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  • 1
    Online Resource
    Online Resource
    Mathematical Analysis : Functions of One Variable (2003)
    Boston, MA :Birkhäuser Boston :
    Details
    UID:
    almahu_9947362898602882
    Format: XIII, 353 p. , online resource.
    ISBN: 9781461200079
    Content: 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.
    Note: 1. Numbers, Functions and their Graphs -- 1.1 Real Numbers: a Description -- 1.2 The Cartesian Plane -- 1.3 Elementary Functions -- 1.4 Remarks on Common Language and the Language of Mathematics -- 1.5 Exercises -- 2. Limits and Continuity -- 2.1 Limits -- 2.2. Continuous Functions -- 2.3. Continuous functions on an interval -- 2.4 Weierstrass’s Theorem -- 2.5 Summing Up -- 2.6 Exercises -- 3. The Fundamental Ideas of the Differential and Integral Calculus -- 3.1 Differential Calculus -- 3.2 Integral Calculus -- 3.3 The Fundamental Theorem of Calculus -- 3.4 Calculus: Some Historical Remarks -- 3.5 Summing Up -- 3.6 Exercises -- 4. The Calculus of Derivatives and of Integrals -- 4.1 Computation of Derivatives -- 4.2 Integrals and Primitives -- 4.3 A Definition of the Trigonometric, Logarithmic and Exponential Functions -- 4.4 Some Differential Equations -- 4.5 Generalized Integrals -- 4.6 Summing Up -- 4.7 Exercises -- 5. Further Developments in Calculus -- 5.1 Taylor’s Formula -- 5.2 The Calculus of Limits -- 5.3 Convex Functions -- 5.4 Some Inequalities -- 5.5 Graphing a Function -- 5.6 Summing Up -- 5.7 Exercises -- 6. Toward Differential Equations and Minimum Principles -- 6.1 Linear Ordinary Differential Equations -- 6.2 First Order ODEs -- 6.3 One-Dimensional Motions -- 6.4 Optimization Problems -- 6.5 Summing Up -- 6.6 Exercises -- A. Matematicians and Other Scientists -- B. Bibliographical Notes -- C. Index.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9781461265702
    Language: English
    DOI: 10.1007/978-1-4612-0007-9
    URL: http://dx.doi.org/10.1007/978-1-4612-0007-9
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Open Access Request
    HU Berlin
  • 2
    Online Resource
    Online Resource
    Mathematical Analysis : Functions of One Variable (2003)
    Boston, MA : Birkhäuser Boston
    Details
    UID:
    b3kat_BV042419402
    Format: 1 Online-Ressource (XIII, 353 p)
    ISBN: 9781461200079 , 9781461265702
    Note: 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
    Language: English
    Keywords: Differentialrechnung ; Integralrechnung ; Differentialungleichung ; Funktion ; Mehrere Variable ; Funktionentheorie ; Mehrere Variable ; Funktion ; Mehrere Variable ; Analysis ; Einführung ; Lehrbuch
    DOI: 10.1007/978-1-4612-0007-9
    URL: Volltext
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Online Access
    Open Access Request
    BTU Cottbus
  • 3
    Online Resource
    Online Resource
    Mathematical Analysis : Functions of One Variable (2003)
    Boston, MA : Birkhäuser
    Details
    UID:
    gbv_165501191X
    Format: Online-Ressource (XIII, 353 p, online resource)
    ISBN: 9781461200079
    Series Statement: SpringerLink
    Content: This self-contained work introduces the main ideas and fundamental methods of analysis at the advanced undergraduate/graduate level. It provides the historical context out of which these concepts emerged, and aims to develop connections between analysis and other mathematical disciplines (e.g., topology and geometry) as well as physics and engineering. A rigorous exposition, numerous examples, beautiful illustrations, good problems, comprehensive bibliography, and index are some of the key features of the book. Excellent for self -study or the classroom
    Additional Edition: ISBN 9781461265702
    Additional Edition: Druckausg. ISBN 978-146-126-570-2
    Language: English
    DOI: 10.1007/978-1-4612-0007-9
    URL: Volltext  (lizenzpflichtig)
    URL: Cover
    Author information: Giaquinta, Mariano 1947-
    Library Location Call Number Volume/Issue/Year Availability
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    Online Resource
    Online Access
    Open Access Request
    UB Potsdam
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