Introduction to Scientific Computing
True Error [MATHEMATICA] Approximate Error [MATHEMATICA]
Decimal to binary representation [MATHEMATICA] Binary to decimal representation [MATHEMATICA]
Decimal to floating point representation [MATHEMATICA] Binary to floating point representation [MATHEMATICA]
Propagation of Errors [MATHEMATICA]
Differentiation
Forward Divided Difference [MATHEMATICA] Backward Divided Difference [MATHEMATICA] Central Divided Difference [MATHEMATICA] Continuous functions Second Order Derivative [MATHEMATICA]
Discrete functions [MATHEMATICA]
Nonlinear Equations
Method [MATHEMATICA] Convergence [MATHEMATICA] Pitfall: Slow convergence of bisection method simulation [MATHEMATICA]
Method [MATHEMATICA] Convergence [MATHEMATICA] Pitfall: Division by zero [MATHEMATICA] Pitfall: Slow Convergence at Inflection Points [MATHEMATICA] Pitfall: Root jumps over several roots [MATHEMATICA] Pitfall: Roots oscillates around local maxima and minima [MATHEMATICA]
Simulation of secant method [MATHEMATICA] Convergence Simulation of secant method [MATHEMATICA] Pitfall: Division by zero in secant method simulation [MATHEMATICA] Pitfall: Root jumps over several roots in secant method [MATHEMATICA]
Simultaneous Linear Equations
Method [MATHEMATICA]
Method [MATHEMATICA] Convergence [MATHEMATICA]
Method [MATHEMATICA]
Interpolation
Method [MATHEMATICA]
Newton’s Divided Difference Method
Method [MATHEMATICA]
Method [MATHEMATICA]
Method [MATHEMATICA]
Regression
Method [MATHEMATICA]
Without Data Linearization [MATHEMATICA] With Data Linearization [MATHEMATICA] Polynomial Regression [MATHEMATICA] Comparing with and without Data Linearization [MATHEMATICA]
Adequacy of a Regression Model
Adequacy [MATHEMATICA]
Integration
Method [MATHEMATICA] Convergence [MATHEMATICA]
Method [MATHEMATICA] Convergence [MATHEMATICA]
Method [MATHEMATICA] Convergence [MATHEMATICA]
Method [MATHEMATICA] Convergence [MATHEMATICA]
Integrating Discrete Functions
Integrating discrete functions [MATHEMATICA]
Ordinary Differential Equations
Method [MATHEMATICA] Convergence [MATHEMATICA]
Method [MATHEMATICA] Convergence [MATHEMATICA]
Method [MATHEMATICA] Convergence [MATHEMATICA]
Method [MATHEMATICA]
Method [MATHEMATICA]
Optimization
Method [MATHEMATICA]
Method [MATHEMATICA]
Multidimensional Direct Search Method
Method [MATHEMATICA]
Multidimensional Gradient Method
Method [MATHEMATICA]
Partial Differential Equations
Parabolic Partial Differential Equations
Explicit Method [MATHEMATICA] Implicit Method Parabolic PDEs [MATHEMATICA] Crank Nicolson Method Parabolic PDEs [MATHEMATICA]
Elliptic Partial Differential Equations
Direct Method [MATHEMATICA] Gauss-Seidel Method [MATHEMATICA] Lieberman Method [MATHEMATICA]
Fast Fourier Transforms
Method [MATHEMATICA]
Method [MATHEMATICA]
Method [MATHEMATICA]