What you'll learn:
- Program using VBA Programming Language
- Approximate functions using Taylor series expansions
- Approximate derivatives using conventional and high accuracy formulas
- Approximate integrals using Trapezoidal rule, Simpson's 1/3 rule and Romberg integration
- Find roots of equations using bisection, False position, newton Raphson and secant methods
- Find analytically the optimum min and max of a function
- Solve Ordinary differential Equations using Runge Kutta Methods (i.e. Euler, Heun's, Midpoint and Ralston Methods in addition to fourth order Runge Kutta Method
- Find numerically the optimum min and max using Golden section Search method, newton Raphson Technique and finally the gradient decent/ascent method
- Solve Systems of Equations using Gauss elimination, Gauss Jordan and LU Decomposition and generate inverse matrices
- Perform curve fitting using regression analysis including linear and polynomial regression in addition to linearization for fitting more complex functions
- Perform curve fitting using Cubic Spline
Numerical modeling is a very powerful branch of mathematics. It is capable to solve very complex problems using very simple techniques.
It is a branch that can differentiate and integral without the need to use any of the sometimes complex differentiation and integration rules. It can create best fit models with just knowing a data set. It can create functions where the only thing we know is its derivative and a condition. And best of all, it can generate approximations that have such a low percentage error that they are as good as the true value.
But...
There is a limitation to numerical methods. They depend of iterative calculations. If for example you want an approximation with a low error, for example 0.001%, this will require a large amount of calculations which can be sometimes impossible to do by hand not to mention tedious. This is where programming comes in.
In this course I will walk you through not only the workings of each technique but a step by step process on how to program each of these techniques and preform hundreds if not thousands of calculations with a click of a button using one of the most powerful softwares created, EXCEL. And I'll be using excel's inbuilt programming language, VBA.
The great thing about programming languages is they all follow the same programming structure, sequence, repetition and decision making. Meaning, if you know one language you can learn another very easily by just knowing how these structures are defined in the new language.
In this course you'll have a very good grasp of these structure so if you decide to learn another language afterwards it will be very easy.
This project was a means for me to give back and contribute. I hope you find some value in this course.
Thank you and Enjoy!!
