| Mathematical Analysis: Functions of One Variable 2003 Edition Contributor(s): Giaquinta, Mariano (Author), Modica, Giuseppe (Author) |
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ISBN: 0817643125 ISBN-13: 9780817643126 Publisher: Birkhauser OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: May 2003 Annotation: This self-contained work in mathematical analysis introduces the main ideas and fundamental methods of the subject, focusing on a simple and direct exposition of differential and integral calculus for functions of one variable with some of its applications. Key features: * Interesting and valuable historical account of ideas and methods in analysis with beautiful illustrations * Topics: functions of one variable, differential and integral calculus, asymptotic expansion and inequalities, basic ordinary differential equations (including 1-dimensional motions, central motions, Kepler's laws and free and forced vibrations), and a discussion of elementary minimum principles in physics and geometry (such as refraction laws, Steiner's problem, isoperimetric problems, Dijkstra's algorithm for minimal connections in graphs); the preliminaries treat the real numbers, trigonometric functions and some elementary Cartesian geometry * Rigorous exposition with full proofs motivated by numerous examples * Exercises, comprehensive bibliography and index This work is a first step toward developing connections between analysis and other mathematical disciplines (e.g., topology and geometry) as well as physics and engineering. An excellent resource for self-study or for classroom use at the advanced undergraduate or graduate level. |
| Additional Information |
| BISAC Categories: - Mathematics | Mathematical Analysis - Mathematics | Calculus - Mathematics | Differential Equations - General |
| Dewey: 515 |
| LCCN: 2003044367 |
| Physical Information: 0.85" H x 6.12" W x 9.62" (1.41 lbs) 353 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: For more than two thousand years some familiarity with mathematics has been regarded as an indispensable part of the intellectual equipment of every cultured person. Today the traditional place of mathematics in education is in grave danger. Unfortunately, professional representatives of mathematics share in the reponsibiIity. The teaching of mathematics has sometimes degen- erated into empty drill in problem solving, which may develop formal ability but does not lead to real understanding or to greater intellectual indepen- dence. Mathematical research has shown a tendency toward overspecialization and over-emphasis on abstraction. Applications and connections with other fields have been neglected . . . But . . . understanding of mathematics cannot be transmitted by painless entertainment any more than education in music can be brought by the most brilliant journalism to those who never have lis- tened intensively. Actual contact with the content of living mathematics is necessary. Nevertheless technicalities and detours should be avoided, and the presentation of mathematics should be just as free from emphasis on routine as from forbidding dogmatism which refuses to disclose motive or goal and which is an unfair obstacle to honest effort. (From the preface to the first edition of What is Mathematics? by Richard Courant and Herbert Robbins, 1941. |