1 Day Mathematica

We discuss how to evaluate a cell and define variables in Mathematica. We also check how to perform numerical operations on variables and Mathematica's in-built 'Numeric function'.

To evaluate any cell, we can click on the settings icon on the rightmost side of that cell and choose 'Evaluate Cell' from the menu.

Or we can also use the keyboard shortcut Shift + Enter.

We discuss how to make a Mathematica notebook look better. We check various formatting options, section type, font size, background colour, etc. in both the Online and Desktop versions.

We discuss how to define/type Greek symbols in Mathematica. There's a shortcut, ex. if we want to write the ' β ' (beta)  symbol, we hit the escape key, type 'beta', and again hit the escape key.

Esc key + beta + Esc key

This will print the β (beta) symbol.

We discuss some of the important in-built functions in Mathematica.

1) Simplify

2) FullSimplify

3) Expand

4) PowerExpand

5) FullExpand

6) Sum

7) NSum

8) Product

We discuss two useful functions - Series and Solve.

1) Series helps us to write any function as a power series in terms of a variable x, about point x0 and up to n terms.

2) Solve helps us to solve 'n' number of equations simultaneously to solve for 'n' variables.

We discuss useful Calculus concepts using Mathematica - Limit of a function, Partial Differentiation, Total Differentiation and Integration.

We discuss how to take the 'Fourier Transform' and 'Inverse Fourier Transform' of any function in Mathematica. We also discuss how to approximate any function using 'Fourier Exponential Series' and 'Fourier Trigonometric Series'.

We briefly discuss how to use Mathematica's 'Laplace Transform' and 'Inverse Laplace Transform' functions with some examples.

We discuss how to use Condition and ReplaceAll in Mathematica.

We discuss how to define matrices. We also discuss how to find their determinant, trace, inverse, transpose, eigenvalues and eigenvectors.

We discuss plotting in Mathematica, covering 2D plotting, 3D plotting, 2D Parametric plotting, 3D Parametric plotting and Contour plotting.

We discuss how to define a custom function in Mathematica. Being able to define a general function allows us to solve problems efficiently.

We discuss various use cases of 'Table' in Mathematica. A table can create copies, arrays, and matrices that follow a certain rule.

We discuss Do, For and While loops. We also understand how to use If and Break statements along with these loops.

We discuss how to solve differential equations using Mathematica.

We discuss the final project and explain the tasks involved in this project. Hints and steps to solve are also discussed.

We discuss the solution to the first part of our project, we solve and visualize the wave equation in 2D and 3D. We also briefly discuss the 'Manipulate' function of Mathematica.

Thank you so much for completing the course!