Mathematica 9 for Beginners

Here I teach about the Mathematica Environment.

The fact that to evaluate something, you have to press [Shift]+[Enter]

The fact that all built-in functions in Mathematica start with upper-case letters.

The fact that constants such as π and e are entered as Pi and E

The fact that whatever the function applies to is in square brackets [...]

I show the basic arithmetic operations +,-,* and /

The trignometric and the log funtions, also the fact that the trigonometric functions are always evaluated in radians, and the log is always the natural log.

Here I show you the fact that the N function can evaluate to any number of decimal figures.

Here I show you that Mathematica can, take log to practically any base.

I show you that Mathematica handles exponents gracefully.

I show you a fancy way of writing roots to a number.

I also introduce the problem with taking the nth root of a number, where n > 3.

In this and the previous lecture I introduce the fact that Mathematica can also evaluate trigonometry in terms of degrees.

I introduce the concept of entering symbols using the [Esc] key.

I also introduce the fact that Mathematica can convert between degrees and radians.

I finally also introduce the concept of inverse trigonometric functions.

In this lecture I show you how to define a variable, and the fact that practically anything can be a variable.

I show you some conventions for naming variables.

I show you how to find out information about a variable.

I show you the fact that variables are global and what that really means in practice.

Here I show you how to substitute one or more variables into an expression that has already been typed.

Here I show you the common algebra functions that Mathematica can do:

I show you Expand to expand a binomial expression

I show you, how that can be used with Coefficient to find the coefficient of a monomial in a Binomial expression.

I show you Simplify

I show you Apart and Together

Here I show you about the Solve[...] function, and the fact that it can solve almost anything.
I discuss the intricacies of = vs == here.

I also show you how Mathematica can solve generic equations

Here I generalize the solve function to solve multiple equations

Here I show you the notation for defining a function and some intricacies of functions.

I also define the InverseFunction [...]

Here I demonstrate the fact that Solve[...] does not solve quintic (fifth order) equations algebraiccally, and how to work around that.

Here I show you how to conditionally solve an equation, i.e. how to solve for Reals and Complexes and Integers

Here I show Reduce as used to solve inequalities.

I also show Reduce [...] used to:

-Solve equations of any degree

-Solve systems of Linear Equations

-Solve inequations and systems of inequalities

-Reduce logical expressions to True or False

In this video I introduce the concept of lists:

-that lists can contain, numbers, images, algebraic expressions, pictures etc

-that lists can contain other lists

-that lists can be named

-the naming conventions behind naming lists

Very short vide. Here I show the fact that almost any function taken on a list applies to each and every element of said list

Here I show that you can, add, subtract, multiply and divide two lists.

Here I show you how to get basic information from lists:

like length, max, min, etc.

I also show you how to get parts of a list.

Here I show you how to search for information out of lists:

I show you how to search for elements of a list that meet a criteria or a combination of criteria.
I also show you about Position[ ] and MemberQ[ ] function.

Here I show you how to join two lists.

I also show you how to insert, replace and delete parts of lists.

Here I show you the difference between the Split[...] and Partition[...] function

Here I show you how to use lists to do set calculations:

I show you how to intersect and unionize(?) sets.

I show you how to delete duplicates in a list and how to take the powerset of a list.

Finally I show you how to take the Cartesian product of two sets, using the Combinatorica package.

Here I show you how make tables:

I show you how make tables using a basic equation.

How to loop using the Table[...] function

How make lists with depth n, where n >2

Here I show you how to draw basic plots using Mathematica. I show you how to draw 2D Cartesian Graphs.

Here I show you how to plot Parametric2D. I show you common Parametric graphs.

Here I generalize the concept of plotting graphs to plotting multiple graphs in Mathematica.

In this course, I show you how to Polar equations, and show you the plots of common polar equations.

In this video, I show you how to draw 3D functions, given three parameters, basically I draw space curves and show you how to do it.

In this equation I show you how to draw surfaces, given two parameters and how to plot surfaces in general.

Here I introduce the concept of contour plotting, both 3d and 2d using ContourPlor[ ] and ContourPlot3D[ ] respectively.

Here I introduce spherical plots.

Here I show you two common options for plotting graphs: PlotRange and AspectRatio and how you can use them to adjust a plot.

Here I introduce the concept of shading graphs and how you can shade top or bottom and shade between two graphs.

Here I show you how to label a graph, including its axes and how to adjust the ticks on a graph.

Here I show you how to change the PlotStyle of a graph. Basically how to colour individual graphs, how to adjust thickness of plots and how to adjust the style (dotted vs solid) of plots.

Here i show you some 3D options for plots, including the BoxRatio, the ViewPoint and how to change the color of graphs.

Here I introduce the Limits capability of Mathematica. I show you how it can approach a limit from two sides, I also show you assumptions in limits.

Here I show you how Mathematica takes derivatives, including some fairly complex ones.

Here I show how Mathematica can calculate the anti-derivative of an expression, including definite, indefinite and improper.

Here I show you how Mathematica can perform the Laplace transform, of constant, and expressions, including some fairly complex ones.

Here I show how Mathematica can solve differential equations, first, second, linear, ordinary and partial.

Here I show you how Mathematica handles matrices. The proper way to input matrices into Mathematica.

Here I show you how to enter special matrices into Mathematica. This includes, diagonal, identity, using the Table[ ] function and using sparsearrays.

Here I show you simple stuff like finding the determinant and the inverse of a 2x2 matrix.

Here I show you even more advanced stuff like row reducing, finding the rank and the eigenvalues and eigenvectors of a matrix

Here I give a brief introduction to vectors and how Mathematica handles them. Basically the conventions Mathematica uses when handling vectors.

Here I show common functions on vectors like norm, projection, orthogonalization etc.

Here I introduce the concept of plotting vector fields in 2D and 3D using the VectorPlot and VectorPlot3D functions

Here I show you how Mathematica calculates, Grads, Curls and Divergences of a vector field.

Here I show you a bonus lesson. The lesson is on the Manipulate function and how it can be used to add interactivity to any calculations. I use it to dynamically calculate the best angle to throw something in order for it to land the farthest.