An Introduction To Differential Equations

This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more. Numerous figures, problems with solutions, notes. 1994 edition. Includes 268 figures and 23 tables.

For more than half a century, stochastic calculus and stochastic differential equations have played a major role in analyzing the dynamic phenomena in the biological and physical sciences, as well as engineering. the advancement of knowledge in stochastic differential equations is spreading rapidly across the graduate and postgraduate programs in universities around the globe. This will be the first available book that can be used in any undergraduate/graduate stochastic modeling/applied mathematics courses and that can be used by an interdisciplinary researcher with a minimal academic background.An Introduction to Differential Equations: Volume 2 is a stochastic version of Volume 1 ("An Introduction to Differential Equations: Deterministic Modeling, Methods and Analysis"). Both books have a similar design, but naturally, differ by calculi. Again, both volumes use an innovative style in the presentation of the topics, methods and concepts with adequate preparation in deterministic Calculus.

This brief modern introduction to the subject of ordinary differential equations emphasizes stability theory. Concisely and lucidly expressed, it is intended as a supplementary text for advanced undergraduates or beginning graduate students who have completed a first course in ordinary differential equations. The author begins by developing the notions of a fundamental system of solutions, the Wronskian, and the corresponding fundamental matrix. Subsequent chapters explore the linear equation with constant coefficients, stability theory for autonomous and nonautonomous systems, and the problems of the existence and uniqueness of solutions and related topics. Problems at the end of each chapter and two Appendixes on special topics enrich the text.

Skillfully organized introductory text examines origin of differential equations, then defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors; dilution and accretion problems; linearization of first order systems; Laplace Transforms; Newton's Interpolation Formulas, more.

This text introduces students to the theory and practice of differential equations, which are fundamental to the mathematical formulation of problems in physics, chemistry, biology, economics, and other sciences. The book is ideally suited for undergraduate or beginning graduate students in mathematics, and will also be useful for students in the physical sciences and engineering who have already taken a three-course calculus sequence.This second edition incorporates much new material, including sections on the Laplace transform and the matrix Laplace transform, a section devoted to Bessel's equation, and sections on applications of variational methods to geodesics and to rigid body motion. There is also a more complete treatment of the Runge-Kutta scheme, as well as numerous additions and improvements to the original text.

Excellent introductory text focuses on complex numbers, determinants, orthonormal bases, symmetric and hermitian matrices, first order non-linear equations, linear differential equations, Laplace transforms, Bessel functions, more. Includes 48 black-and-white illustrations. Exercises with solutions. Index.

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.