MA 6459 Numerical Methods Notes Pdf or M4 Maths Notes Anna University 4th Semester maths Notes are available here. All the five units subject of the lecture Notes is covered.
Numerical Methods Notes pdf – Lecture Notes/Study Materials
Numerical Methods Lecture Notes are as per Anna University syllabus from regulation 2013 and having important two marks and sixteen marks Questions with Answers in separate units here.
MA 6459 Numerical Methods Notes pdf – M4 Maths Notes
Numerical Methods Notes pdf for M4 4th Sem Notes. This course aims at providing the necessary basic concepts of a few numerical methods and give procedures for solving numerically different kinds of problems occurring in engineering and technology
Numerical Methods Study Materials
Method of False position (Or) Regula-Falsi method (Or) Linear interpolation method
In bisection method the interval is always divided into half. If a function changes sign over an interval, the function value at the midpoint is evaluated. In bisection method the interval from a to b into equal intervals ,no account are taken of the magnitude of .An alternative method that exploits this graphical insights is to join by a straight line.
The intersection of this line with the X-axis represents an improved estimates of the root.The replacement of the curve by a straight line gives a “false position” of the root is the origin of the name ,method of false position ,or in Latin ,Regula false .It is also called the linear interpolation method.
UNIT- I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS
Solution of algebraic and transcendental equations – Fixed point iteration method – Newton Raphson method- Solution of linear system of equations – Gauss elimination method – Pivoting – Gauss Jordan method – Iterative methods of Gauss Jacobi and Gauss Seidel – Matrix Inversion by Gauss Jordan method – Eigen values of a matrix by Power method
UNIT – II INTERPOLATION AND APPROXIMATION
Interpolation with unequal intervals – Lagrange’s interpolation – Newton‟s divided difference interpolation – Cubic Splines – Interpolation with equal intervals – Newton‟s forward and backward difference formulae.
UNIT – III NUMERICAL DIFFERENTIATION AND INTEGRATION
Approximation of derivatives using interpolation polynomials – Numerical integration using Trapezoidal, Simpson‟s 1/3 rule – Romberg‟s method – Two point and three point Gaussian quadrature formulae – Evaluation of double integrals by Trapezoidal and Simpson‟s 1/3 rules.
UNIT- IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
Single Step methods – Taylor‟s series method – Euler‟s method – Modified Euler‟s method – Fourth order Runge-Kutta method for solving first order equations – Multi step methods – Milne‟s and Adams-Bash forth predictor corrector methods for solving first order equations.
UNIT- V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
Finite difference methods for solving two-point linear boundary value problems – Finite difference techniques for the solution of two dimensional Laplace‟s and Poisson‟s equations on rectangular domain – One dimensional heat flow equation by explicit and implicit (Crank Nicholson) methods – One dimensional wave equation by explicit method.
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