These notes and exercises were written by Prof. Arthur Mattuck and are designed to supplement the textbook.
Part I: Notes
| SECTIONS | TOPICS |
|---|---|
| D | Determinants (PDF) |
| M | Matrices and Linear Algebra (PDF) |
| K | Kepler’s Second Law (PDF) |
| TA | The Tangent Approximation (PDF) |
| SD | Second Derivative Test (PDF) |
| LS | Least Squares Interpolation (PDF) |
| N | Non-independent Variables (PDF) |
| P | Partial Differential Equations (PDF) |
| I | Limits in Iterated Integrals (PDF) |
| CV | Changing Variables in Multiple Integrals (PDF) |
| G | Gravitational Attraction (PDF) |
Part II: Vector Integral Calculus
| SECTIONS | TOPICS |
|---|---|
| V1 | Plane Vector Fields (PDF) |
| V2 | Gradient Fields and Exact Differentials (PDF) |
| V3 | Two-dimensional Flux (PDF) |
| V4 | Green’s Theorem in Normal Form (PDF) |
| V5 | Simply-connected Regions (PDF) |
| V6 | Multiply-connected Regions; Topology (PDF) |
| V7 | Laplace’s Equation and Harmonic Functions (PDF) |
| V8 | Vector Fields in Space (PDF) |
| V9 | Surface Integrals (PDF) |
| V10 | The Divergence Theorem (PDF) |
| V11 | Line Integrals in Space (PDF) |
| V12 | Gradient Fields in Space (PDF) |
| V13 | Stokes’ Theorem (PDF) |
| V14 | Some Topological Questions (PDF) |
| V15 | Relation to Physics (PDF) |
Part III: Exercises
| SECTIONS | TOPICS |
|---|---|
| Problems* | |
| 1 | Vectors and Matrices (PDF) |
| 2 | Partial Differentiation (PDF) |
| 3 | Double Integrals (PDF) |
| 4 | Line Integrals in the Plane (PDF) |
| 5 | Triple Integrals (PDF) |
| 6 | Vector Integral Calculus in Space (PDF) |
| Solutions | |
| 1 | Vectors and Matrices (PDF) |
| 2 | Partial Differentiation (PDF) |
| 3 | Double Integrals (PDF) |
| 4 | Line Integrals in the Plane (PDF) |
| 5 | Triple Integrals (PDF) |
| 6 | Vector Integral Calculus in Space (PDF) |
* Problems with * are not solved
