Review of syntax for programming in C- The C character type -Identifiers and Keywords - Data types- Constants – Variables and Arrays - Declaration - Expressions- Statements - Symbolic Constants – Arithmetic, Unary, Relational and Logical Operators - Library Functions – Input functions – Output functions – Formatted input/output – Running a program – Error diagnostics – Control statements - Unconditional control - Bidirectional conditional control - Multi conditional control - Loop control structures –Functions –Files -Arrays

Transcendental and Polynomial Equations: Direct and Iterative methods comparison – Initial approximations – Bisection method- Secant and Regula Falsi methods – Newton Raphson method - Rate of convergence (ii)Curve Fitting Method of least squares – Straight line fit – Exponential fit – Power law fit – Polynomial of nth degree fit

Interpolation – Errors in polynomial interpolation – Newton’s forward difference interpolation formula – Newton’s backward difference interpolation formula – Gauss central difference formula – Lagrange interpolation formula – Newton’s general interpolation formula (ii) Algebraic Equations Solving simultaneous equations: Gauss Elimination method – Pivoting – Gauss-Jordan elimination method – Error analysis

Trapezoidal rule – Simpson’s 1/3 rule – Simpson’s 3/8 rule –Newton cotes quadrature - Euler method – Improved Euler method – Runge-Kutta fourth order method Compare numerical solutions of Euler, improved Euler and RK4 methods with exact solutions of simple harmonic oscillator

Comparative study of various methods to determine the roots of polynomials. Applications of RK4 methods to problems in Classical Mechanics –Ex. Free falling body, Projectile motion and Double pendulum– Curve fitting and extrapolation of datas related to material science experiments –Plot the classical and quantum statistical distribution functions as function of temperature –Plot Lissajous figures by numerically solving the respective two dimensional polynomial equation