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