Differential Equations: A Problem Solving Approach Based on MATLAB

✍ Scribed by P. Mohana Shankar

• Publisher: CRC Press
• Year: 2018
• Tongue: English
• Leaves: 459
• Edition: 1
• Category: Library

✦ Synopsis

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

Content: First Order Differential EquationsIntroductionD-field plots Methods of solving first order differential equationsAdditional examples on D-field plotsAutonomous Differential EquationsSummaryExercises ã Linear Second Order Differential Equations with constant CoefficientsIntroductionHomogeneous Differential EquationsNon-homogeneous Differential Equations: Particular Solutions and Complete SolutionsSummaryExercisesã Linear Higher Order Differential Equations with Constant CoefficientsIntroduction Homogeneous differential equations (n&lt
5)Non-homogeneous Differential equations and Particular solutions (n&lt
5) Additional methods of obtaining the solution and verificationHigher order differential equations (n&gt
4)Examples SummaryExercisesFirst order coupled differential equations with constant coefficientsIntroduction A pair of coupled differential equationsMultiple first order coupled differential equations of constant coefficientsNumerical Solutions Examples SummaryExercises

✦ Subjects

MATLAB.;Computational Numerical Analysis.;Mathematics & Statistics for Engineers.;Differential Equations.;MATHnetBASE.;SCI-TECHnetBASE.;STMnetBASE.;Differential equations -- Numerical solutions -- Data processing.;MATHEMATICS / Calculus;MATHEMATICS / Mathematical Analysis