Introduction to Scientific Computing
Introduction to numerical methods [PDF] [PPT] [MORE] Measuring errors [PDF] [PPT] [MORE] Sources of error [PDF] [PPT] [MORE] Binary representation of numbers [PDF] [PPT] [MORE] Floating point representation of numbers [PDF] [PPT] [MORE] Propagation of errors [PDF] [PPT] [MORE] Taylor series [PDF] [PPT] [MORE]
Differentiation
Continuous functions [PDF] [PPT] [MORE] Discrete functions [PDF] [PPT] [MORE] Effect of step size on accuracy of numerical first derivative: Forward Divided Difference [PDF] [PPT] Effect of step size on accuracy of numerical first derivative Backward Divided Difference [PDF] [PPT] Effect of step size on accuracy of numerical first derivative: Central Divided Difference [PDF] [PPT]
Nonlinear Equations
Bisection Method [PDF] [PPT] [MORE] Newton-Raphson Method [PDF] [PPT] [MORE] Secant Method [PDF] [PPT] [MORE]
Simultaneous Linear Equations
Gaussian Elimination [PDF] [PPT] [MORE] LU Decomposition method [PDF] [PPT] [MORE] Gauss-Seidel method [PDF] [PPT] [MORE]
Interpolation
Direct Method [PDF] [PPT] [MORE] Newton’s Divided Difference Method [PDF] [PPT] [MORE] Lagrange Method [PDF] [PPT] [MORE] Spline Method [PDF] [PPT] [MORE]
Regression
Linear Regression [PDF] [PPT] [MORE] Nonlinear regression [PDF] [PPT] [MORE]
Integration
Trapezoidal Rule [PDF] [PPT] [MORE] Simpson’s 1/3rd Rule [PDF] [PPT] [MORE] Romberg Rule [PDF] [PPT] [MORE] Gauss-Quadrature Rule [PDF] [PPT] [MORE]
Ordinary Differential Equations
Euler’s Method [PDF] [PPT] [MORE] Runge-Kutta 2nd order Method [PDF] [PPT] [MORE] Runge-Kutta 4th order Method [PDF] [PPT] [MORE] Shooting Method [PDF] [PPT] [MORE] Finite Difference Method [PDF] [PPT] [MORE]
Optimization
Golden Section Search Method [PDF] [PPT] [MORE] Newton’s Method [PDF] [PPT] [MORE] Multidimensional Direct Search Method [PDF] [PPT] [MORE] Multidimensional Gradient Method [PDF] [PPT] [MORE]
Partial Differential Equations
Introduction to Partial Differential Equations [PDF] [PPT] [MORE] Parabolic Partial Differential Equations [PDF] [PPT] [MORE] Elliptic Partial Differential Equations [PDF] [PPT] [MORE]
Fast Fourier Transforms
Introduction to Fourier Series [PDF] [PPT] [MORE] Continuous Fourier Series [PDF] [PPT] [MORE] Fourier Transform Pair [PDF] [PPT] [MORE] Discrete Fourier Transform [PDF] [PPT] [MORE] Informal Development of Fast Fourier Transform [PDF] [PPT] [MORE]