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About this book :-
Introduction to Partial Differential Equations with Applications written by
EC Zachmanoglou, Dale W Thoe.
In writing this introductory book on the old but still rapidly expanding field of Mathematics known as Partial Differential Equations. our objective has been to present an elementary treatment of the most important topics of the theory together with applications to problems from the physical sciences and engineering. The book should be accessible to students with a modest mathematical background and should be useful to those who will actually need to use partial differential equations in solving physical problems. At the same time we hope that the book will provide a good basis for those students who will pursue the study of more advanced topics including what is now known as the modern theory.
Throughout the book, the importance of the proper formulation of problems associated with partial differential equations is emphasized. Methods of solution of any particular problem for a given partial differential equation are discussed only after a large collection of elementary solutions of the equation has been constructed.
During the last five years, the book has been used in the form of lecture notes for a semester course at Purdue University. The students are advanced undergraduate or beginning graduate students in mathematics, engineering or one of the physical sciences. A course in Advanced Calculus or a strong course in Calculus with extensive treatment of functions of several variables, and a very elementary introduction to Ordinary Differential Equations constitute adequate preparation for the understanding of the book. In any case, the basic results of advanced calculus are recalled whenever needed.
The book begins with a short review of calculus and ordinary differential equations. A new elementary treatment of first order quasi-linear partial differential equations is then presented. The geometrical background necessary for the study of these equations is carefully developed. Several applications are discussed such as applications to problems in gas dynamics (the development of shocks), traffic flow, telephone networks, and biology (birth and death processes and control of disease).
The method of probability generating functions in the study of stochastic processes is discussed and illustrated by many examples. In recent books the topic of first order equations is either omitted or treated inadequately. In older books the treatment of this topic is probably inaccessible to most students.
A brief discussion of series solutions in connection with one of the basic results of the theory, known as the Cauchy-Kovalevsky theorem, is included. The characteristics, classification and canonical forms of linear partial differential equations are carefully discussed.
For students with little or no background in physics, Chapter VI, "Equations of Mathematical Physics," should be helpful. In Chapters VII, VIII and IX where the equations of Laplace, wave and heat are studied, the physical problems associated with these equations are always used to motivate and illustrate the theory. The question of determining the wellposed problems associated with each equation is fundamental throughout the discussion.
(EC Zachmanoglou, Dale W Thoe)
Book Detail :-
Title: Introduction to Partial Differential Equations with Applications
Edition:
Author(s): EC Zachmanoglou, Dale W Thoe
Publisher: Dover Publications
Series:
Year: 1987
Pages: 417
Type: PDF
Language: English
ISBN: 0486652513, 9780486652511
Country: US
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About Author :-
The author EC Zachmanoglou, Professor of Mathematics, Purdue University, West Lafayette, Indiana, United States.
The author Dale W Thoe, Professor of Mathematics, Purdue University, West Lafayette, Indiana, United States
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Book Contents :-
Introduction to Partial Differential Equations with Applications written by
EC Zachmanoglou, Dale W Thoe
cover the following topics.
'
1. SOMECONCEPTS FROM CALCULUS AND ORDINARY DIFFERENTIAL EQUATIONS
2. INTEGRAL CURVES AND SURFACES OF VECTOR FIELDS
3. THEORY AND APPLICATIONS OF QUASI-LINEAR AND LINEAR EQUATIONS OF FIRST ORDER
4. SERIES SOLUTIONS. THE CAUCHY-KO VALE VSKY THEOREM
5. LINEAR PARTIAL DIFFEREN TIAL EQUATIONS. CHARACTERISTICS, CLASSIFICATION AND CANONICAL FORMS
6. EQUATIONS OF MATHEMATICAL PHYSICS
7. LAPLACE'S EQUATION
8. THE WAVE EQUATION
9. THE HEAT EQUATION
10. SYSTEMS OF FIRST ORDER LINEAR AND QUASI-LINEAR EQUATIONS
GUIDETOFURTHERSTUDY
BIBLIOGRAPHY FOR FURTHER STUDY
ANSWERS TO SELECTED PROBLEMS
Index
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