Elsevier S & T

Introductory Analysis: A Deeper View of Calculus

Bagby, Richard J.

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Table of contents
  • Copyright Pageiv
  • Contentsv
  • Acknowledgmentsix
  • Prefacexi
  • Chapter I. The Real Number System1
  • 1. Familiar Number Systems1
  • 2. Intervals6
  • 3. Suprema and Infima11
  • 4. Exact Arithmetic in R17
  • 5. Topics for Further Study22
  • Chapter II. Continuous Functions23
  • 1. Functions in Mathematics23
  • 2. Continuity of Numerical Functions28
  • 3. The Intermediate Value Theorem33
  • 4. More Ways to Form Continuous Functions36
  • 5. Extreme Values40
  • Chapter III. Limits45
  • 1. Sequences and Limits46
  • 2. Limits and Removing Discontinuities49
  • 3. Limits Involving infinity53
  • Chapter IV. The Derivative57
  • 1. Differentiability57
  • 2. Combining Differentiable Functions62
  • 3. Mean Values66
  • 4. Second Derivatives and Approximations72
  • 5. Higher Derivatives75
  • 6. Inverse Functions79
  • 7. Implicit Functions and Implicit Differentiation84
  • Chapter V. The Riemann Integral92
  • 1. Areas and Riemann Sums93
  • 2. Simplifying the Conditions for Integrability98
  • 3. Recognizing Integrability102
  • 4. Functions Defined by Integrals107
  • 5. The Fundamental Theorem of Calculus112
  • 6. Topics for Further Study115
  • Chapter VI. Exponential and Logarithmic Functions116
  • 1. Exponents and Logarithms116
  • 2. Algebraic Laws as Definitions119
  • 3. The Natural Logarithm124
  • 4. The Natural Exponential Function127
  • 5. An Important Limit129
  • Chapter VII. Curves and Arc Length132
  • 1. The Concept of Arc Length132
  • 2. Arc Length and Integration139
  • 3. Arc Length as a Parameter143
  • 4. The Arctangent and Arcsine Functions147
  • 5. The Fundamental Trigonometric Limit150
  • Chapter VIII. Sequences and Series of Functions153
  • 1. Functions Defined by Limits153
  • 2. Continuity and Uniform Convergence160
  • 3. Integrals and Derivatives164
  • 4. Taylor's Theorem168
  • 5. Power Series172
  • 6. Topics for Further Study177
  • Chapter IX. Additional Computational Methods179
  • 1. L’Hôpital’s Rule179
  • 2. Newton’s Method184
  • 3. Simpson’s Rule187
  • 4. The Substitution Rule for Integrals191
  • References197
  • Index198
Book details
  • Vendor Elsevier S & T
  • SKU 9780120725502
  • ISBN-13 9780080549422
  • Author Bagby, Richard J.
  • Category Mathematics
  • Subject Calculus

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Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.

* Written in an engaging, conversational tone and readable style while softening the rigor and theory
* Takes a realistic approach to the necessary and accessible level of abstraction for the secondary education students
* A thorough concentration of basic topics of calculus
* Features a student-friendly introduction to delta-epsilon arguments
* Includes a limited use of abstract generalizations for easy use
* Covers natural logarithms and exponential functions
* Provides the computational techniques often encountered in basic calculus