04131nam a22002417a 4500 20220111093628.0 220110b ||||| |||| 00| 0 eng d 9789352836109 AL Eng 23 515.35 RAIO Raisinghania M D 12858 Ordinary and Partial Differential Equations Ed 20. New Delhi S Chand And Company Limited 2021 xxx,318 p. PB 24x16.5 cm. 4971 ₹559.20 ₹ ₹699.00 20% 06-01-2022 This well-acclaimed book, now in its twentieth edition, continues to offer an in-depth presentation of the fundamental concepts and their applications of ordinary and partial differential equations providing systematic solution techniques. The book provides step-by-step proofs of theorems to enhance students' problem-solving skill and includes plenty of carefully chosen solved examples to illustrate the concepts discussed. Designed as a textbook for undergraduate and postgraduate students of Mathematics and Physics as well as undergraduate students of all branches of Engineering and AMIE, this book would also be useful for the aspirants of GATE, CSIR-UGC (NET) and other competitive examinations. Key Features A new chapter on "Miscellaneous Methods and Existence and Uniqueness Theorem for Solutions of First Order Initial Value Problems Clear exposition of Picard's theorem and Picard's iterative method of successive approximations Detailed discussion on Lipschitz condition, Lipschitz constant, Lipschitz continuous function, Gronwall inequality and existence and uniqueness of solutions to first order initial value problems For practice a number of exercises including questions asked in different university examinations, GATE, CSIR-UGC (NET) and other competitive examinations Contents PART I: ELEMENTARY DIFFERENTIAL EQUATIONS 1. Differential Equations: Their Formation and Solutions 2. Equations of First Order and First Degree 3. Trajectories 4. Equations of the First Order but Not of the First Degree and Singular Solutions and Extraneous Loci 5. Linear Differential Equations with Constant 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 Equations of Second Order 11. Applications of Differential Equations 12. Miscellaneous Methods and Existence and Uniqueness Theorem for Solutions of First Order Initial Value Problems PART II: ADVANCED ORDINARY DIFFERENTIAL EQUATIONS, FOURIER SERIES AND SPECIAL FUNCTIONS 1. Picard's Iterative Method, Picard's Theorem and Existence and Uniqueness of Solutions to First Order Initial Value Problems 2. Simultaneous Equations of the Form (dx)/P =(dy)/Q =(dz)/R 3. Total (or Pfaffian) Differential Equations 4. Beta and Gamma Functions 5. Chebyshev Polynomials 6. Fourier Series 7. Power Series 8. Integration in Series 9. Legendre Polynomials 10. Legendre Functions of the Second Kind—Qn(x) 11. Bessel Functions 12. Orthogonal Sets 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 Variable Coefficients 8. Classification of P.D.E. Reduction to Canonical or Normal Forms Riemann Method 9. Monge's Methods 10. Transport Equation 11. Cauchy Initial Value Problem for Linear First Order Partial Differential Equations Miscellaneous problems based on Part III of the book Differential equations 12802 RAISINGHANIA (M D) 12803 ddc BK 221136 221136 0 0 ddc 0 0 MAT AL AL 2022-01-10 Biblios Book Point 559.00 5 515.35 RAIO 075307 2025-10-04 09:07:45 2025-06-24 699.00 2022-01-10 BK