A large number of physical phenomena are modeled by nonlinear partial differential equations, subject to appropriate initial/ boundary conditions; these equations, in general, do not admit exact solution. The present monograph gives constructive mathematical techniques which bring out large time behavior of solutions of these model equations. These approaches, in conjunction with modern computational methods, help solve physical problems in a satisfactory manner. The asymptotic methods dealt with here include self-similarity, balancing argument, and matched asymptotic expansions.
Well written and accessible to undergraduates or anybody who would like to obtain a quick but well-rounded introduction to fractal analysis. It is highly recommended and will certainly find a well-deserving place on many bookshelves. -- Peter R. Massopust Mathematical Reviews The subject matter of this book is important to all mathematical scientists... Is this a good book for your library? It's better than that. Put this slim volume in your backpack next time you hiking by the sea. -- Michael F. Barnsley SIAM Review
The Theory of Differential Equations: Classical and Qualitative
For over 300 years, differential equations have served as an essential tool for describing and analyzing problems in many scientific disciplines. This carefully-written textbook provides an introduction to many of the important topics associated with ordinary differential equations.
Learn the basics of algebra from former USA Mathematical Olympiad winner and Art of Problem Solving founder Richard Rusczyk. Topics covered in the book include linear equations, ratios, quadratic equations, special factorizations, complex numbers, graphing linear and quadratic equations, linear and quadratic inequalities, functions, polynomials, exponents and logarithms, absolute value, sequences and series, and much more! The text is structured to inspire the reader to explore and develop new ideas.
Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems
The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions.
