Two-Dimensional Calculus (2011)
Chapter 1. Background
Chapter 2. Differentiation
4. Partial derivatives and plane domains
6. Directional derivatives and gradient
8. Level curves and the implicit function theorem
9. Maximum and minimum along a curve
12. Taylor’s theorem; maxima and minima
Chapter 3. Transformations
13. Pairs of functions; geometric representation
15. Special linear transformations; composition
16. Differentiable transformations
17. Composition; inverse mappings
18. Functional dependence; conformal mapping
Chapter 4. Integration
22. Potential functions; independence of path
25. Green’s theorem for a rectangle
26. Green’s theorem for arbitrary figures; applications
27. Mean value theorem for the double integral; vector forms of Green’s theorem
28. Transformation rule for double integrals