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