Learn the workings of the most common numerical methods and a step by step process on how to program each of them
What you’ll learn:
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
Perform curve fitting using regression analysis including linear and polynomial regression in addition to linearization for fitting more complex functions
Requirements
Computer & Access to Microsoft Excel
Knowledge of basic Algebra, Geometry & Calculus Concepts
Knowledge of basic Python Programming
Description
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 popular programming language – Python.
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.
Who this course is for
Students enrolled in their first numerical Methods Class and interested in additional mentoring
Students interested to learn the most common Numerical Methods Techniques used in science and engineering
Students interested in understanding how to program and create Numerical Modeling Techniques
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