Advanced Calculus

Angus Ellis Taylor (October 13, 1911 – April 6, 1999) was a mathematician and professor at various universities in the University of California system. He earned his undergraduate degree at Harvard summa cum laude in 1933 and his PhD at Caltech in 1936 under Aristotle Michal with a dissertation on analytic functions. By 1944 he had risen to full professor at UCLA, whose mathematics department he later chaired (1958–1964). Taylor was also an astute administrator and eventually rose through the UC system to become provost and then chancellor of UC Santa Cruz. He authored a number of mathematical texts, one of which, Advanced Calculus (1955, Ginn and Co.), became a standard for a generation of mathematics students.

1. Fundamentals of Elementary Calculus.

2. The Real Number System.

3. Continuous Functions.

4. Extensions of the Law of the Mean.

5. Functions of Several Variables.

6. The Elements of Partial Differentiation.

7. General Theorems of Partial Differentiation.

8. Implicit-Function Theorems.

9. The Inverse Function Theorem with Applications.

10. Vectors and Vector Fields.

11. Linear Transformations.

12. Differential Calculus of Functions from R¯nto R¯m.

13. Double and Triple Integrals.

14. Curves and Surfaces.

15. Line and Surface Integrals.

16. Point-Set Theory.

17. Fundamental Theorems on Continuous Functions.

18. The Theory of Integration.

19. Infinite Series.

20. Uniform Convergence.

21. Power Series.

22. Improper Integrals.

Answers to Selected Exercises.

Index.