This course is designed as a self-study program in differential calculus. The content is organized into “chapters” below.
| 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 |
