# Ordinary Differential Equations: An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences

Courier Dover Publications, 1963 - Mathematics - 808 pages

This unusually well-written, skillfully organized introductory text provides an exhaustive survey of ordinary differential equations — equations which express the relationship between variables and their derivatives. In a disarmingly simple, step-by-step style that never sacrifices mathematical rigor, the authors — Morris Tenenbaum of Cornell University, and Harry Pollard of Purdue University — introduce and explain complex, critically-important concepts to undergraduate students of mathematics, engineering and the sciences.
The book begins with a section that examines the origin of differential equations, defines basic terms and outlines the general solution of a differential equation-the solution that actually contains every solution of such an equation. Subsequent sections deal with such subjects as: integrating factors; dilution and accretion problems; the algebra of complex numbers; the linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas; and Picard's Method of Successive Approximations.
The book contains two exceptional chapters: one on series methods of solving differential equations, the second on numerical methods of solving differential equations. The first includes a discussion of the Legendre Differential Equation, Legendre Functions, Legendre Polynomials, the Bessel Differential Equation, and the Laguerre Differential Equation. Throughout the book, every term is clearly defined and every theorem lucidly and thoroughly analyzed, and there is an admirable balance between the theory of differential equations and their application. An abundance of solved problems and practice exercises enhances the value of Ordinary Differential Equations as a classroom text for undergraduate students and teaching professionals. The book concludes with an in-depth examination of existence and uniqueness theorems about a variety of differential equations, as well as an introduction to the theory of determinants and theorems about Wronskians.

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#### LibraryThing Review

User Review - LibraryThing

There are a lot of examples, a lot of explanation, and many good recources presented in this book. It is kinda thick, and I think it is meant to be a suppliment to a class and textbook. I would say it is a good book for those in engineering, sciences, or mathematics.

User Review - Flag as inappropriate

An excellent source of solution methods for well-defined classes of ordinary differential equations. The first few chapters are a very well written introduction to the topic as well, showcasing common pitfalls in interpreting solutions of differential equations and the behavior of direction fields.

### Contents

 I xv II xvii III 1 IV 5 VI 6 VII 11 VIII 14 IX 24
 XC 323 XCI 338 XCII 347 XCIV 359 XCV 369 XCVII 375 XCVIII 380 XCIX 381

 X 28 XI 31 XII 33 XIII 38 XIV 41 XV 46 XVI 47 XVII 50 XVIII 51 XIX 57 XX 58 XXI 62 XXII 63 XXIII 66 XXIV 67 XXV 70 XXVI 72 XXVII 73 XXVIII 80 XXIX 82 XXX 84 XXXI 91 XXXII 92 XXXIII 94 XXXIV 95 XXXV 99 XXXVI 101 XXXVII 107 XXXVIII 115 XXXIX 117 XL 122 XLI 131 XLII 134 XLIII 138 XLIV 139 XLV 160 XLVI 164 XLVII 168 XLVIII 177 XLIX 183 L 184 LI 185 LII 186 LIII 188 LIV 189 LV 191 LVI 193 LVII 196 LVIII 197 LIX 200 LX 201 LXI 205 LXII 207 LXIII 211 LXIV 213 LXV 214 LXVI 217 LXVII 221 LXIX 230 LXX 241 LXXI 242 LXXII 250 LXXIII 251 LXXIV 255 LXXV 260 LXXVI 262 LXXVII 268 LXXVIII 269 LXXIX 272 LXXX 283 LXXXI 288 LXXXII 290 LXXXIII 292 LXXXIV 295 LXXXV 296 LXXXVI 302 LXXXVII 306 LXXXVIII 313 LXXXIX 317
 C 383 CII 393 CIII 394 CIV 396 CV 398 CVI 405 CVII 413 CVIII 415 CIX 418 CX 424 CXI 440 CXII 451 CXIII 459 CXV 463 CXVI 470 CXVII 473 CXVIII 476 CXIX 491 CXX 500 CXXII 502 CXXIII 503 CXXIV 506 CXXV 521 CXXVI 523 CXXVII 528 CXXVIII 531 CXXIX 537 CXXX 548 CXXXI 555 CXXXII 559 CXXXIII 562 CXXXIV 570 CXXXV 572 CXXXVI 591 CXXXVII 593 CXXXVIII 598 CXXXIX 609 CXL 611 CXLI 615 CXLII 619 CXLIII 624 CXLIV 625 CXLV 627 CXLVI 629 CXLVII 631 CXLVIII 632 CXLIX 641 CL 646 CLII 653 CLIII 659 CLV 663 CLVI 670 CLVII 684 CLVIII 690 CLIX 691 CLX 692 CLXI 694 CLXII 702 CLXIII 707 CLXIV 713 CLXV 715 CLXVI 719 CLXVII 720 CLXVIII 728 CLXX 733 CLXXI 744 CLXXII 748 CLXXIII 754 CLXXIV 757 CLXXV 763 CLXXVI 765 CLXXVII 768 CLXXVIII 770 CLXXIX 774 CLXXX 778 CLXXXI 783 CLXXXII 791 CLXXXIII 793 Copyright

### References from web pages

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