The book takes a problem solving approach in presenting the topic of differential equations. It provides a complete narrative of differential equations showing the theoretical aspects of the problem (the how's and why's), various steps in arriving at solutions, multiple ways of obtaining solutions and comparison of solutions. A large number of comprehensive examples are provided to show depth and breadth and these are presented in a manner very similar to the instructor's class room work. The examples contain solutions from Laplace transform based approaches alongside the solutions based on eigenvalues and eigenvectors and characteristic equations. The verification of the results in examples is additionally provided using Runge-Kutta offering a holistic means to interpret and understand the solutions. Wherever necessary, phase plots are provided to support the analytical results. All the examples are worked out using MATLAB® taking advantage of the Symbolic Toolbox and LaTex for displaying equations. With the subject matter being presented through these descriptive examples, students will find it easy to grasp the concepts. A large number of exercises have been provided in each chapter to allow instructors and students to explore various aspects of differential equations.
Table of Contents
First Order Differential Equations
Methods of solving first order differential equations
Additional examples on D-field plots
Autonomous Differential Equations
Linear Second Order Differential Equations with constant Coefficients
Homogeneous Differential Equations
Non-homogeneous Differential Equations: Particular Solutions and Complete Solutions
Linear Higher Order Differential Equations with Constant Coefficients
Homogeneous differential equations (n<5)
Non-homogeneous Differential equations and Particular solutions (n<5)
Additional methods of obtaining the solution and verification
Higher order differential equations (n>4)
First order coupled differential equations with constant coefficients
A pair of coupled differential equations
Multiple first order coupled differential equations of constant coefficients
Professor P. Mohana Shankar received his B.Sc. (Physics) and M.Sc. (Physics) from Kerala University and M. Tech. (Applied Optics) and Ph. D. (Electrical Engineering) from the Indian Institute of Technology, Delhi, India. He was the William Girling Watson visiting scholar at the School of Electrical Engineering, University of Sydney, Australia from 1981-1982. He has been at Drexel University since November 1982. He started as a postdoctoral fellow in Biomedical Engineering and since 2001, he is the Allen Rothwarf Professor in the department of Electrical and Computer Engineering. He has more than 100 archival journal publications covering the fields of nonlinear acoustics, ultrasonic contrast agents, ultrasonic non-destructive testing, ultrasonic tissue characterization, statistical signal processing, medical statistics, fiberoptic communications, fiberoptic biosensors, wireless communications, modeling of fading and shadowing wireless channels, etc. His publications also include work in pedagogy of differential equations, linear algebra, wireless communications, and engineering probability, all with emphasis on the use of Matlab (www.mathworks.com). He is the author of three books in wireless communications.
"It introduces the basic theoretical notions and methods concerning the aforementioned topics and provides the MATLAB tools and codes for solving the basic classes of ordinary differential equations(ODEs) and systems of ODEs: rst order differential equations (DEs), second order linear DEs with constant coe□cients, higher-order linear DEs with constant coeffi□cients, systems of first order DEs with constant coe□cients. There are considered especially the issues of graphical representation for time evolution, state space, qualitative analysis of the equilibrium points, vector eld representation."
-- Daniela Danciu (Craiova). Zentralblatt MATH 1406