Credits: 3 (3-0-0)
Description
Introduction: Mathematical foundations of structural theory. Linear algebra: vector spaces and linear transformations. Linear differential equations and function spaces. Partial differential equations; Elliptic, parabolic and hyperbolic PDEs. Nonlinear differential equations. Gaussian Elimination; Factorization Techniques - LU, Cholesky; Iterative Methods of Solution of Linear Simultaneous Equations. Properties of Eigenvalues and Eigenvectors; Similarity Transforms; Diagonalization and Numerical Techniques to Compute Eigenvalues
- Vector Iteration, QR algorithm, Jacobi Method. Time Marching Schemes (Step by Step Solutions); Euler’s Method; Runge Kutta Method; Newmark Beta Method. Numerical Solution of Boundary Value Problems - Finite Difference Method, Explicit and Implicit Approaches; Method of Weighted Residuals, Galerkin’s Method. Numerical Integration: Gauss- Legendre Method, Newton-Cotes Method. Regression Analysis and Curve Fitting. Applications of mathematical and numerical methods to static, dynamic and stability analysis of elastic structures and cables.