RES.18-008 | Fall 2011 | Undergraduate

# Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra

## Study Materials

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.

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.

## Course Info

Fall 2011
##### Learning Resource Types
Lecture Videos
Problem Sets with Solutions
Lecture Notes