UNIT I SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS

1.1 Introduction - Bisection method

1.2 Method of false position

1.3 Iteration method, Iterative methods of Gauss Jacobi and Gauss Seidel

1.4 Newton - Raphson method (One variable and simultaneous Equations)

UNIT II INTERPOLATION

2.1 Introduction, Errors in polynomial interpolation

2.2 Finite differences

2.3 Forward differences-Backward differences-Central differences

2.4 Symbolic relations and separation of symbols, Differences of a polynomial

2.5 Newton’s formulae for interpolation

2.6 Interpolation with unequal intervals - Lagrange’s interpolation formula.

UNIT III NUMERICAL INTEGRATION AND SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS

3.1 Trapezoidal rule and Simpson’s 1/3rd and 3/8th rule

3.2 Solution of ordinary differential equations by Taylor’s series

3.3 Picard’s method of successive approximations

3.4 Euler’s method

3.5 Runge - Kutta method (second and fourth order).

UNIT IV FOURIER SERIES

4.1 Introduction: Periodic functions, Fourier series of periodic function

4.2 Dirichlet’s conditions

4.3 Even and odd functions - Change of interval

4.4 Half-range sine and cosine series

UNIT V APPLICATIONS OF PDE

5.1 Method of separation of Variables

5.2 Solution of One dimensional Wave equation

5.3 Solution of One dimensional Heat equation, One dimensional heat equation with the initial and boundary conditions

5.4 Two-dimensional Laplace equation

UNIT VI FOURIER TRANSFORMS

6.1 Fourier integral theorem (without proof), Fourier sine and cosine integrals

6.2 Sine and cosine transforms, properties, inverse transforms, Finite Fourier transforms