Contents v

10.3. The Integral over a Jordan Region 288

10.4. Iterated Integrals 294

10.5. The Change of Variables Formula 303

Chapter 11. Vector Calculus 317

11.1. 1-forms and Path Integrals 317

11.2. Change of Variables 323

11.3. Differential Forms of Higher Order 331

11.4. Green’s Theorem 338

11.5. Surface Integrals and Stokes’s Theorem 348

11.6. Gauss’s Theorem 358

11.7. Chains and Cycles 365

Appendix. Degrees of Infinity 375

A.1. Cardinality of Sets 375

A.2. Countable Sets 378

A.3. Uncountable Sets 380

A.4. The Axiom of Choice 382

Bibliography 387

Index 389