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Science & Mathematics - Introduction to Partial Differential Equations with Applications (Dover Books on Mathematics)

Description

Book Synopsis: This book has been widely acclaimed for its clear, cogent presentation of the theory of partial differential equations, and the incisive application of its principal topics to commonly encountered problems in the physical sciences and engineering. It was developed and tested at Purdue University over a period of five years in classes for advanced undergraduate and beginning graduate students in mathematics, engineering, and the physical sciences.

The book begins with a short review of calculus and ordinary differential equations, then moves on to explore integral curves and surfaces of vector fields, quasi-linear and linear equations of first order, series solutions and the Cauchy Kovalevsky theorem. It then delves into linear partial differential equations, examines the Laplace, wave, and heat equations, and concludes with a brief treatment of hyperbolic systems of equations.

Among the most important features of the text are the challenging problems at the end of each section which require a wide variety of responses from students, from providing details of the derivation of an item presented to solving specific problems associated with partial differential equations. Requiring only a modest mathematical background, the text will be indispensable to those who need to use partial differential equations in solving physical problems. It will provide as well the mathematical fundamentals for those who intend to pursue the study of more advanced topics, including modern theory.

Details

Looking to understand and apply partial differential equations in real-world situations? Look no further than "Introduction to Partial Differential Equations with Applications". With its clear and concise presentation, this book has been widely acclaimed for its ability to explain complex concepts in a way that is accessible to advanced undergraduate and beginning graduate students in mathematics, engineering, and the physical sciences.

Developed and tested at Purdue University, this book is the result of five years of experience in the classroom. It begins with a brief review of calculus and ordinary differential equations, providing a solid foundation for the topics that follow. From there, it explores integral curves and surfaces of vector fields, quasi-linear and linear equations of the first order, and series solutions, just to name a few.

What sets this book apart are the challenging problems at the end of each section. These problems require students to think critically and apply their knowledge to specific situations. By working through these problems, students not only gain a deeper understanding of the material, but also develop problem-solving skills that are essential in the real world.

You don't need a strong mathematical background to benefit from this book. Whether you're an aspiring engineer or a student in the physical sciences, "Introduction to Partial Differential Equations with Applications" will equip you with the tools you need to tackle complex problems and find practical solutions.

Don't miss out on this invaluable resource. Take your understanding of partial differential equations to the next level. Get your copy now.

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