To introduce the basic concepts of solving algebraic and transcendental equations.
To introduce the numerical techniques of interpolation in various intervals in real life situations.
To acquaint the student with understanding of numerical techniques of differentiation and
integration which plays an important role in engineering and technology disciplines.
To acquaint the knowledge of various techniques and methods of solving ordinary differential equations.
To understand the knowledge of various techniques and methods of solving various types of partial differential equations.
UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS 12
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 – Eigenvalues of a matrix by Power method and Jacobi’s method for symmetric matrices.
UNIT II INTERPOLATION AND APPROXIMATION 12
Interpolation with unequal intervals – Lagrange’s interpolation – Newton’s divided difference interpolation – Cubic Splines – Difference operators and relations – Interpolation with equal intervals – Newton’s forward and backward difference formulae.
UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION 12
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 12
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 12
Finite difference methods for solving second order 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.
TOTAL : 60 PERIODS
Upon successful completion of the course, students should be able to:
Understand the basic concepts and techniques of solving algebraic and transcendental equations.
Appreciate the numerical techniques of interpolation and error approximations in various intervals in real life situations.
Apply the numerical techniques of differentiation and integration for engineering problems.
Understand the knowledge of various techniques and methods for solving first and second order ordinary differential equations.
Solve the partial and ordinary differential equations with initial and boundary conditions by using certain techniques with engineering applications.
- Burden, R.L and Faires, J.D, “Numerical Analysis”, 9th Edition, Cengage Learning, 2016.
- Grewal, B.S., and Grewal, J.S., “Numerical Methods in Engineering and Science”, Khanna Publishers, 10th Edition, New Delhi, 2015.
- Brian Bradie, “A Friendly Introduction to Numerical Analysis”, Pearson Education, Asia, New Delhi, 2007.
- Gerald. C. F. and Wheatley. P. O., “Applied Numerical Analysis”, Pearson Education, Asia, 6th Edition, New Delhi, 2006.
- Mathews, J.H. “Numerical Methods for Mathematics, Science and Engineering”, 2nd Edition, Prentice Hall, 1992.
- Sankara Rao. K., “Numerical Methods for Scientists and Engineers”, Prentice Hall of India Pvt. Ltd, 3rd Edition, New Delhi, 2007.
- Sastry, S.S, “Introductory Methods of Numerical Analysis”, PHI Learning Pvt. Ltd, 5th Edition, 2015.