JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Course Objectives

To impart knowledge about various methods of analysing linear equations and

understand the different mathematical techniques.

Course Outcomes

The learner will be able to apply various mathematical techniques to Structural

engineering problems.

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. 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.

UNIT - II

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 formulae 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 – Applications to Simply Supported Beams, Columns and Rectangular Plates.

UNIT - IV

Numerical Differentiation: Difference methods based on undetermined coefficients- optimum choice of step length– Partial differentiation. Numerical Integration: Method based on interpolation-method based on undetermined coefficient – Gauss – Lagrange interpolation method- Radaua integration method- composite integration method – Double integration using Trapezoidal and Simpson’s method – New Marks Method and Application to Beams – Calculation of Slopes and Deflections.

UNIT - V

Ordinary Differential Equation: Euler’s method – Backward Euler method – Midpoint method – single step method, Taylor’s series method- Boundary value problems.

TEXT BOOKS:

• 1. Numerical methods for scientific and engineering computations. M.K. Jain-S.R.K. Iyengar – R.K. Jain Willey Eastern Limited
• 2. Numerical Methods for Engineering Problems, N. Krishna Raju, KU Muthu, Mac-Millan publishers

REFERENCES:

• 1. Introductory Numerical Methods by S.S. Shastry, PHI Learning Pvt. Ltd.
• 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. Computer based numerical analysis by Dr. M. Shanta Kumar, Khanna Book publishers, New Delhi.