You are here

An Invitation to Applied Mathematics

Carmen Chicone
Academic Press
Publication Date: 
Number of Pages: 
[Reviewed by
Dhruba Adhikari
, on

This is fantastic resource for anyone who is looking for a single volume that extensively covers differential equations arising from diverse phenomena in physics, biology, chemistry, and engineering. This book is suitable for an upper level undergraduate and beginning graduate course in applied mathematics.

The presentation is clear and motivational. There are numerous exercises at the end of every section. Two dedicated chapters include Problems and Projects that are open-ended and helpful for designing undergraduate research projects. The areas for the projects range from fundamental phenomena (e.g. reaction-diffusion-convection) to advanced ones, such as Maxwell’s laws and electromagnetic boundary value problems.

The beginning part of the book contains material accessible to a disciplinarily diverse group of learners. It focuses on the principle of conservation of mass with regard to phenomena that occur in biology, chemistry, physics and engineering. Models with both ordinary and partial differential equations are introduced and analyzed qualitatively and numerically. Reaction, diffusion, and convection processes; transport of electric signals on neurons; feedback control with regard to heat control of a chamber and one-dimensional heated chamber with PID control; and random walks and diffusion are some interesting topics included in this part. The second part covers equations of fluid motion; Eulerian flow; fluid motion on moving coordinates; water waves; computational fluid dynamics; channel flow that includes boundary layer theory, hydraulic jump, and surface waves; elasticity, weak formulation of one-dimensional boundary value problems, finite element method; and problems and projects from a variety of areas in physics, chemistry, biology and engineering. The last part covers classical electromagnetism with a focus on Maxwell’s laws and transmission lines. There is a chapter on problems and projects on waveguides and cavity resonators. An appendix contains extensive coverage of results from mathematical analysis and differential equations essential for the material in the book.

The book is suitable not only as a textbook, but also as an indispensable resource for anyone interested in applied mathematics where differential equations and related numerics make up the core.

Dhruba Adhikari is Associate Professor of Mathematics at Kennesaw State University, Georgia.

See the table of contents in the publisher’s webpage.