9780817684112

Advanced Calculus: A Differential Forms Approach

Harold M. Edwards

In a book written for mathematicians, teachers of mathematics, and highly motivated students, Harold Edwards has taken a bold and unusual approach to the presentation of advanced calculus. He begins with a lucid discussion of differential forms and quickly moves to the fundamental theorems of calculus and Stokes' theorem. The result is genuine mathematics, both in spirit a

2-1

Non-Constant Forms

Exercises

p.23

2-2

Integration

Exercises

p.27

2-3

Definition of Certain Simple Integrals. Convergence and the Cauchy Criterion

Exercises

p.34

2-4

Integrals and Pullbacks

Exercises

p.43

2-5

Independence of Parameter

Exercises

p.48

2-6

Summary, Basic Properties of Integrals

Exercises

p.51

8-1

Vector Calculus

Exercises

p.269

8-2

Elementary Differential Equations

Exercises

p.276

8-3

Harmonic Functions and Conformal Coordinates

Exercises

p.288

8-4

Functions of a Complex Variable

Exercises

p.310

8-5

Integrability Conditions

Exercises

p.319

8-6

Introduction to Homology Theory

Exercises

p.326

8-7

Flows

Exercises

p.333

8-8

Applications to Mathematical Physics

Exercises

p.354

9-1

The Real Number System

Exercises

p.375

9-2

Real Functions of Real variables

Exercises

p.386

9-3

Uniform Continuity and Differentiability

Exercises

p.391

9-4

Compactness

Exercises

p.398

9-5

Other Types of Limits

Exercises

p.404

9-6

Interchange of Limits

Exercises

p.419

9-7

Lebesgue Integration

Exercises

p.446

9-8

Banach Spaces

Exercises

p.452