Research Catalog
A first course in real analysis
- Title
- A first course in real analysis / M.H. Protter, C.B. Morrey, Jr.
- Author
- Protter, Murray H.
- Publication
- New York : Springer-Verlag, ©1977.
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| Status | Format | Access | Call Number | Item Location |
|---|---|---|---|---|
| Text | Use in library | QA300 .P968 | Off-site |
Details
- Additional Authors
- Morrey, Charles Bradfield, 1907-1984
- Description
- xi, 507 : illustrations; 24 cm
- Summary
- This book is designed for a first course in real analysis which follows the standard course in elementary calculus. Since many students encounter rigorous mathematical theory for the first time in this course, the authors include such elementary topics as the axioms of algebra and their immediate consequences and proofs of theorems on limits. The pace is deliberately slow, the proofs are detailed. The emphasis of the presentation is on theory, but the books also contains a full treatment (with many illustrative examples and exercises) of the standard topics in infinite series, Fourier series, multidimensional calculus, elements of metric spaces, and vector field theory. There are many problems which require the student to learn techniques of proofs and the standard tools of analysis. -- Back cover.
- Series Statement
- Undergraduate texts in mathematics
- Uniform Title
- Undergraduate texts in mathematics.
- Subject
- Note
- Includes index.
- Bibliography (note)
- Includes index.
- Contents
- The real number system -- Continuity and limits -- Basic properties of functions on R₁ -- Elementary theory of differentiation -- Elementary theory of integration -- Metric spaces and mappings -- Differentiation in R[subscript n] -- Integration in R[subscript n] -- Infinite sequences and infinite series -- Fourier series -- Functions defined by integrals -- Functions of bounded variation and the Riemann-Stieltjes integral -- Contraction mappings and differential equations -- Implicit function theorems and differentiable maps -- Functions on metric spaces -- Vector field theory. The theorems of Green and Stokes -- Appendices: 1. Absolute value -- 2. Solution of inequalities by factoring -- 3. Expansions of real numbers in an arbitrary base -- 4. Vectors in E[subscript N].
- ISBN
- 0387902155
- 9780387902159
- 3540902155
- 9783540902157
- LCCN
- 76043978
- OCLC
- ocm02493359
- 2493359
- SCSB-276853
- Owning Institutions
- Princeton University Library