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Practical analysis in one variable /

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Bibliographic Details
Main Author: Estep, Donald J., 1959-
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York : Springer, [2002]
Series:Undergraduate texts in mathematics.
Subjects:
Mathematical analysis.
Mathematics.
Religion.
MATHEMATICS > Calculus.
MATHEMATICS > Mathematical Analysis.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Cover
  • Preface
  • Table of Contents
  • Introduction
  • Part I-Numbers and Functions, Sequences and Limits
  • 1. Mathematical Modeling
  • 2. Natural NUmbers Just Arent Enough
  • 3. Infinity and Mathematical Induction
  • 4. Rational Numbers
  • 5. Functions
  • 6. Polynomials
  • 7. Functions, Functions and More Functions
  • 8. LIpschitz Continuity
  • 9. Sequences and Limits
  • 10. Solving the Muddy Yard Model
  • 11. Real Numbers
  • 12. Functions of Real Numbers
  • 13. The Bisection Algorithm
  • 14. Inverse Functions
  • 15. Fixed Points and Contraction Maps
  • Part II-Differential and Integral Calculus
  • 16. The Linearization of a Function at a Point
  • 17. Analyzing the Behaviour of a Population Model
  • 18. Interpretations of the Derivative
  • 19. Differentiability on Intervals
  • 20. Using Properties of the Derivative
  • 21. The Mean Value Theorum
  • 22. Derivative of Inverse Functions
  • 23. Modeling with Differential Equations
  • 24. Antidifferentiation
  • 25. Integration
  • 26. Properties of the Integral
  • 27. Applications of the Integral
  • 28. Rocket Propulsion and the Logarithm
  • 29. Constant Relative Rate of Change and the Exponential
  • 30. A Mass Spring System and the Trigonometric Functions
  • 31. Fixed Point Iteration and Newton's Method
  • Calculus Quagmires
  • Part III-You Want Anaylsis? We've Got Your Analysis Right Here
  • 32. Notions Of Continuity and Differentiability
  • 33. Sequences of Functions
  • 34. Relaxing Integration
  • 35. Delicate Limits and Gross Behaviour
  • 36. The Weierstrass Approximation Theorem
  • 37. The Taylor Polynomial
  • 38. Polynomial Interpolation
  • 39. Nonlinear Differential Equations
  • 40. The Picard Iteration
  • 41. The Forward Euler Method
  • A Conclusion or an Introduction?
  • References.