Introduction to Applied Partial Differential Equations
First Edition   ©2013

Introduction to Applied Partial Differential Equations

John M. Davis (Baylor University)

  • ISBN-10: 1-4292-7592-8; ISBN-13: 978-1-4292-7592-7; Format: Cloth Text, 313 pages

Focus on Deeper Concepts Not Mundane Computation
The text requires hand calculation selectively, and encourages the use of appropriate computing technology throughoutÑfor example, in computing the integrals arising in Fourier series coefficients or plotting 3D animations of solution surfaces. By utilizing technology appropriately, the focus can be placed on more complex, realistic problems.

Emphasis on Geometric Iinsight and Physical Interpretation
Davis' text gives the computational aspect of the course a vivid context by continually reflecting on what the combination of calculation, visualization, and physical interpretation reveals about a problem. This helps students gain some understanding of the qualitative properties of solutions and what they tell us about the real world physical system.
 
Embraces the Tools and Language of Vector Calculus
The book takes full advantage of the opportunity of using the partial differential equation course to solidify students' understanding of vector calculus. For example, deriving the multidimensional heat and wave equations from a variational viewpoint are occasions to invoke the Divergence Theorem and Stokes' Theorem.
 
Sets the Stage for Future Topics in Analysis
To make sure students are prepared for upper level mathematics courses, the text introduces a number of topics (tackle vector spaces, inner product spaces, eigenvalue problems, orthogonality, various modes of convergence, and basic L2 theory) at an appropriate level.