Course Title:Numerical Methods and Optimization

Annexure ‘CD-01’

Course Title:Numerical Methods and Optimization

Course Code:MATH201

Credit Units:4

Level: UG

Course Objectives:

By the end of the semester, students will be able to deals with the techniques of numerical analysis and optimization, which gives the solution to applied problem when ordinary analytical method fails.

Prerequisites:

Students must have knowledge of Differential Calculus, Integral Calculus, and Partial Derivatives.

Course Contents/Syllabus:

• Error in a series approximation,
• Bisection Method,
• Iterative Method,
• Method of false position,
• Newton-Raphson method
• Gauss elimination method,
• Jacobi iteration method,
• Gauss Seidal method

• Finite Differences,
• Difference tables
• Polynomial Interpolation: Newton’s forward and backward formula
• Central Difference Formulae: Gauss forward and backward formula.
• Interpolation with unequal intervals: Lagrange’s Interpolation,
• Newton Divided difference formula .

• Introduction, Numerical differentiation
• Numerical Integration:
• Trapezoidal rule, Simpson’s 1/3 and 3/8 rules,
• solution of differential equations: Euler’s Method,
• Runga-Kutta Methods.

• Formulation of the problem,
• Graphical method,
• Canonical and Standard forms of L.P.P.
• Simplex Method,
• Artificial variable Techniques-M-method,
• Two phase method.

Student Learning Outcomes:

Upon successful completion of this course, student will be able to

• Find the Error in a series approximation
• Apply the iterative method to solve the simultaneous equations and algebraic equations.
• Solve transcendental equations using numerical methods.
• Form a polynomial/curve satisfying the given data when the intervals are equally/unequally spaced using different numerical methods
• Find the value of first derivative and higher order derivatives from the given data even when function is not given.
• Apply concept of numerical methods to solve the differential equations and integrations.
• Formulate linear programming problem.
• Solve LPP using Simplex and two phase method.

Pedagogy for Course Delivery:

The class will be taught using theory by providing time for practice.Problem solving sessions and by taking tests and quiz on regular basis.

Assessment/ Examination Scheme:

Theory Assessment (L&T):

Lab/ Practical/ Studio Assessment: NA

Text:

1. Rajaraman V, “Computer Oriented Numerical Methods”, Pearson Education
2. Gerald & Whealey, “Applied Numerical Analyses”, AW
3. Jain, Iyengar and Jain, “Numerical Methods for Scientific and Engineering Computations”, New Age Int.
4. Grewal B S, “Numerical methods in Engineering and Science”, Khanna Publishers, Delhi.
5. . G. Hadley, Linear Programming, Narosa Publishing House, New Delhi, 2002

References:

1. T Veerarajan, T Ramachandran, “Theory and Problems in Numerical Methods, TMH
2. Pradip Niyogi, “Numerical Analysis and Algorithms”, TMH
3. Francis Scheld, ” Numerical Analysis”, TMH
4. Sastry S. S, “Introductory Methods of Numerical Analysis”, Pearson Education.
5. Gupta C.B., Vijay Gupta, “Introduction to Statistical Methods”, Vikas Publishing.
6. Goyal, M, “Computer Based Numerical and Statistical Techniques”, Firewall Media, New Delhi.
7. Kantiswarup and gupta, “Operation Research”, S. Chand, New Delhi.

Remarks and Suggestions:

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