Introduction to Partial Differential Equations with Applications., E.C. Zachmanoglou, Dale W. Thoe
The book contains roughly twenty-five percent more material than canbe covered in a one-semester course. This provides flexibility for planningeither a more theoretical or a more applied course. For a more theoreticalcourse, some of the sections on applications should be omitted. For amore applied version of the course, the instructor should only outline theresults in the following sections: Chapter III, Section 4; Chapter IV,Sections 1 and 2; Chapter V Sections 5, 6, 7, 8, and 9 (the classificationand characteristics of second order equations should be carefully dis-cussed, however); Chapter VII, the proof of Theorem 10.1 and Section11.
Topics are discussed in this book as following :
CHAPTER I. SOME CONCEPTS FROM CALCULUS AND ORDINARY DIFFERENTIAL EQUATION
CHAPTER II. INTEGRAL CURVES AND SUR-FACES OF VECTOR FIELDS
CHAPTER III. THEORY AND APPLICATIONS OF QUASI-LINEAR AND LINEAR EQUATIONS OF FIRST ORDER
CHAPTER IV. SERIES SOLUTIONS. THECAUCHY-KO VALE VSKY THEOREM
CHAPTER V. LINEAR PARTIAL DIFFERENTIAL EQUATIONS. CHARACTERISTICS, CLASSIFICATIONAND CANONICAL FORMS
CHAPTER VI. EQUATIONS OF MATHEMAT-ICAL PHYSICS
CHAPTER VII. LAPLACE'S EQUATION
CHAPTER VIII. THE WAVE EQUATION
CHAPTER IX. THE HEAT EQUATION
CHAPTER X. SYSTEMS OF FIRST ORDER LINEAR AND QUASI-LINEAR EQUATIONS
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