Numerical Analysis and Computer programming
Good Books for reference:
Numerical analysis (R. L. Burden and J. D. Faires)
Syllabus for Numerical analysis and computer programming
Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton-Raphson
methods
Lecture 1: Numerical Analysis (Root finding methods)
Lecture 2: Numerical Analysis (Bisection method introduction)
Lecture 3: Numerical Analysis (Problem based on bisection method)
Lecture 4: Numerical Analysis (Number of iterations for bisection method)
Lecture 5: Numerical Analysis (Questions on Bisection method)
Lecture 6: Numerical Analysis (Fixed point iteration method introduction)
Lecture 7: Numerical Analysis (Number of iterations in fixed point iteration method)
Lecture 8: Numerical Analysis (Problems on Fixed point iteration method)
Lecture 9: Numerical Analysis (Problems on fixed point iteration method-2)
Lecture 10: Numerical Analysis (Newton method)
Lecture 11: Numerical Analysis (Problems on Newton method)
Lecture 12: Numerical Analysis (Secant method)
Lecture 13: Numerical Analysis (order of convergence definition)
Lecture 14: Numerical Analysis (Order of convergence of bisection and Newton method)
Lecture 15: Numerical Analysis (Order of convergence of fixed point iteration method)
Lecture 16: Numerical Analysis (Problems on order of convergence of fixed point iteration method)
Lecture 17: Numerical Analysis (Modified Newton method(why do we need it?))
Lecture 18: Numerical Analysis (Modified Newton method)
Solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss-Seidel(iterative) methods
Newton’s (forward and backward) interpolation
Please note this content would be covered later.
Lagrange’s interpolation
Lecture 19: Numerical Analysis (Lagrange interpolation)
Lecture 20: Numerical Analysis (Error introduced in Lagrange interpolation)
Lecture 21: Numerical Analysis (Problems one error bound of Lagrange interpolation)
Numerical integration: Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula
Numerical Integration 1 (Formula for the trapezoidal rule)
Numerical Integration 2 (Error in trapezoidal rule)
Numerical Integration 3 (Simpsons 1/3 rule of integration)
Numerical Integration 4 (Degree of precision or accuracy)
Numerical solution of ordinary differential equations: Euler and Runga Kutta-methods
Computer Programming: Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimal systems
Conversion to and from decimal systems
Algebra of binary numbers
Elements of computer systems and concept of memory
Basic logic gates and truth tables
Boolean algebra
Normal forms
Representation of unsigned integers
Signed integers and reals
Double precision reals and long integers
Algorithms and flow charts for solving numerical analysis problems
Please note this content would be covered later.