# applied differential equations the primary course textbooks in mathematics

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## Applied Differential Equations

ISBN : 9781498728355
Genre : Mathematics
File Size : 51. 41 MB
Format : PDF, Mobi

A Contemporary Approach to Teaching Differential Equations Applied Differential Equations: An Introduction presents a contemporary treatment of ordinary differential equations (ODEs) and an introduction to partial differential equations (PDEs), including their applications in engineering and the sciences. Designed for a two-semester undergraduate course, the text offers a true alternative to books published for past generations of students. It enables students majoring in a range of fields to obtain a solid foundation in differential equations. The text covers traditional material, along with novel approaches to mathematical modeling that harness the capabilities of numerical algorithms and popular computer software packages. It contains practical techniques for solving the equations as well as corresponding codes for numerical solvers. Many examples and exercises help students master effective solution techniques, including reliable numerical approximations. This book describes differential equations in the context of applications and presents the main techniques needed for modeling and systems analysis. It teaches students how to formulate a mathematical model, solve differential equations analytically and numerically, analyze them qualitatively, and interpret the results.

## Applied Differential Equations With Boundary Value Problems

ISBN : 9781498733724
Genre : Mathematics
File Size : 29. 32 MB
Format : PDF, ePub

Applied Differential Equations with Boundary Value Problems presents a contemporary treatment of ordinary differential equations (ODEs) and an introduction to partial differential equations (PDEs), including their applications in engineering and the sciences. This new edition of the author’s popular textbook adds coverage of boundary value problems. The text covers traditional material, along with novel approaches to mathematical modeling that harness the capabilities of numerical algorithms and popular computer software packages. It contains practical techniques for solving the equations as well as corresponding codes for numerical solvers. Many examples and exercises help students master effective solution techniques, including reliable numerical approximations. This book describes differential equations in the context of applications and presents the main techniques needed for modeling and systems analysis. It teaches students how to formulate a mathematical model, solve differential equations analytically and numerically, analyze them qualitatively, and interpret the results.

## Mathematical Modeling

Author : Crista Arangala
ISBN : 9781498770736
Genre : Mathematics
File Size : 44. 24 MB
Format : PDF, Kindle

Mathematical Modeling: Branching Beyond Calculus reveals the versatility of mathematical modeling. The authors present the subject in an attractive manner and flexibley manner. Students will discover that the topic not only focuses on math, but biology, engineering, and both social and physical sciences. The book is written in a way to meet the needs of any modeling course. Each chapter includes examples, exercises, and projects offering opportunities for more in-depth investigations into the world of mathematical models. The authors encourage students to approach the models from various angles while creating a more complete understanding. The assortment of disciplines covered within the book and its flexible structure produce an intriguing and promising foundation for any mathematical modeling course or for self-study.

## Elementary Differential Equations

Author : Kenneth Kuttler
ISBN : 9781351727273
Genre : Mathematics
File Size : 90. 71 MB
Format : PDF, ePub, Mobi

Elementary Differential Equations presents the standard material in a first course on di?erential equations, including all standard methods which have been a part of the subject since the time of Newton and the Bernoulli brothers. The emphasis in this book is on theory and methods and di?erential equations as a part of analysis. Di?erential equations is worth studying, rather than merely some recipes to be used in physical science. The text gives substantial emphasis to methods which are generally presented ?rst with theoretical considerations following. Essentially all proofs of the theorems used are included, making the book more useful as a reference. The book mentions the main computer algebra systems, yet the emphasis is placed on MATLAB and numerical methods which include graphing the solutions and obtaining tables of values. Featured applications are easily understood. Complete explanations of the mathematics and emphasis on methods for ?nding solutions are included.

## A First Course In Ordinary Differential Equations

Author : Martin Hermann
ISBN : 9788132218357
Genre : Mathematics
File Size : 71. 64 MB
Format : PDF, ePub

This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists, chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a reference work and tool for independent study. The book has been prepared within the framework of a German–Iranian research project on mathematical methods for ODEs, which was started in early 2012.

## Modelling With Ordinary Differential Equations

Author : T.P. Dreyer
ISBN : 0849386365
Genre : Mathematics
File Size : 47. 99 MB
Format : PDF, ePub

Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study. This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores the elementary theory of systems of differential equations, Laplace transforms, and numerical solutions. Theorems on the existence and uniqueness of solutions are a central feature. Topics such as curve fitting, time-delay equations, and phase plane diagrams are introduced. The book includes algorithms for computer programs as an integral part of the answer-finding process. Professionals and students in the social and biological sciences, as well as those in physics and mathematics will find this text/reference indispensable for self-study.

## Advanced Mathematics For Engineers And Scientists

Author : Paul DuChateau
ISBN : 9780486141596
Genre : Mathematics
File Size : 47. 88 MB
Format : PDF, ePub, Mobi

This primary text and supplemental reference focuses on linear algebra, calculus, and ordinary differential equations. Additional topics include partial differential equations and approximation methods. Includes solved problems. 1992 edition.

## Beginning Partial Differential Equations

Author : Peter V. O'Neil
ISBN : 9781118629987
Genre : Mathematics
File Size : 38. 40 MB
Format : PDF, ePub

A broad introduction to PDEs with an emphasis on specialized topics and applications occurring in a variety of fields Featuring a thoroughly revised presentation of topics, Beginning Partial Differential Equations, Third Edition provides a challenging, yet accessible, combination of techniques, applications, and introductory theory on the subjectof partial differential equations. The new edition offers nonstandard coverageon material including Burger’s equation, the telegraph equation, damped wavemotion, and the use of characteristics to solve nonhomogeneous problems. The Third Edition is organized around four themes: methods of solution for initial-boundary value problems; applications of partial differential equations; existence and properties of solutions; and the use of software to experiment with graphics and carry out computations. With a primary focus on wave and diffusion processes, Beginning Partial Differential Equations, Third Edition also includes: Proofs of theorems incorporated within the topical presentation, such as the existence of a solution for the Dirichlet problem The incorporation of Maple™ to perform computations and experiments Unusual applications, such as Poe’s pendulum Advanced topical coverage of special functions, such as Bessel, Legendre polynomials, and spherical harmonics Fourier and Laplace transform techniques to solve important problems Beginning of Partial Differential Equations, Third Edition is an ideal textbook for upper-undergraduate and first-year graduate-level courses in analysis and applied mathematics, science, and engineering.

## Lectures On The Differential Equations Of Mathematical Physics

Author : Gerhard Freiling
ISBN : 160456928X
Genre : Science
File Size : 54. 91 MB
Format : PDF, ePub

The theory of partial differential equations of mathematical physics has been one of the most important fields of study in applied mathematics. This is essentially due to the frequent occurrence of partial differential equations in many branches of natural sciences and engineering. The present lecture notes have been written for the purpose of presenting an approach based mainly on the mathematical problems and their related solutions. The primary concern, therefore, is not with the general theory, but to provide students with the fundamental concepts, the underlying principles, and the techniques and methods of solution of partial differential equations of mathematical physics. One of the authors main goals is to present a fairly elementary and complete introduction to this subject which is suitable for the "first reading" and accessible for students of different specialities. The material in these lecture notes has been developed and extended from a set of lectures given at Saratov State University and reflects partially the research interests of the authors. It is intended for graduate and advanced undergraduate students in applied mathematics, computer sciences, physics, engineering, and other specialities. The prerequisites for its study are a standard basic course in mathematical analysis or advanced calculus, including elementary ordinary differential equations. Although various differential equations and problems considered in these lecture notes are physically motivated, a knowledge of the physics involved is not necessary for understanding the mathematical aspects of the solution of these problems.

## Differential Equations

Author : Clay C. Ross
ISBN : 9781475739497
Genre : Mathematics
File Size : 78. 70 MB
Format : PDF, Docs