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Differential equations. --- 517.91 Differential equations --- Differential equations
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Differential equations. --- 517.91 Differential equations --- Differential equations
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Finding and interpreting the solutions of differential equations is a central and essential part of applied mathematics. This book aims to enable the reader to develop the required skills needed for a thorough understanding of the subject. The authors focus on the business of constructing solutions analytically, and interpreting their meaning, using rigorous analysis where needed. MATLAB is used extensively to illustrate the material. There are many worked examples based on interesting and unusual real world problems. A large selection of exercises is provided, including several lengthier projects, some of which involve the use of MATLAB. The coverage is broad, ranging from basic second-order ODEs and PDEs, through to techniques for nonlinear differential equations, chaos, asymptotics and control theory. This broad coverage, the authors' clear presentation and the fact that the book has been thoroughly class-tested will increase its attraction to undergraduates at each stage of their studies.
Differential equations. --- 517.91 Differential equations --- Differential equations
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This is an introductory course to the theory of ordinary differential equations: techniques of number theory, basic results of existence theorems, singularities, and uniformity of the solutions of differential equations. This work describes number theory methods such as peano numbers and axioms. Exercises and problems are provided. This is a work for graduate students in the sciences or engineering school or for math teachers.
Differential equations. --- Differential equations --- 517.91 Differential equations --- Numerical solutions.
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This book provides a systematic treatment of the Volterra integral equation by means of a modern integration theory which extends considerably the field of differential equations. It contains many new concepts and results in the framework of a unifying theory. In particular, this new approach is suitable in situations where fast oscillations occur.
Differential equations. --- 517.91 Differential equations --- Differential equations --- Integral equations
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Differential equations. --- 517.91 Differential equations --- Differential equations
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Ordinary Differential Equations introduces key concepts and techniques in the field and shows how they are used in current mathematical research and modelling. It deals specifically with initial value problems, which play a fundamental role in a wide range of scientific disciplines, including mathematics, physics, computer science, statistics and biology. This practical book is ideal for students and beginning researchers working in any of these fields who need to understand the area of ordinary differential equations in a short time.
Differential equations. --- 517.91 Differential equations --- Differential equations
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Building on introductory calculus courses, this text provides a sound foundation in the underlying principles of ordinary differential equations. Important concepts, including uniqueness and existence theorems, are worked through in detail and the student is encouraged to develop much of the routine material themselves, thus helping to ensure a solid understanding of the fundamentals required.The wide use of exercises, problems and self-assessment questions helps to promote a deeper understanding of the material and it is developed in such a way that it lays the groundwork for further
Differential equations. --- 517.91 Differential equations --- Differential equations
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Written in a clear, logical and concise manner, this comprehensive resource allows students to quickly understand the key principles, techniques and applications of ordinary differential equations. Important topics including first and second order linear equations, initial value problems and qualitative theory are presented in separate chapters. The concepts of two point boundary value problems, physical models and first order partial differential equations are discussed in detail. The text uses tools of calculus and real analysis to get solutions in explicit form. While discussing first order linear systems, linear algebra techniques are used. The real-life applications are interspersed throughout the book to invoke reader's interest. The methods and tricks to solve numerous mathematical problems with sufficient derivations and explanation are provided. The proofs of theorems are explained for the benefit of the readers.
Differential equations. --- 517.91 Differential equations --- Differential equations
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Differential equations --- Numerical solutions. --- 517.91 Differential equations