Murray R. Richard Bronson. Thomas Huckle. Leonard Susskind.
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Gilbert Strang. David Williams. Walter A. Sidney I. Vladimir I. Mark A. Bert Mendelson. Charles C. George Gamow. Frederick Mosteller. George Polya. Richard J. Ian Stewart. Morton D. Chapter 1 is a brief review of some ideas from multivariable calculus and first order ODEs. Section 2. This section does not have enough problems, but later sections are better in this respect.
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Chapter 3 continues to develop the first order linear theory. Sections 3.
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Section 3. The last two sections are on applications, including an example of a shock wave in a traffic flow problem. Chapter 4 is quite short and is on series solutions. Section 4. Together with the first several paragraphs of section 3. The authors might have said much more here — they merely call the result of the problem Lagrange series, with neither an article nor the possessive, and give a reference to a then-recent application to gas flow — and the temptation to do so would be hard for me to resist if I were lecturing on this subject.
Chapter 5 transitions to higher order equations. It discusses characteristics, gives a very brief treatment of the general initial value problem, and then brings in canonical forms for first and higher order equations, leading to the classification of second order equations as either elliptic, parabolic, or hyperbolic.
Chapter 6 is very short. It begins with a little vector analysis and ends with a brief discussion of what it means for a problem to be well posed: existence and uniqueness of solutions together with continuous dependence on the initial conditions.
Basic Linear Partial Differential Equations
Taylor, M. Partial Differential Equations, Vol.
Trott, M. Webster, A. Partial Differential Equations of Mathematical Physics, 2nd corr. Weisstein, E. Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, Weisstein, Eric W. Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more.