# An Introduction to Ordinary Differential Equations

## Earl A. Coddington

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"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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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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## 1.An Introduction to Ordinary Differential Equations

Editore: Dover Publications (1989)
ISBN 10: 0486659429 ISBN 13: 9780486659428
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Descrizione libro Dover Publications, 1989. Condizione libro: New. *Price HAS BEEN temporarily REDUCED by 10% until Monday, March 27. Order now for BEST SAVINGS* 320 pp., Paperback, new. Codice libro della libreria ZB1059907

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## 2.An Introduction to Ordinary Differential Equations

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Descrizione libro Paperback. Condizione libro: New. Softcover Book, Condition: New. 1st Edition. [Please Read Carefully Before Buying], This Is An International Edition. Printed In Black and White. , Book Cover And ISBN No May Be Different From US Edition. Restricted Sales Disclaimer Wordings Not For Sales In USA And Canada May Be Printed On The Cover Of The Book. Standard Shipping 7-14 Business Days. Expedited Shiping 4-8 Business Days. ***WE DO NOT ENTERTAIN BULK ORDERS.*** The Books May Be Ship From Overseas For Inventory Purpose. Codice libro della libreria 321722

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## 3.An Introduction to Ordinary Differential Equations

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Descrizione libro Dover Pubns, 1989. PAP. Condizione libro: New. New Book. Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria V0-9780486659428

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## 5.An Introduction to Ordinary Differential Equations

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Descrizione libro Paperback. Condizione libro: New. New Softcover International Edition, Printed in Black and White, Different ISBN, Same Content As US edition, Book Cover may be Different, in English Language. Codice libro della libreria 13589

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## 6.An Introduction to Ordinary Differential Equations

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Descrizione libro Dover Publications Inc., 1990. PAP. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria IB-9780486659428

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## 7.An Introduction to Ordinary Differential Equations (Paperback)

Editore: Dover Publications Inc., United States (1990)
ISBN 10: 0486659429 ISBN 13: 9780486659428
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Descrizione libro Dover Publications Inc., United States, 1990. Paperback. Condizione libro: New. New edition. 213 x 135 mm. Language: English . Brand New Book. Written in an admirably cleancut and economical style. Mathematical Reviews. This concise text offers undergraduates in mathematics and science a thorough and systematic first course in elementary differential equations. Presuming a knowledge of basic calculus, the book first reviews the mathematical essentials required to master the materials to be presented. The next four chapters take up linear equations, those of the first order and those with constant coefficients, variable coefficients, and regular singular points. The last two chapters address the existence and uniqueness of solutions to both first order equations and to systems and n-th order equations. Throughout the book, the author carries the theory far enough to include the statements and proofs of the simpler existence and uniqueness theorems. Dr. Coddington, who has taught at MIT, Princeton, and UCLA, has included many exercises designed to develop the student s technique in solving equations. He has also included problems (with answers) selected to sharpen understanding of the mathematical structure of the subject, and to introduce a variety of relevant topics not covered in the text, e.g. stability, equations with periodic coefficients, and boundary value problems. Codice libro della libreria AAC9780486659428

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## 8.An Introduction to Ordinary Differential Equations (Paperback)

Editore: Dover Publications Inc., United States (1990)
ISBN 10: 0486659429 ISBN 13: 9780486659428
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Descrizione libro Dover Publications Inc., United States, 1990. Paperback. Condizione libro: New. New edition. 213 x 135 mm. Language: English . Brand New Book. Written in an admirably cleancut and economical style. Mathematical Reviews. This concise text offers undergraduates in mathematics and science a thorough and systematic first course in elementary differential equations. Presuming a knowledge of basic calculus, the book first reviews the mathematical essentials required to master the materials to be presented. The next four chapters take up linear equations, those of the first order and those with constant coefficients, variable coefficients, and regular singular points. The last two chapters address the existence and uniqueness of solutions to both first order equations and to systems and n-th order equations. Throughout the book, the author carries the theory far enough to include the statements and proofs of the simpler existence and uniqueness theorems. Dr. Coddington, who has taught at MIT, Princeton, and UCLA, has included many exercises designed to develop the student s technique in solving equations. He has also included problems (with answers) selected to sharpen understanding of the mathematical structure of the subject, and to introduce a variety of relevant topics not covered in the text, e.g. stability, equations with periodic coefficients, and boundary value problems. Codice libro della libreria AAC9780486659428

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## 9.An Introduction to Ordinary Differential Equations (Dover Books on Mathematics)

Editore: Dover Publications (1989)
ISBN 10: 0486659429 ISBN 13: 9780486659428
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Descrizione libro Dover Publications, 1989. Paperback. Condizione libro: New. Codice libro della libreria 0486659429

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## 10.An Introduction to Ordinary Differential Equations (Dover Books on Mathematics)

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Descrizione libro Dover Publications. PAPERBACK. Condizione libro: New. 0486659429 Brand New Book. Ships from the United States. 30 Day Satisfaction Guarantee!. Codice libro della libreria 4324430

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