These notes and exercises were written by Prof. Arthur Mattuck and are designed to supplement the textbook.
Part I: Notes
Course supplementary notes and problems.
| 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
Course supplementary notes and problems.
| 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
Course supplementary notes and problems.
| 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
