 ## Mathematics & Science Learning Center Computer Laboratory

### Mathematica Basics—Contents

The following menu contains a list of mathematical topics that you may learn how to deal with by using the Mathematica environment. Their treatment is somewhat sequential, though you may be able to skip certain topics with the guidance of your instructor.

 The Environment A whirlwind tour of the Mathematica interface, built-in help, and shortcuts. Arithmetic A very quick coverage of the overall layout of a Mathematica notebook window, and the basics of doing arithmetic in Mathematica. Using Variables A brief overview of Mathematica's peculiarities in naming and assigning values to its variables. Working with Lists A guide to forming and manipulating the list construct in Mathematica. Vectors & Matrices Naming, forming, formatting and manipulating vectors and matrices in Mathematica. Algebraic Ops I Basic operations on polynomials and algebraic fractions. Partial fractions. Immediate versus delayed assignment of values to variables. Substitution and evaluation. Algebraic Ops II Defining equations in Mathematica. Solving equations exactly and numerically. Dealing with systems of equations. Poorly conditioned equations. Functions The anatomy of function definitions. The importance of each of the definition's parts. Functions of more than one variable. Calculus Ops I Taking limits. Total, implicit, and partial derivatives. Calculus Ops II Taking indefinite and definite integrals. Numerical integration. Generating the Taylor series of a function, and manipulating infinite series. Graphics I Plotting functions in two dimensions using Mathematica. Controlling the look of the final picture. Graphics II Plotting functions parametrically. Polar plots. Graphics III Plotting functions of two variables using contour, density, and three dimensional plots. Main Table of Contents for All ODE Laboratories

ODE Laboratories: A Sabbatical Project by Christopher A. Barker

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