Module #1 Introduction to Numerical Methods Overview of numerical methods, importance in engineering, and types of numerical methods
Module #2 Error Analysis Sources of error, types of error, and error propagation in numerical methods
Module #3 Numerical Solution of Linear Algebraic Equations Direct and iterative methods for solving systems of linear equations
Module #4 Gaussian Elimination Implementation and example problems of Gaussian elimination method
Module #5 LU Decomposition LU decomposition method for solving systems of linear equations
Module #6 Iterative Methods for Linear Systems Jacobi, Gauss-Seidel, and SOR methods for solving systems of linear equations
Module #7 Eigenvalue and Eigenvector Computation Power method, inverse power method, and QR algorithm for eigenvalue and eigenvector computation
Module #8 Numerical Differentiation Finite difference methods for numerical differentiation
Module #9 Numerical Integration Newton-Cotes formulas, Gaussian quadrature, and Monte Carlo methods for numerical integration
Module #10 Root Finding Methods Bisection, Newton-Raphson, and secant methods for finding roots of nonlinear equations
Module #11 Numerical Solution of Ordinary Differential Equations Eulers method, Runge-Kutta methods, and multistep methods for solving ODEs
Module #12 Finite Difference Method for PDEs Finite difference method for solving partial differential equations
Module #13 Finite Element Method Introduction to finite element method for solving PDEs
Module #14 Numerical Solution of Partial Differential Equations Method of characteristics, finite difference method, and finite element method for solving PDEs
Module #15 Interpolation and Approximation Lagrange interpolation, spline interpolation, and least squares approximation
Module #16 Curve Fitting Linear and nonlinear regression, and polynomial curve fitting
Module #17 Numerical Methods for Optimization Unconstrained and constrained optimization using numerical methods
Module #18 Introduction to MATLAB Basic programming and numerical computations in MATLAB
Module #19 Numerical Methods in MATLAB Implementation of numerical methods in MATLAB
Module #20 Case Study:Structural Analysis Application of numerical methods to structural analysis problems
Module #21 Case Study:Fluid Dynamics Application of numerical methods to fluid dynamics problems
Module #22 Case Study:Heat Transfer Application of numerical methods to heat transfer problems
Module #23 Numerical Methods in Engineering Applications Overview of numerical methods in various engineering fields
Module #24 Project Development Development of a project using numerical methods in a specific engineering field
Module #25 Course Wrap-Up & Conclusion Planning next steps in Numerical Methods in Engineering career
