PowerPoint Presentations

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]