The book has been thoroughly revised according to the New Syllabaii of Gautam Buddha Technical University, Lucknow. Question papers of 2010, 2011 and 2012 have been solved & included at the end of textbook. The misprints which came to my knowledge, have been removed. The previous edition book had the text material for both First & Second Semesters. Now to make the book handy, we have bifurcated the book in two parts, Volume I and Volume II. Volume II of the book is for Second Semester Students.

The main features of the book are as follows:

1. Objective Type Questions.

2. Multiple Choice Questions.

3. Fill in the Blanks

4. True/Flase.

5. Matching Type (Total number of objective type questions are more than 600).

6. Additional Important Examples Question Papers of 2012 and 2013 have been solved and included in text. A number of new example are solved and included in the body of the text.

**Unit - I : Differential Equations **

Linear differential equations of nth order with constant coefficients, Complementary functions and particular integrals, Simultaneous linear differential equations, Solution of second order differential equation by changing dependent and independent variables, Method of variation of parameters, Applications to engineering problems (without derivation).

**Unit - II : Series Solution and Special Functions**

Series solution of ordinary differential equation of 2 nd order with variable coefficients (Frobenius Method), Bessel and Legendre equations and their series solutions, Properties of Bessel functions and Legendre polynomials.

**Unit - III : Laplace Transform**

Laplace transform, Existence theorem, Laplace transform of derivatives and integrals, Inverse Laplace transform, Unit step function, Dirac delta function, Laplace transform of periodic functions, Convolution theorem, Application to solve simple linear and simultaneous differential equations.

**Unit - IV : Fourier Series and Partial Differential Equations**

Periodic functions, Trigonometric series, Fourier series of period 2, Eulers formulae, Functions having arbitrary period, Change of interval, Even and odd functions, Half range sine and cosine series, Harmonic analysis. Solution of first order Lagrange’s linear partial differential equations, Linear partial differential equations with constant coefficients of 2nd o.

**Unit - V : Applications of Partial Differential Equations**

Method of separation of variables for solving partial differential equations, Wave equation up to two-dimensions, Laplace equation in two-dimensions, Heat conduction equations up to two-dimensions, Equations of transmission lines.