Mathematica 9 for Beginners

A course that teaches Mathematica 9 for beginners to the software. It teaches Mathematica for college and high school
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  • Lectures 53
  • Contents Video: 9 hours
  • Skill Level Beginner Level
  • Languages English
  • Includes Lifetime access
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    Available on iOS and Android
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About This Course

Published 1/2014 English

Course Description

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:

Follow me on Twitter @2shakilrafi

What are the requirements?

  • A version of Wolfram Mathematica 9
  • A textbook on Pure Mathematics in General

What am I going to get from this course?

  • To teach you how to do arithmetic using Mathematica
  • To teach you how to handle algebra using Mathematica
  • To teach you how to draw basic graphs using Mathematica
  • To teach you how to adjust graphs using Mathematica
  • To teach you how to handle lists using Mathematica
  • To teach you how to handle sets using Mathematica
  • To teach you how to do calculus using Mathematica
  • To teach you how to handle the basics of matrices
  • To teach you how to handle the basics of vectors

What is the target audience?

  • Advanced High School Students
  • High School Students who have Mathematica in their curriculum
  • College students whose major requires Mathematica
  • Math, Science or Engineering Majors who would like to have a valuable skill at their disposal
  • Hobbyists or Enthusiasts who just like to learn a new skill

What you get with this course?

Not for you? No problem.
30 day money back guarantee.

Forever yours.
Lifetime access.

Learn on the go.
Desktop, iOS and Android.

Get rewarded.
Certificate of completion.


Section 1: Bits and Bolts and Bolts and Bits

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:

Music by:

"Pamgaea" Kevin MacLeod (

Licensed under Creative Commons: By Attribution 3.0

4 questions

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

Getting the hang
4 questions
Section 2: Arithmetic a.k.a. your TI-82 has competition

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.

7 questions

Basics of Arithmetic Using Mathematica


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

5 questions

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.

Quiz on Log Function Detailed
5 questions
Trig Functions detailed

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.

Quiz on Trig Functions detailed
6 questions
Section 3: Algebra a.k.a now your professor has competition

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.

6 questions

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

Variable substitution
3 questions

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

Algebraic Manipulation
6 questions

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

5 questions

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

I also define the InverseFunction [...]

5 questions

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

More about solve
2 questions

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

Conditional Solve
2 questions

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

5 questions
Section 4: Lists a.k.a. more than your average shopping list

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

Intro to Lists
5 questions

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

Functions on Lists
2 questions

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

Functions between two lists
5 questions

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.

Getting info out of lists
5 questions

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.

Searching Lists
5 questions

Here I show you how to join two lists.

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

Manipulating Lists
5 questions

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

Partitioning Lists
2 questions

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.

Lists as Sets
5 questions

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

2 questions
Section 5: Drawing Graphs a.k.a. making calculations pretty

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

2D Cartesian Graphs
4 questions

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

2D Parametric
2 questions

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

Plotting Multiple Graphs
2 questions

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

2D Polar
2 questions

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.

3D Parametric and Surfaces
6 questions

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

Contour Plotting
3 questions

Here I introduce spherical plots.

Spherical Graphs
1 question

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

PlotRange & AspectRatio
4 questions

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

Shading 2D Graphs
2 questions

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

Labeling and Ticks
5 questions

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.

2 questions

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

Some 3D options
5 questions
Section 6: Calculus a.k.a the coolest sounding branch of Mathematics

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.

5 questions

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

6 questions

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

4 questions

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

Laplace Transform
3 questions

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

Differential Equations
1 question
Section 7: Matrices and Vectors a.k.a Neo and a Mosquito walks into a bar...

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.

Intro to Matrices
5 questions

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

More about Matrices
3 questions

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

Even more about Matrices
3 questions

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

Introduction to Vectors
5 questions

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

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Instructor Biography

Shakil Rafi, Math Tutor, Mathematician in Training

Hi there!

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 !

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