Introduction to programming in MATLAB, examples. Error definitions, Taylor series and error propagation. Roots of equations – Bisection method, fixed point iteration, Newton-Raphson method, secant method, systems of nonlinear equations. Numerical linear algebra – Gauss elimination, LU decomposition, matric inversion, power method for finding eigen values, QR factorisation.

Curve Fitting – Linear regression, polynomial regression, nonlinear regression, Newton’s divided difference interpolation, Lagrange interpolation.

Numerical Integration and Differentiation – Trapezoidal rules, Simpson’s rules, Newton-Cotes algorithm, Gauss quadrature, high accuracy differentiation formulas, Richardson extrapolation, partial derivatives.

Differential Equations – Euler’s method, improved Euler’s methods, Runge-Kutta method, systems of equations, Finite difference method, solution of Laplace equation by FDM, explicit methods for parabolic equations, simple implicit method, Crank-Nicolson method

Course Objectives

The course is expected to enable the students

• To familiarize different numerical methods to solve engineering problems.
• To write computer programs and use tool boxes in the software packages.
• To select a specific numerical method to solve practical problems.

Course Outcomes

• CO1: Solve linear and nonlinear algebraic equations and systems of nonlinear equations using numerical techniques
• CO2: Use regression and interpolation methods for curve fitting.
• CO3: Select and apply numerical schemes for differentiating and integrating complicated functions.
• CO4: Apply computational schemes for solving systems of ordinary differential equations.
• CO5: Solve PDEs by numerical methods

CO – PO Mapping

Textbook(s)

• Numerical Methods for Engineers, Steven Chapra and Raymond Canale, Seventh Edition, McGraw Hill, 2015.
• Applied Numerical Analysis, LaureneFausett, Second Edition, Pearson, 2008.
• Advanced Engineering Mathematics, Erwin Kreyszig, Tenth Edition, Wiley, 2011.

Reference(s)

• M. K. Jain, S. R. K. Iyengar and R. K. Jain, Numerical methods for Scientific and Engineering Computation, New Age International Publishers, Fifth edition, 2007.
• C. F Gerald and P. O Wheatley, Applied Numerical Analysis, Seventh Edition, Addison Wesley, 2009. Rizwan Butt, Introduction to Numerical Analysis Using MATLAB, Jones and Bartlett Publisher, 2010. AbdelwahabKharab, Ronald B, An Introduction to Numerical Methods: A MATLAB Approach, Third Edition, CRC Press, 2012

Evaluation Pattern