## Book description

Differential Equations presents the basics of differential equations, adhering to the UGC curriculum for undergraduate courses on differential equations offered by all Indian universities. With equal emphasis on theoretical and practical concepts, the book provides a balanced coverage of all topics essential to master the subject at the undergraduate level, making it an ideal classroom text. Written in lucid, easy-to-understand language, the topics discussed in this student-friendly book are amply supported by exhaustive number of problems as well as over 300 solved examples and 400 end-of-chapter exercises.

1. cover
2. Title Page
3. Contents
5. Preface
6. 1. Formation of a Differential Equation
1. 1.1 Introduction
2. 1.2 Differential equations
1. 1.2.1 Formation of a differential equation
2. 1.2.2 Solution of a differential equation
7. 2. Differential Equations of First Order and First Degree
1. 2.1 First order and first degree differential equations
1. 2.1.1 Variable separable equation
2. 2.1.2 Homogeneous equations
3. 2.1.3 Non-homogeneous equations
4. 2.1.4 Exact equations
5. 2.1.5 Inexact equation—Reducible to exact equation by integrating factors
6. 2.1.6 Linear equations
7. 2.1.7 Bernoulli's equation
2. 2.2 Applications of ordinary differential equations
1. Exercise 2.9
2. 2.2.1 Geometrical applications
8. 3. Linear Differential Equations with Constant Coefficients
1. 3.1 Introduction
2. 3.2 General solution of linear equation f(D)y = Q(x)
1. Exercise 3.4
2. 3.2.1 Short methods for finding the particular integrals in special cases
3. 3.2.2 Linear equations with variable coefficients—Euler–Cauchy equations (Equidimensional equations)
4. 3.2.3 Legendre's linear equation
5. 3.2.4 Method of variation of parameters
6. 3.2.5 Systems of simultaneous linear differential equations with constant coefficients
9. 4. Differential Equations of the First Order but not of the First Degree
1. 4.1 Equations solvable for p
2. 4.2 Equations solvable for y
3. 4.3 Equations solvable for x
10. 5. Linear Equation of the Second Order with Variable Coefficients
1. 5.1 To find the integral in C.F. by inspection, i.e. to find a solution of
2. 5.2 General solution of by changing the dependent variable and removing the first derivative (Reduction to normal form)
3. 5.3 General solution of by changing the independent variable
11. 6. Integration in Series: Legendre, Bessel and Chebyshev Functions
1. 6.1 Legendre functions
2. 6.2 Bessel functions
3. 6.3 Chebyshev polynomials
12. 7. Fourier Integral Transforms
1. 7.1 Introduction
2. 7.2 Integral transforms
3. 7.3 Fourier integral theorem
4. 7.4 Fourier integral in complex form
5. 7.5 Fourier transform of f(x)
6. 7.6 Finite Fourier sine transform and finite Fourier cosine transform (FFCT)
7. 7.7 Convolution theorem for Fourier transforms
8. 7.8 Properties of Fourier transform
1. 7.8.1 Linearity property
2. 7.8.2 Change of scale property or damping rule
3. 7.8.3 Shifting property
4. 7.8.4 Modulation theorem
9. 7.9 Parseval's identity for Fourier transforms
10. 7.10 Parseval's identities for Fourier sine and cosine transforms
13. 8. Partial Differential Equations
1. 8.1 Introduction
2. 8.2 Order, linearity and homogeneity of a partial differential equation
3. 8.3 Origin of partial differential equation
4. 8.4 Formation of partial differential equation by elimination of two arbitrary constants
5. 8.5 Formation of partial differential equations by elimination of arbitrary functions
6. 8.6 Classification of first-order partial differential equations
7. 8.7 Classification of solutions of first-order partial differential equation
8. 8.8 Equations solvable by direct integration
9. 8.9 Quasi-linear equations of first order
10. 8.10 Solution of linear, semi-linear and quasi-linear equations
1. 8.10.1 All the variables are separable
2. 8.10.2 Two variables are separable
3. 8.10.3 Method of multipliers
11. 8.11 Non-linear equations of first order
12. 8.12 Euler's method of separation of variables
13. 8.13 Classification of second-order partial differential equations 8-54
1. 8.13.1 Introduction
2. 8.13.2 Classification of equations
3. 8.13.3 Initial and boundary value problems and their solution
4. 8.13.4 Solution of one-dimensional heat equation (or diffusion equation)
5. 8.13.5 One-dimensional wave equation
6. 8.13.6 Vibrating string with zero initial velocity
7. 8.13.7 Vibrating string with given initial velocity and zero initial displacement
8. 8.13.8 Vibrating string with initial displacement and initial velocity
9. 8.13.9 Laplace's equation or potential equation or two-dimensional steady-state heat flow equation
14. Acknowledgements