This is an example based course aiming to teach Mathematica at an understandable level to students in college. Advanced high school students, or students whose high school teaches Mathematica will also find this course invaluable.
It assumes no understanding of programming languages, although knowledge, even rudimentary, of C/C++/Java is a plus.
This course does NOT teach Mathematica as a programming language.
This course does NOT teach Mathematics in general. Although a textbook on Pure Mathematics will come in handy for reference.
Any high school textbook that teaches college level Pure Mathematics is recommended. College students may use their course textbooks recommended by their Professor.
Students are expected to:
1. Know basic arithmetic and algebra including basic transcendental functions (exponential and trigonometric)
2. Know what a function is, including function composition, inverse and the definition of one-to-one functions
4. How to solve equations and inequalities.
3. Know common graphs of functions
4. Basic knowledge of set theory (preferably including partitioning and powersets)
5. Knowledge of matrices and vectors, preferably also knowledge of vector fields.
6. Rudimentary knowledge of 3D functions and functions on more than one variable
7. A broad knowledge of calculus including the basics of differential equations
8. Rudimentary knowledge of complex numbers
This course is in no way affiliated with Wolfram Research, Inc. The software, the Mathematica trademark and the associated logo belongs to Wolfram Research, Inc.
ScreenFlow, the software and associated trademarks belong to Telestream, Inc.
To contact me please e-mail: email@example.com
Follow me on Twitter @2shakilrafi
This video, introduces who I am [Shakil Rafi] and to what Mathematica is.
Here I explain the fact that chances are your college/university will have a site license. What that means is that your college has probably bought a bulk license for Mathematica, and its students can access it for the low, low price of zero, ask your academic advisor.
If your college does not have a site license, you can still get it though, but you will need to verify your studenthood by entering your college email id: firstname.lastname@example.org
"Pamgaea" Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0
In this video I show you how the course is arranged:
1. Arithmetic (+,-,*,/,N,Trig,Exp)
2. Algebra (Manipulation and how to solve algebraic expressions)
3. Lists (defining lists, changing them, getting information out of them)
4. Graphs (how to draw the most common types and how to adjust them)
5. Calculus (differentiation and integration, including differential equations and the laplace transform)
6. Matrices and Vectors (matrices and vectors and how to perform operations on them.
There is a quiz after almost all of these lectures, so beware!
Here I also introduce the concept of notebooks and how to save notebooks:
Some basic keys that my software, ScreenFlow will record for me is also shown
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.
Basics of Arithmetic Using Mathematica
Here I show you the fact that the N function can evaluate to any number of decimal figures.
This is a quiz on the "N function detailed lecture"
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.
I am a Math Major at Troy University in Alabama. I am currently a Junior and I have been using software to do my math for me for quite a while. Partly because its easy and partly because my course requires it. I will be instructing you on Mathematica 9. Have a blast !