This document provides an overview of the capabilities of Mathematica, including performing numerical calculations with exact or approximate results, evaluating standard mathematical functions, generating 3D graphics and sound, performing algebraic, calculus, and equation solving operations, working with lists, vectors and matrices, and symbolic computation using transformation rules and definitions.

1. Tour of Mathematica
ME 443 Mathematica for Engineers

2. Numerical Calculations
You can do arithmetic with Mathematica just as you would on a calculator.
Unlike a calculator, however, Mathematica can give you exact results.
You can use Mathematica function N to get approximate numerical results.

3. You can find numerical results to any degree of precision.
Mathematica can evaluate all standard mathematical functions.
Here is a root of sin(2x) near x=2.

5. Graphics

6. Here is a three-dimensional surface plot of a function of two variables.

7. This generates a three-dimensional parametric surface. The x, y and z coordinates of points on the surface are specified as a function of the parameters t and u. The space in u Sin[t] denotes multiplication.

8. Here is a more complicated parametric surface.

9. Mathematica allows you to combine different pieces of graphics together. The % stands for the last result; %% for the result before that.

10. Mathematica serves as a graphics language in which you can build up graphics from components.

11. On computer systems with sound output, this generates an 8-second long sound with the specified amplitude as a function of time.

12. Algebra

14. Calculus

16. Solving Equations

18. Lists

20. Vectors and Matrices

23. Transformation Rules and Definitions

26. Advanced Topic: Symbolic Computation