## 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