In addition to the videos, the following study materials are available:
Study Guides
The Study Guides include pre-tests, photographs of every chalkboard used in the videotapes, reading assignments in the supplementary notes and textbook, and exercises with solutions.
| LEC # | TOPICS | PHOTOS, READINGS, and EXERCISES | SOLUTIONS |
|---|---|---|---|
| Part I: Complex Variables | |||
| 1 | The Complex Numbers | ( PDF - 1.8MB) | (PDF - 5.1MB) |
| 2 | Functions of a Complex Variable | (PDF) | (PDF - 4.7MB) |
| 3 | Conformal Mappings | (PDF) | (PDF - 2.9MB) |
| 4 | Sequences and Series | (PDF) | (PDF - 2.8MB) |
| 5 | Integrating Complex Functions | (PDF) | (PDF - 5.5MB) |
| Part II: Differential Equations | |||
| 1 | The Concept of a General Solution | (PDF - 2.3MB) | (PDF - 15.3MB) |
| 2 | Linear Differential Equations | (PDF) | (PDF - 4.0MB) |
| 3 | Solving the Linear Equations L(y) = 0; Constant Coefficients | (PDF) | (PDF - 3.2MB) |
| 4 | Undetermined Coefficients | (PDF) | (PDF - 4.4MB) |
| 5 | Variations of Parameters | (PDF) | (PDF - 4.0MB) |
| 6 | Power Series Solutions | (PDF - 1.7MB) | (PDF - 3.7MB) |
| 7 | Laplace Transforms | (PDF - 1.2MB) | (PDF - 8.2MB) |
| Part III: Linear Algebra | |||
| 1 | Vector Spaces | (PDF - 1.7MB) | (PDF - 4.4MB) |
| 2 | Calculus of Several Variables | (PDF) | (PDF - 3.3MB) |
| 3 | Constructing Bases | (PDF) | (PDF - 2.5MB) |
| 4 | Linear Transformations | (PDF) | (PDF - 5.5MB) |
| 5 | Determinants | (PDF) | (PDF - 5.3MB) |
| 6 | Eigenvectors | (PDF) | (PDF - 3.8MB) |
| 7 | Dot Products | (PDF) | (PDF - 5.8MB) |
| 8 | Orthogonal Functions | (PDF) | (PDF - 5.9MB) |
Supplementary Notes for Complex Variables, Differential Equations, and Linear Algebra
Prerequisite materials, detailed proofs, and deeper treatments of selected topics.
- Invented Number Systems (PDF - 2.9MB)
- Development of the Complex Numbers (PDF - 1.1MB)
- Linear Independance (PDF - 3.0MB)
- Some Notes on Differential Operators (PDF - 4.0MB)
Textbook: The course makes reference to the out-of-print textbook cited below, but any newer textbook will suffice to expand on topics covered in the video lectures.
Thomas, George B. Calculus and Analytic Geometry. Addison-Wesley, 1968. ISBN: 9780201075250.