Differential equations : a problem solving approach based on MATLAB /
by P. Mohana Shankar.
- First edition.
- 1 online resource (458 pages) : 231 illustrations
First Order Differential Equations -- Introduction -- D-field plots -- Methods of solving first order differential equations -- Additional examples on D-field plots -- Autonomous Differential Equations -- Summary -- Exercises -- -- Linear Second Order Differential Equations with constant Coefficients -- Introduction -- Homogeneous Differential Equations -- Non-homogeneous Differential Equations: Particular Solutions and Complete Solutions -- Summary -- Exercises -- -- Linear Higher Order Differential Equations with Constant Coefficients -- Introduction -- 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) -- Examples -- Summary -- Exercises -- -- First order coupled differential equations with constant coefficients -- Introduction -- A pair of coupled differential equations -- Multiple first order coupled differential equations of constant coefficients -- Numerical Solutions -- Examples -- Summary -- Exercises.
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 MATLABŪ 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.
9781315144429
Computational Numerical Analysis. Differential Equations. Mathematics & Statistics for Engineers. MATHEMATICS / Calculus. MATHEMATICS / Mathematical Analysis. MATHEMATICS / Differential Equations. MATHEMATICS / Number Systems. Differential Equations And Matlab. Equilibrium And Differential Equations. Matlab Based Solutions For Differential Equations. Stability And Differential Equations. Symbolic Toolbox Based Solutions To Differential Equations. Differential equations--Numerical solutions--Data processing.