In these “Numerical AnalysisNotes PDF”, you will study the various computational techniques to find approximate value for possible root(s) of non-algebraic equations, to find the approximate solutions of system of linear equations and ordinary differential equations. Also, the use of Computer Algebra System (CAS) by which the numerical problems can be solved both numerically and analytically, and to enhance the problem solving skills.
The topics we will cover will be taken from the following list:
Methods for Solving Algebraic and Transcendental Equations: Algorithms, Convergence, Bisection method, False position method, Fixed point iteration method, Newton’s method and Secant method.
Techniques to Solve Linear Systems: Partial and scaled partial pivoting, LU decomposition and its applications, Iterative methods: Gauss−Jacobi, Gauss−Seidel and SOR methods.
Interpolation: Lagrange and Newton interpolation, Piecewise linear interpolation.
Numerical Differentiation and Integration: First and higher order approximation for first derivative, Approximation for second derivative, Richardson extrapolation method; Numerical integration by closed Newton−Cotes formulae: Trapezoidal rule, Simpson’s rule and its error analysis; Euler’s method to solve ODE’s, Second order Runge−Kutta Methods: Modified Euler’s method, Heun’s method and optimal RK2 method.
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