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Ordinary Differential Equations: An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences by Morris Tenenbaum, Harry Pollard
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About this book :-
Ordinary Differential Equations: An Elementary Textbook for Sstudents of Mathematics, Engineering, and the Sciences written by
Morris Tenenbaum, Harry Pollard .
In this textbook, author has been aim to make it readable for the student, to include topocs of increasing importance (such as transforms, numerical analysis, the perturbation concept) and to avoid the errors traditionally transmitted in an elementry text. In this last connection, the authors have abandoned the use of the terminology "general solution" of a differential equation unless the solution is in fact general, i.e., unless the solution actually contains every solutiojn of the differential equation. Authors have exercised great care in defining function, differentials and solutions in particular we have tried to make it clear that functions have domains.
Book Detail :-
Title: Ordinary Differential Equations: An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences
Edition:
Author(s): Morris Tenenbaum, Harry Pollard
Publisher: Courier Dover Publications
Series:
Year: 1985
Pages: 819
Type: PDF
Language: English
ISBN: 0486649407,9780486649405
Country: US
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About Author :-
The author Morris Tanenbaum , born 1928, is an American physical chemist and executive who has worked at Bell Laboratories and AT&T Corporation.
Tanenbaum made significant contributions in the fields of transistor development and semiconductor manufacturing. Although it was not made public at the time, he developed the first silicon transistor, demonstrating it on January 26, 1954 at Bell Labs.[1][2] He also helped develop the first gas-diffused silicon transistor, which convinced Bell administrators to support the use of silicon over germanium in their transistor design. He later led a team that developed the first high-field superconducting magnets.
Later in his career he became an executive. He dealt with the separation of Bell Laboratories and AT&T, and became the first Chief Executive Officer and Chairman of the Board at AT&T Corporation as of January 1, 1984.
All Famous Books of this Author :-
Here is list all books, text books, editions, versions, solution manuals or solved notes avaliable of this author, We recomended you to download all.
• Download PDF The Theory of Algebraic Numbers by Harry Pollard
• Download PDF Ordinary Differential Equations: for Mathematics, Engineering, Sciences by Morris Tenenbaum, Harry Pollard
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Book Contents :-
Ordinary Differential Equations: An Elementary Textbook for Students of Mathematics, Engineering, and the Sciences written by
Morris Tenenbaum, Harry Pollard
cover the following topics.
Part-1 Basic Concepts
1. How Differential Equations Originate
2. The Meaning of the Terms Set and Function. Implicit Functions. Elementary Functions.
3. The Differential Equations
4. The General Solution of a Differentail Equation.
5. Direction Field.
Part-2. Special Types of Differential Equations of the First Order
6. Meaning of the Differential of a Function Separable Differential Equations.
7. First Order Differential Equation with Homogeneous Coefficients.
8. Differential Equations with Linear Coefficients.
9. Exact Differential Equations
10. Recognizable Exact Differential Equations Integrating Factors
11. The Linear Differential Equation of the First Order Bernoulli Equation.
12. Miscellaneous Methods of Solving a First Order Differential Equation.
Part-3. Problems Leading to Differential Equations of the First Order.
13. Geometric Problems
14. Trajectories
15. Dilution and Accretion Problems. Interest Problems. Termperature Problems. Decomposition and Growth Problems. Second Order Processes.
16. Motion of a Particle Along a Straight Line Vertical Horizontal Inclined.
17. Pursui9t Curves. Relative Pursuit Curves.
17M Miscellaneous Type of Problems Leading to Equations of the First Order
Part-4. Linear Differential Equations of Order Greater Than One.
18. Complex Numbers and Complex Functions.
19. Linear Independence of Functions. The Linear Differential Equation of Order n.
20. Solution of the Homogenous Linear Differential Equation of Order n with Constant Coefficients
21. Solution of the Nonhomogenous Linear Differential Equation of Order n with Constant Coefficient.
22. Solution of the Nonhomogenous Linear Differential Equation by the Method of Variation of Parameters.
23. Solution of the Linear Differential Equation with nonConstant Coefficients. Reduction of Order Method.
Part-5. Operators and Laplace Tranforms
24. Operators and Laplace Transforms
25. Inverse Operators
26. Solution of Linear Differential Equation by Mean of the Partial Fraction Expansion of Inverse Operatros
27. Laplace Tranforms. Gamma Function.
Part-6. Problems Leading to Linear Differential Equations of Order Two.
28. Undamped Motion
29. Damped Motion
30. Electric Circuits. Analog Computation
30M Miscellaneous Types of Problems Leading to Linear Equations of the Second Order.
Part 7. System of Differential Equations Linearization of First Order Systems
31. Solution of a System of Differential Equations
32. Linearization of First Order Systems
Part-8. Problems Giving Rise to System of Equatons Special Types of Second Order Linear and Non Linear Equations Solvable by Reducing to Systems
33. Mechanical, Biological, Electrical Problems Giving Rise to Systems of Equations.
34. Plane Motions Giving Rise to Sytems of Equations.
35. Special types of Second Order Linear and Nonlinear Differential Equations Solvable by Reduction to a System of Two First Order Equations.
36. Problems Giving Rise to Special type of Second Order Nonlinear Equations.
Part-9. Series Methods
37. Power Series Solutions of Linear Differential Equations.
38. Series Solution of Y=f(x,y)
39. Series Solution of a Nonlinear Differential Equation of Order Greater than One and Of a System of first Order Differential Equations.
40. Ordinary Points and Singularities of a Linear Differential Equation. Method of Frobenius.
41. The Legendre Differential Equation. Legendre Functions. Legendre Polynomials Pk(x). Properties of Legendre Polynomials Pk(x).
42. The Bessel Differential Equation. Bessel Function of the First Kind Jk(x). Differential Equations Leading to a Bessel Equation. Properties of Jk(x).
43. The Lagueree Differential Equation. Laguerre Polynomials Lk(x). Properties of Lk(x).
Part-10. Numerial Methods.
44. Starting Method. Polygonal Approximation.
45. An Improvement of the Polygonal Starting Method.
46. Starting Method-Taylor Series
47. Starting Method-Runge Kutta Formulas
48. Finite Differences. Interpolation.
49. Newton's Interpolation Formulas.
50. Approximation Formulas Including Simpson's and Weddle's Rule.
51. Milne's Method of Finding an Approximate Numerical Solution of Y=f(x,y)
52. General Comments. Selecting h. Reducing h. summary and an Example
53. Numerical Methods Applied to a System of Two First Order Equations.
54. Numerical Solution of a Second Order Differential Equations.
55. Peturbation Method. Fist Order Equation.
56. Peturbation Method. Second Order Equation.
Part-11 Existence and Uniqueness Theorems for The First Order Differential Equations y'=f(x,y) Picard's Method. Envelopes. Clairaut Equation.
57. Picard's Method of Successive Approximations.
58. An Existence and Uniqueness Theorem for the Fist Order Differential Equation y'=f(x,y) Satisfying y(x0)=y0.
59. The Ordinary and Singular Points of a First Order Differential Equation y'=f(x,y)
60. Enveloppes
61. The Clairaut Equation
Part-12 Existence and Uniqueness Theorems for a System of First Order Differential Equations and For Linear and Nonlinear Differential Equatons of Order Greater than one Wronskians.
62. An Existence and Uniqueness Theorem for a system of n First Order Differential Equations and for a Nonlienar Differential Equations of Order Greater Than One.
63. Determinants. Wronskians
64. Theorems About Wronskians and the Linear Independence of a Set of Solutions of a Homogeneous Linear Diffential Equation.
65. Existence and Uniqueness Theorem for the Linear Differential Equation of Order n.
Bibliography
Index
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