📘 Ordinary and Partial Differential Equations (20th Edition) By Dr. M.D. Raisinghania This well-acclaimed book, now in its twentieth edition, continues to provide an in-depth exploration of ordinary and partial differential equations, offering systematic solution techniques and step-by-step proofs to enhance problem-solving skills. Carefully selected solved examples illustrate key concepts, making it an invaluable resource. 📌 Designed for: ✔ Undergraduate & Postgraduate students of Mathematics & Physics ✔ Engineering students (all branches) & AMIE ✔ Aspirants of GATE, CSIR-UGC (NET), and other competitive exams ✨ Key Features: 📖 New Chapter: Miscellaneous Methods and Existence & Uniqueness Theorem for First-Order Initial Value Problems 🔍 In-depth Coverage: Picard's Theorem & Iterative Method of Successive Approximations 📊 Essential Concepts: Lipschitz Condition, Lipschitz Constant, Lipschitz Continuous Function, Gronwall Inequality 📝 Practice-Oriented: Extensive exercises, including university exam questions and competitive exam problems (GATE, CSIR-UGC NET, etc.) 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

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