Differential Equations & Laplace Transform – Krishna’s Educational Publishers

Differential Equations & Laplace Transform by Krishna’s Educational Publishers is a mathematics textbook for B.A. and B.Sc. First Year students of colleges affiliated with D.D.U. Gorakhpur University, Gorakhpur, Uttar Pradesh. This revised edition follows the 2019–20 syllabus mentioned on the book cover.

The book is authored by A. R. Vasistha, U.K. Gupta, Amit Kumar Rai and Sudhanshu Agarwal. It covers differential equations, methods of solving first-order and higher-order equations, orthogonal trajectories, simultaneous differential equations, Laplace transforms and their applications.

Key Features

• Designed for B.A. and B.Sc. First Year Mathematics students
• Covers Differential Equations and Laplace Transform in one book
• Includes illustrative examples and step-by-step mathematical methods
• Follows the D.D.U. Gorakhpur University syllabus stated in the book
• Useful for university-level mathematics study and examination preparation

Detailed Contents

Section A: Differential Equations

Chapter 0: Differential Equations of First Order and First Degree

• Definitions and fundamental concepts
• General and particular solutions
• Illustrative examples and methods of solving differential equations

Chapter 1: Differential Equations of the First Order but Not of the First Degree

• Equations of first order
• Equations solvable for p, y and x
• Clairaut’s form and related solution methods

Chapter 2: Orthogonal Trajectories

• Orthogonal trajectories and their applications
• Geometrical interpretation of differential equations

Chapter 3: Linear Differential Equations with Constant Coefficients

• Linear differential equations
• Complementary functions and particular integrals
• Methods of solving equations with constant coefficients

Chapter 4: Homogeneous Linear Differential Equations (Cauchy-Euler Equations)

• Homogeneous linear differential equations
• Cauchy-Euler equations and their solution methods

Chapter 5: Ordinary Simultaneous Differential Equations

• Linear simultaneous equations
• Methods of solving ordinary simultaneous differential equations

Chapter 6: Linear Equations of Second Order with Variable Coefficients

• Second-order linear differential equations
• Change of dependent and independent variables
• Variation of parameters

Chapter 7: Total Differential Equations

• Total differential equations
• Conditions and methods for solving these equations

Section B: Laplace Transform

Chapter 1: The Laplace Transform

• Existence theorem for Laplace transforms
• Properties of Laplace transforms
• Laplace transforms of derivatives and integrals
• Unit step and Dirac delta functions

Chapter 2: The Inverse Laplace Transform

• Properties of inverse Laplace transforms
• Inverse transforms of derivatives and integrals
• Methods of finding inverse transforms

Chapter 3: Applications of Laplace Transform

• Convolution theorem
• Solutions of ordinary differential equations using Laplace transforms
• Solutions of simultaneous differential equations
• Applications to differential and integral equations

Book Details

• Title: Differential Equations & Laplace Transform
• Publisher: Krishna’s Educational Publishers / Krishna Prakashan Media (P) Ltd.
• Language: English
• Subject: Mathematics
• Course: B.A. / B.Sc. First Year
• University: D.D.U. Gorakhpur University, Gorakhpur
• Edition Information: Revised edition as per the 2019–20 syllabus printed on the cover
• Authors: A. R. Vasistha, U.K. Gupta, Amit Kumar Rai and Sudhanshu Agarwal

This book brings together core differential equation techniques and Laplace transform methods in a single reference for undergraduate mathematics students. Students should verify the applicable syllabus and edition requirements with their university or college before purchasing.