An Introduction to Ordinary Differential Equations [NOOK Book]

Overview



"Written in an admirably cleancut and economical style." ? Mathematical Review. A thorough, systematic first course in elementary differential equations for undergraduates in mathematics and science, requiring only basic calculus for a background, and including many exercises designed to develop students' technique in solving equations. With problems and answers. Index.
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An Introduction to Ordinary Differential Equations

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Overview



"Written in an admirably cleancut and economical style." — Mathematical Review. A thorough, systematic first course in elementary differential equations for undergraduates in mathematics and science, requiring only basic calculus for a background, and including many exercises designed to develop students' technique in solving equations. With problems and answers. Index.
Read More Show Less

Product Details

  • ISBN-13: 9780486131832
  • Publisher: Dover Publications
  • Publication date: 3/23/2012
  • Series: Dover Books on Mathematics
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 320
  • Sales rank: 421,697
  • File size: 26 MB
  • Note: This product may take a few minutes to download.

Table of Contents

Chapter 0. Preliminaries
1. Introduction
2 Complex numbers
3 Functions
4 Polynomials
5. Complex series and the exponential function
6. Determinants
7. Remarks on methods of discovery and proof
Chapter 1. Introduction--Linear Equations of the First Order
1. Introduction
2. Differential equations
3. Problems associated with differential equations
4. Linear equations of the first order
5. The equation y'+ay=0
6. The equation y'+ay=b(x)
7. The general linear equation of the first order
Chapter 2. Linear Equations with Constant Coefficients
1. Introduction
2. The second order homogeneous equation
3. Initial value problems for second order equations
4. Linear dependence and independence
5. A formula for the Wronskian
6. The non-homogeneous equation of order two
7. The homogeneous equation of order n
8. Initial value problems for n-th order equations
9. Equations with real constants
10. The non-homogeneous equation of order n
11. A special method for solving the non-homogeneous equation
12. Algebra of constant coefficient operators
Chapter 3. Linear Equations with Variable Coefficients
1. Introduction
2. Initial value problems for the homogeneous equation
3. Solutions of the homogeneous equation
4. The Wronskian and linear independence
5. Reduction of the order of a homogeneous equation
6. The non-homogeneous equation
7. Homogeneous equations with analytic coefficients
8. The Legendre equation
9. Justification of the power series method
Chapter 4. Linear Equations with Regular Singular Points
1. Introduction
2. The Euler equation
3. Second order equations with regular singular points--an example
4. Second order equations with regular singular points--the general case
5. A convergence proof
6. The exceptional cases
7. The Bessel equation
8. The Bessel equation (continued)
9. Regular singular points at infinity
Chapter 5. Existence and Uniqueness of Solutions to First Order Equations
1. Introduction
2. Equations with variables separated
3. Exact equations
4. The method of successive approximations
5. The Lipschitz condition
6. Convergence of the successive approximations
7. Non-local existence of solutions
8. Approximations to, and uniqueness of, solutions
9. Equations with complex-valued functions
Chapter 6. Existence and Uniqueness of Solutions to Systems and n-th Order Equations
1. Introduction
2. An example--central forces and planetary motion
3. Some special equations
4. Complex n-dimensional space
5. Systems as vector equations
6. Existence and uniqueness of solutions to systems
7. Existence and uniqueness for linear systems
8. Equations of order n
References; Answers to Exercises; Index
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Sort by: Showing 1 Customer Reviews
  • Anonymous

    Posted December 16, 2005

    a nice book at a great price

    i am tired of the game publishers play of releasing a new edition every year or so of basically the same book, and jacking up the price, while letting the old cheap ones go out of existence, while the professors cooperate by requiring the new one. mathematically and pedagogically there is often no difference, except the newer ones may be dumbed down more, which is arguably harmful. this is a fine little treatment of the elementary aspects of o.d.e. with clear full proofs and examples, in the same form it took early on in its life. we used this at harvard in an undergrad course in 1963. it only lacks the phase plane theory, for the qualitative analysis of equations that cannot be solved explicitly, and that I like to present. my solution may be to combine this clean treatment of the theory of easily solved equations, with another reasonable but high quality dover book, like hurewicz or waltman, for the qualitative theory.

    2 out of 2 people found this review helpful.

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