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
