## Syllabus

# UNIT- I

**Numerical Methods: **Solution of Algebraic and Transcendental equations: Bisection method, Newton-Raphson method, Solution of linear system of equations: Gauss elimination method, Gauss- Seidel iteration method, Interpolation: Lagrange’s interpolation, Newton’s divided difference interpolation, Newton’s Forward and Backward difference interpolations, Numerical differentiation, Numerical solutions of ordinary differential equations : Taylor’s series method, Euler method, Runge-Kutta method of 4^{th} order.

# UNIT- II

**Fourier Transforms: **Introduction, Fourier integrals, Fourier sine and cosine integrals, Complex form of Fourier integral, Fourier transform, Fourier sine and cosine transforms, Finite Fourier sine and cosine transforms, Properties of Fourier transforms, Convolution theorem for Fourier transforms.

# UNIT- III

**Number Theory: **Divisibility and Modular arithmetic, integer representation, primes and gcd, solving linear congruences, Chinese remainder theorem and its applications, Fermat’s theorem, Willson theorem and their applications.

# UNIT- IV

**Probability: **Random variables, Uniform, Normal, Exponential distributions, Mean, median, mode and standard deviation, Conditional probability and Baye’s theorem, Tests of

significance, t-test, F-test and

*c* 2 test.

# UNIT- V

**Curve Fitting: **Curve fitting by method of least squares, correlation and regression, types of correlations, Karl Pearson’s coefficient of correlation, Spearman’s rank correlation coefficient, equal ranks, equations to the lines of regression.