This course is designed as a self-study program in differential calculus. The content is organized into "chapters" below.
Course calendar.
| chapter # |
Topics |
|
Preface |
| 0 |
The Spreadsheet |
| 1 |
Philosophy, Numbers and Functions |
| 2 |
The Exponential Function and Trigonometric Functions |
| 3 |
Vectors, Dot Products, Matrix Multiplication and Distance |
| 4 |
Area of a Parallelogram, Determinants, Volume and Hypervolume, the Vector Product |
| 5 |
Vectors and Geometry in Two and Three Dimensions |
| 6 |
Differentiable Functions, the Derivative and Differentials |
| 7 |
Computation of Derivatives from their Definition |
| 8 |
Calculation of Derivatives by Rule |
| 9 |
Derivatives of Vector Fields and the Gradient in Polar Coordinates |
| 10 |
Higher Derivatives, Taylor Series, Quadratic Approximations and Accuracy of Approximations |
| 11 |
Quadratic Approximations in Several Dimensions |
| 12 |
Applications of Differentiation: Direct Use of Linear Approximation |
| 13 |
Solving Equations |
| 14 |
Extrema |
| 15 |
Curves |
| 16 |
Some Important Examples and a Formulation in Physics |
| 17 |
The Product Rule and Differentiating Vectors |
| 18 |
Complex Numbers and Functions of Them |
| 19 |
The Anti-derivative or Indefinite Integral |
| 20 |
The Area under a Curve and its Many Generalizations |
| 21 |
The Fundamental Theorem of Calculus in One Dimension |
| 22 |
The Fundamental Theorem of Calculus in Higher Dimensions; Additive Measures, Stokes Theorem and the Divergence Theorem |
| 23 |
Reducing a Line Integral to an Ordinary Integral and Related Reductions |
| 24 |
Reducing a Surface Integral to a Multiple Integral and the Jacobian |
| 25 |
Numerical Integration |
| 26 |
Numerical Solution of Differential Equations |
| 27 |
Doing Integrals |
| 28 |
Introduction to Electric and Magnetic Fields |
| 29 |
Magnetic Fields, Magnetic Induction and Electrodynamics |
| 30 |
Series |
| 31 |
Doing Area, Surface and Volume Integrals |
| 32 |
Some Linear Algebra |
| 33 |
Second Order Differential Equations |