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Mathematical Analysis I

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68,99 € UVP 82,49 €

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Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

11.03.2016

Abbildungen

XX, 66 illus. in color., farbige Illustrationen

Verlag

Springer Berlin

Seitenzahl

616

Maße (L/B/H)

24,1/16/4 cm

Gewicht

10697 g

Auflage

2nd edition 2015

Originaltitel

Математический анализ (Matematicheskij Analiz). Part I. 6th edition, Moscow, Publisher MCCME 2012.

Übersetzt von

Roger Cooke + weitere

Sprache

Englisch

ISBN

978-3-662-48790-7

Beschreibung

Rezension

“This is a thorough and easy-to-follow text for a beginning course in real analysis … . In coverage the book is slanted towards physics (mostly mechanics), and in particular there is a lot about line and surface integrals. … Will be popular with students because of the detailed explanations and the worked examples.” (Allen Stenger, MAA Reviews, maa.org, May, 2016)

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

11.03.2016

Abbildungen

XX, 66 illus. in color., farbige Illustrationen

Verlag

Springer Berlin

Seitenzahl

616

Maße (L/B/H)

24,1/16/4 cm

Gewicht

10697 g

Auflage

2nd edition 2015

Originaltitel

Математический анализ (Matematicheskij Analiz). Part I. 6th edition, Moscow, Publisher MCCME 2012.

Übersetzt von

  • Roger Cooke
  • Octavio Paniagua Taboada

Sprache

Englisch

ISBN

978-3-662-48790-7

Herstelleradresse

Springer-Verlag KG
Sachsenplatz 4-6
1201 Wien
AT

Email: GPSR Kontakt

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  • Produktbild: Mathematical Analysis I
  • Produktbild: Mathematical Analysis I

  • 1 Some General Mathematical Concepts and Notation: 1.1 Logical Symbolism.- 1.2 Sets and Elementary Operations on them.- 1.3 Functions.- 1.4 Supplementary Material.- 2 The Real Numbers: 2.1 Axioms and Properties of Real Numbers.- 2.2 Classes of Real Numbers and Computations.- 2.3 Basic Lemmas on Completeness.- 2.4 Countable and Uncountable Sets.- 3 Limits: 3.1 The Limit of a Sequence.- 3.2 The Limit of a Function.- 4 Continuous Functions: 4.1 Basic Definitions and Examples.- 4.2 Properties of Continuous Functions.- 5 Differential Calculus: 5.1 Differentiable Functions.- 5.2 The Basic Rules of Differentiation.- 5.3 The Basic Theorems of Differential Calculus.- 5.4 Differential Calculus Used to Study Functions.- 5.5 Complex Numbers and Elementary Functions.- 5.6 Examples of Differential Calculus in Natural Science.- 5.7 Primitives.- 6 Integration: 6.1 Definition of the Integral.- 6.2 Linearity, Additivity and Monotonicity of the Integral.- 6.3 The Integral and the Derivative.- 6.4 Some Applications of Integration.- 6.5 Improper Integrals.- 7 Functions of Several Variables: 7.1 The Space Rm and its Subsets.- 7.2 Limits and Continuity of Functions of Several Variables.- 8 Differential Calculus in Several Variables: 8.1 The Linear Structure on Rm.- 8.2 The Differential of a Function of Several Variables.- 8.3 The Basic Laws of Differentiation.- 8.4 Real-valued Functions of Several Variables.- 8.5 The

    Implicit Function Theorem.- 8.6 Some Corollaries of the Implicit Function Theorem.- 8.7 Surfaces in Rn and Constrained Extrema.- Some Problems from the Midterm Examinations: 1. Introduction to Analysis (Numbers, Functions, Limits).- 2. One-variable Differential Calculus.- 3. Integration. Introduction to Several Variables.- 4. Differential Calculus of Several Variables.- Examination Topics: 1. First Semester: 1.1. Introduction and One-variable Differential Calculus.- 2. Second Semester: 2.1. Integration. Multivariable Differential Calculus.- Appendices: A Mathematical Analysis (Introductory Lecture).- B Numerical Methods for Solving Equations (An Introduction).- C The Legendre Transform (First Discussion).- D The Euler–Maclaurin Formula.- E Riemann–Stieltjes Integral, Delta Function, and Generalized Functions.- F The Implicit Function Theorem (An Alternative Presentation).- References.- Subject Index.- Name Index.