Ordinary and Partial Differential Equations, 18E by M. D. Raisinghania
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About this book :-
Ordinary and Partial Differential Equations, 18E written by
M. D. Raisinghania .
This book has been designed for the use of honours and postgraduate students of various Indian universities. It will also be found useful by the students preparing for various competitive examinations. During my long teaching experience I have fully understood the need of the students and hence I have taken great care to present the subject matter in the most clear, interesting and complete form from the student’s point of view.
Do not start this book with an unreasonable fear. There are no mysteries in Mathematics. It is all simple and honest reasoning explained step by step which anybody can follow with a little effort and concentration. Often a student has difficulty in following a mathematical explanation only because the author skips steps which he assumes the students to be familiar with. If the student fails to recount the missing steps, he may be faced with a gap in the reasoning and the author’s conclusion may become mysterious to him.
This textbook is best for BA, B.Sc. and Honours (Mathematics and Physics), M.A., M.Sc. (Mathematics and Physics), B.E. Students of Various Universities and for I.A.S., P.C.S., A.M.I.E. GATE, C.S.I.R. U.G.C. NET and Various Competitive Examinations
(M. D. Raisinghania)
Book Detail :-
Title: Ordinary and Partial Differential Equations
Author(s): M. D. Raisinghania
Publisher: S. Chand & Co.
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About Author :-
The author Dr. M.D. Raisinghania , M.Sc., Ph.D. Formerly Reader and Head, Department of Mathematics Sanatan Dharm College, Muzaffarnagar, Western Uttar Pradesh, India.
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Book Contents :-
Ordinary and Partial Differential Equations, 18E written by
M. D. Raisinghania
cover the following topics.
PART-I ELEMENTARY DIFFERENTIAL EQUATIONS
1. Differential equations. Their formation and solutions
2. Equations of first order and first degree
4. Equations of the first order but not of the first degree singular solutions and extraneous loci
PART I: Different methods of finding general solutions
PART II: Singular solutions
PART III: Extraneous loci
5. Linear differential equations with constant coefficients
PART I: Usual methods of solving linear differential equations with constant coefficients
PART II: Method of undetermined coefficients
6. Homogeneous linear equations or Cauchy-Euler equations
7. Method of variation of parameters
8. Ordinary simultaneous differential equations
9. Exact differential equations and equations of special forms
10. Linear differential equations of second order
11. Applications of differential equations
PART I : Applications of first order differential equations
PART II: Applications of second order linear differential equations
PART III: Applications to simultaneous differential equations
ADVANCED ORDINARY DIFFERNTIAL EQUATIONS AND SPECIAL FUNCTIONS CHAPTERS PAGES
1. Picard’s iterative method. Uniqueness and existence theorem
2. Simultaneous differential equations of the form (dx)/P = (dy)/Q = (dz)/R
3. Total (or Pfaffian) differential equations
4. Riccati’s equation
5. Chebyshev polynomials
6. Beta and Gamma functions
7. Power series
8. Integration in series
9. Legendre polynomials
PART I: Legendre function of the first kind
PART II: Associated Legendre functions of the first kind 9.43–9.50
10. Legendre functions of the second kind
11. Bessel functions
12 Hermite polynomials
13. Laguerre polynomial
14. Hypergeometric function
15. Orthogonal set of functions and Strum-Liouville problem
PART-III PARTIAL DIFFERENTIAL EQUATIONS
1. Origin of partial differential equations
2. Linear partial differential equations of order one
3. Non-linear partial differential equations of order one
4. Homogeneous linear partial differential equations with constant coefficients
5. Non-homogeneous linear partial differential equations with constant coefficients
6. Partial differential equations reducible to equations with constant coefficients
7. Partial differential equations of order two with variables coefficients
8. Classifiation of partial differential equations Reduction to cononial or normal form. Riemann method
9. Monge’s method
10. Transport equation
Miscellaneous problems based on this part of the book
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