BCS 054 Computer Oriented Numerical Techniques

Numerical Analysis is a branch of mathematics that helps to develop, analysis and evaluation of constructive numerical solutions This course has been designed to solve numerical methods related questions so that student pursuing their BCA/MCA/(B-Tech computer Science) can achieve best in semester exams.  Numerical Analysis has become essentially the discipline of computer Oriented Numerical Analysis. For solving numerical problems, the use of computer puts restrictions on the solution process. so for solving problem there must be careful analysis with respect to quantum of possible error. However, this course has been restricted to discussing some well known methods and their problems along with solutions. This course would include various topics like Linear Algebraic Equations (Gauss Elimination method, Partial Pivoting Methods, Gauss Jacobi method, Gauss Seidel Method), Non-Linear Equations ( Bisection method, Regula-Falsi Method, Secant Method, Newton Raphson Method), Operators(Forward Operator, Backward Operator, Shift Operator, Central Difference Operator, Averaging Operator and their relationships with Shift operators), Interpolation with equal intervals( Newton Forward Method, Newton Backward Method), Interpolation with unequal intervals (Lagrange's Method, Divided Difference Method), Method of Integration (Trapezoidal Rule, Simpson's Rule), Initial Value Problem ( Euler's Method , Runge Kutta Method), Numerical Differentiation( Newton Forward, Newton Backward, Lagrange's method) and Computer Arithmetic ( Error, Absolute Error, Relative Error, Percentage Error, Floating Point Representation, Floating Number Operations, Taylor/Maclaurin Series questions etc..