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