Errors in Numerical Calculations, Sources of Errors, Propagation of Errors, Review of Taylor's Theorem, Solving Non-linear Equations by Trial and Error method, Half-Interval method and Convergence, Newton's method and Convergence, Secant method and Convergence, Fixed point iteration and its convergence, Newton's method for calculating multiple roots, Horner's method

Interpolation vs Extrapolation, Lagrange's Interpolation, Newton's Interpolation using divided differences, forward differences and backward differences, Cubic spline interpolation, Introduction to Regression, Regression vs Interpolation, Least squares method, Linear Regression, Non-linear Regression by fitting Exponential and Polynomial

Differentiating Continuous Functions (Two-Point and Three-Point Formula), Differentiating Tabulated Functions using Newton’s Differences, Maxima and minima of Tabulated Functions, Newton-Cote's Quadrature Formulas, Trapezoidal rule, Multi-Segment Trapezoidal rule, Simpson's 1/3 rule, Multi-Segment Simpson's 1/3 rule, Simpson's 3/8 rule, Multi-Segment Simpson's 3/8 rule, Gaussian integration algorithm, Romberg integration

Review of the existence of solutions and properties of matrices, Gaussian elimination method, pivoting, Gauss-Jordan method, Inverse of matrix using Gauss-Jordan method, Matrix factorization and solving system of linear equations using Dolittle and Cholesky's algorithm, Iterative Solutions of System of Linear Equations: Jacobi Iteration Method, Gauss-Seidel Method, Eigenvalues and eigenvectors problems, solving eigenvalue problems using power method

Review of differential equations, Initial value problem, Taylor series method, Picard's method, Euler's method and its accuracy, Heun's method, Runge-Kutta methods, Solving system of ordinary differential equations, solution of higher order equations, Boundary value problems, Shooting method and its algorithm

Review of partial differential equations, Classification of partial differential equations, Deriving difference equations, Laplacian equation and Poisson's equation, engineering examples