Practice with Vectors Worksheet (Week 2) | |
| 2 | 12.5 | Equations of Lines & Planes | Line in 3D (static) vs Line in 3D (variable) | Lines and Planes Worksheet (Week 3) |
| 14.1 | Functions of Several Variables | A Gallery of Examples | ||
| 14.3 | Partial Derivatives | Cross Sections | Partial Derivatives and Tangent Planes Worksheet (Week 5) | |
| 3 | 14.2 | Limits and Continuity | Limits Handout (Week 3) | |
| 14.4 | Tangent Planes and Linear Approximation | Linear Approximation | ||
| 14.5 | The Chain Rule | Notes on the Chain Rule (Week 3, notes not collected but exercises will be) | ||
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14.6 |
Directional Derivatives and the Gradient Vector | Directional Derivatives Video | ||
| 4 | Exam 1 | Practice Exam 1 and Solutions | ||
| 14.7 | Maximum and Minimum Values | Max and Min Video | Notes on Absolute Maxima and Minima (Week 5, notes not collected but exercises will be) | |
| 5 | 14.8 | Lagrange Multipliers | Absolute Max/Min Video | |
| 15.1 | Double Integrals over Rectangles | Double Integrals over Rectangles Video | Double Integrals and Volume Worksheet (Week 6) | |
| 15.2 | Double Integrals over General Regions | Double Integrals over General Regions Video | ||
| 6 | 15.3 | Double Integrals in Polar Coordinates | ||
| 15.6 | Triple Integrals | Surface Area Video (*helpful for Chapter 16) | Triple Integrals Worksheet (Week 7) | |
| 15.9 | Change of Variables in Multiple Integrals | Change of Variables Video | Notes on Change of Variables (Week 6, notes not collected but exercises will be) | |
| 7 | 15.7 | Triple Integrals in Cylindrical Coordinates | Visualizing Cylindrical Coordinates | |
| 15.8 | Triple Integrals in Spherical Coordinates | Visualizing Spherical Coordinates | ||
| 8 | Exam 2 | Practice Exam 2 and Solutions | ||
| 13.1 | Vector Functions | A Space Curve | Vector Functions and Parameterized Curves (Week 9) Application of Vector Functions (Week 9) |
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| 9 | 13.2
|
Derivatives and Integrals of Vector Functions | ||
| 13.3 | Arc Length | Linear Approximation of Arc Length | ||
| 16.1 | Vector Fields | Simple 2D Vector Field | Vector Fields (Week 10) | |
| 16.2 | Line Integrals | Line Integrals (Week 10) | ||
| 10 | 16.2 | Line Integrals (continued) | ||
| 16.3 | The Fundamental Theorem for Line Integrals | Fundamental Theorem for Line Integrals Video | Line Integral Theorem Practice (Week 11) | |
| 11 | 16.4 | Green’s Theorem | Green’s Theorem Video | |
| 16.5 | Curl and Divergence | |||
| 12 | Exam 3 | Practice Exam 3 and Solutions | ||
| 16.6 | Parametric Surfaces and Their Areas | A Gallery of Examples | Common Parametric Surfaces (Week 13) | |
| 13 | 16.7 | Surface Integrals | Line Integrals vs. Surface Integrals (Week 13) | |
| 16.9 | Divergence Theorem | Using the Divergence Theorem (Week 14) | ||
| 14 | 16.8 | Stokes’ Theorem | ||
| Final Exam Review | Review for Final Exam and Solutions |