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Practical Analysis in One Variable

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Cover of 'Practical Analysis in One Variable'

Table of Contents

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    Book Overview
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    Chapter 1 Introduction
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    Chapter 2 Mathematical Modeling
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    Chapter 3 Natural Numbers Just Aren’t Enough
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    Chapter 4 Infinity and Mathematical Induction
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    Chapter 5 Rational Numbers
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    Chapter 6 Functions
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    Chapter 7 Polynomials
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    Chapter 8 Functions, Functions, and More Functions
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    Chapter 9 Lipschitz Continuity
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    Chapter 10 Sequences and Limits
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    Chapter 11 Solving the Muddy Yard Model
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    Chapter 12 Real Numbers
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    Chapter 13 Functions of Real Numbers
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    Chapter 14 The Bisection Algorithm
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    Chapter 15 Inverse Functions
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    Chapter 16 Fixed Points and Contraction Maps
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    Chapter 17 The Linearization of a Function at a Point
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    Chapter 18 Analyzing the Behavior of a Population Model
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    Chapter 19 Interpretations of the Derivative
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    Chapter 20 Differentiability on Intervals
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    Chapter 21 Useful Properties of the Derivative
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    Chapter 22 The Mean Value Theorem
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    Chapter 23 Derivatives of Inverse Functions
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    Chapter 24 Modeling with Differential Equations
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    Chapter 25 Antidifferentiation
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    Chapter 26 Integration
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    Chapter 27 Properties of the Integral
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    Chapter 28 Applications of the Integral
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    Chapter 29 Rocket Propulsion and the Logarithm
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    Chapter 30 Constant Relative Rate of Change and the Exponential
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    Chapter 31 A Mass-Spring System and the Trigonometric Functions
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    Chapter 32 Fixed Point Iteration and Newton’s Method
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    Chapter 33 Calculus Quagmires
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    Chapter 34 Notions of Continuity and Differentiability
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    Chapter 35 Sequences of Functions
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    Chapter 36 Relaxing Integration
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    Chapter 37 Delicate Limits and Gross Behavior
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    Chapter 38 The Weierstrass Approximation Theorem
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    Chapter 39 The Taylor Polynomial
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    Chapter 40 Polynomial Interpolation
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    Chapter 41 Nonlinear Differential Equations
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    Chapter 42 The Picard Iteration
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    Chapter 43 The Forward Euler Method
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Title
Practical Analysis in One Variable
Published by
Springer-Verlag New York, January 2002
DOI 10.1007/b97698
ISBNs
978-0-387-95484-4, 978-0-387-22644-6, 978-1-4419-3021-7
Authors

Donald Estep, Estep, Donald J., Estep, Donald

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