Teaching Plan of Numerical Techniques (MA 201) Odd Semester: 2017- 2018 Convener: Dr. Vineet Kumar Singh Instructors: Prof. L. P. Singh, Dr. Rajeev, Dr. R. K. Pandey, Dr. Sunil Kumar Week 1:
Unit I: Errors in Numerical Methods: Approximate numbers and Significant figures; Rouding-off numbers; Errors: Absolute, Relative and Percentage; Error in Arithmetical operations; A General Error Formula; Errors in Numerical Computations.
Week 2:
UNIT II: Solution of equations in one variable Bisection method; Iteration method; Regula-Falsi method; order of convergence (Definition), Convergence of Regula-Falsi method; Secant method; Fixed point theorem proof (application for roots finding),
Week 3:
UNIT II: Solution of equations in one variable Newton-Raphson method; convergence analysis, Generalised Method for multiple roots; UNIT III: Numerical solution of system of equations Ill conditioned problems; Gauss elimination method; Residual vector, Error Analysis , GaussJordan method; Jacobi‘s iteration method , Gauss Seidel method. UNIT III: Numerical solution of system of equations Error analysis and number of iteration for Jacobi methods. UNIT IV: Operators Forward difference operator, Backward difference operator, Shift operator, Average operator, Central difference operator and their relations
Week 4:
Week 5:
Week 6:
Interpolation Weierstrass approximation Theorem, Interpolation, Lagrange‘s interpolation formula, formula , Errors in Interpolation, Divided differences. Unit V:
Week 7:
Newton‘s divided difference formula, formula , Newton‘s forward interpolation formula; Newton‘s backward interpolation formula; Central Difference Interpolation Formulae;
Week 8:
Interpolation Gauss‘ Forward central Forward central Difference Formula; Gauss‘ Backward central Difference Formula Stirling‘s Formula; Bessel formula; Sub-Unit V: Numerical Differentiation: Numerical differentiation and applications; Basic ideas of Difference Equations UNIT VI: Numerical integration A general quadrature quadrature formula for equidistant nodes: nodes: Trapezoidal rule; Simpson‘s one-third one -third rule, Simpson‘s three-eight three-eight rule, All Composite Integration Rule. UNIT VI: Numerical integration errors in numerical integrations( Trapezoidal rule, Simpson‘s oneone-third rule, Simpson‘s three-eight three -eight rule), Errors in Composite rule. UNIT VI: Numerical integration Newton-Cotes quadrature formula (or Methods of undetermined), Gaussian quadrature formula. UNIT VII: Numerical Methods of Solution of O.D.E: Picard‘s Method of Successive Approximations Approximations Picard‘s Method for Simultaneous First Order Differential Equations; UNIT VII: Numerical Methods of Solution of O.D.E: Euler‘s Method;; Modified Euler‘s Method; Runge-Kutta method;
Week 9: Week 10:
Week 11:
Week 12:
Week 13:
Unit V:
Prerequisite: Engg. Mathematics I; Desirable Engg. Mathematics II. Books to be followed 4. READINGS 4.1. TEXTBOOK:
1. Introductory Methods of Numerical Analysis, S. S. Sastry, Fifth Edition. 4.2. REFERENCE BOOKS: 1. Numerical Analysis, Richard L. Burden, J. Douglas. 2. Elementary Numerical Analysis, K. Atkinson.
Examination Details 1. 2. 3.
Mid Term Examination: Sep 12-16, 2017 (Tues-Sat) Display of Mid Term Examination Marks: Sep 23, 2017 (Sat) End Semester Examination: Nov 20-Dec 4, 2017 (Mon-Mon) Weightage of marks for the course Numerical Techniques(MA-201)-Odd Semester-20172018 - (Total marks: 100)
1. Mid Term Examination: 30 Marks 2. End Semester Examination: 50 Marks 3. Assignments: 10 Marks (We will supply 4 to 5 Assignments ) 4. Surprise Quiz: 10 Marks (course instructors will conduct 3 test. Instructor will schedule in lecture/Tutorial hours )
