JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Pre-requisites

Mathematics I and II

Course Objectives:

• 1. To apply the basic knowledge of Mathematics in Engineering
• 2. To provide a formidable base for analysis and programming using computer applications
• 3. To develop the ability in programming and solutions based on the various analysis tools
• 4. To check the consistency of system of linear equations

Course Outcomes

After completion of the course, students should be able to

• 1. Apply numerical methods to find the roots of an equation
• 2. Identify mathematical model for solution of common engineering problems
• 3. Formulate simple problems into programming models
• 4. Solve ordinary and partial differential equations

UNIT - I

Solutions of linear equations: Direct method – Cramer’s rule, Guass – Elimination method- Gauss – Jordan elimination – Triangulation (LU Decomposition) method – Iterative methods Jacobi – Iteration method – Gauss – Siedel iteration, Successive over –relaxation method -Applications

UNIT - II

Eigen values and eigen vectors: Jacobi method for symmetric matrices- Given’s method for symmetric matrices-Householder’s method for symmetric matrices-Rutishauser method of arbitrary matrices – Power method, Fast Fourier Transform (FFT) Interpolation: Linear Interpolation - Higher order Interpolation - Lagrange Interpolation – Interpolating polynomials using finites differences- Hermite Interpolation -piece-wise and spline Interpolation.

UNIT - III

Finite Difference and their Applications: Introduction- Differentiation formulas by Interpolating parabolas – Backward and forward and central differences- Derivation of Differentiation formulas using Taylor series- Boundary conditions- Beam deflection – Solution of characteristic value problems- Richardson’s extrapolation- Use of unevenly spaced pivotal points- Integration formulae by interpolating parabolas- Numerical solution to spatial differential equations.

UNIT - IV

Numerical Differentiation: Difference methods based on undetermined coefficients- optimum choice of step length- extrapolation method – Partial differentiation. Numerical Integration: Method based on interpolation-method based on undetermined coefficient – Gauss – legrange interpolation method- radaua integration method- composite integration method – Double integration using Trapezoidal and Simpson’s method.

UNIT - V

Ordinary Differential Equation: Euler’s method – Backward Euler method – Midpoint method – single step method, Taylor’s series method, Runge-Kutta method Predictor-Corrector Method -Trapezoidal and Midpoint method – Implicit Runge Kutta method – Boundary value problem – Difference method – Shooting method -Structural Engineering Applications

REFERENCES:

• 1. Numerical Methods for Scientific and Engineering Computations. M. K. Jain - S. R. K. Iyengar – R. K. Jain Willey Eastern Limited.
• 2. Applied numerical Analysis by – Curtis I. Gerala- Addission Wasley – published campus.
• 3. Numerical Methods for Engineers Stevan C. Chopra, Raymond P. Canal Mc. Graw Hill book company.
• 4. C Language and Numerical Methods by C. Xavier – New age international publisher.
• 5. Numerical methods using MATLAB by George Lindfield and John penny, Academic press M. Tech in COMPUTER AIDED STRUCTURAL ENGINEERING I YEAR I – SEMESTER