# Pre-Packaged Courseware

Mathable has many turn-key courseware ready for you to start teaching and mentoring your students right away. The content includes all the lessons and homework problems your students will need which combined with your help and feedback can help them learn the subjects very deeply. You can make changes, mix-and-match content to fit your needs, or write your own course from scratch. Here are some courseware suggestions for typical courses taught at higher education institutions:

## Math Before Calculus

With a focus on looking forward to what lies ahead in calculus, this course is based on studying the behavior of functions with a look at how functions grow, including percentage growth. Topics include: how to read the plot of a function; the difference between formulas and equations; when estimates are preferable to exact answers; proportion and scaling; raw growth versus percentage growth; extensive experience in functions that are used in engineering and science: linear, exponential, oscillating and power functions; frequency versus period; linear and exponential data analysis; area measurement estimation; radians; unit circle; imaginary numbers; modeling linear, exponential and periodic data; linear estimation; rotations and reflections; right triangle trigonometry; inequalities.

Math Before Calculus (MBC) is designed to address several issues. For students who have been enjoying their school math, this course is an opportunity to learn what is important at the university level before they get to the university. For students who have been turned off by school math, this course is an opportunity for a new start and a fast track to the math (in context) that actually arises in science, engineering, technology, and in the workplace. In MBC, the understanding students get through visualization and experimentation minimizes the need for memorization. In MBC, only after an issue has been set up visually do the words go on. Using interactive lessons and the power of Mathematica, students in this course will learn hands-on through experimentation.

Courseware: Math Before Calculus

**Calculus 1**

A first course in calculus; including the basic techniques of differentiation, integration and parametric functions, including parameterization of circular and elliptical functions. The course starts with data based questions about growth, moves on to average growth, and then to derivatives via instantaneous growth rates. Coverage of the Race Track Principle, the mean value theorem and the fundamental formula of calculus. There’s a heavy introductory dose of differential equations to help internalize the idea that derivatives measure growth. Treatment of accumulation for measuring area leads into integration and antiderivatives. The course includes all types of functions, linear, exponential, polynomials, trigonometric as well as functions defined by datafitting.

Courseware: Depending on the length of teaching term and course syllabus, you may wish to extract contents from Calculus:Book 1 – Growth and/or Calculus:Book 2 – Accumulation to build your course materials.

## Calculus 2

Second course in calculus; continues with techniques of integration, parametric plotting, polar coordinates, and infinite series. Series is motivated through the use of splines and continues on to power functions and Taylor series.

Courseware: Depending on the length of teaching term and course syllabus, you may wish to extract contents from Calculus:Book 2 – Accumulation and/or Calculus:Book 3 – Approximation to build your course materials.

## Calculus 3

This is a combined course in calculus of several variables, and a course in what has been called Advanced Calculus for Engineers, or Vector Calculus. The emphasis is on gradients and what they measure, flows and how you analyze them, and the famous integral theorems of Gauss and Stokes. This is where the power of Mathematica really shines. The two and three dimensional graphics capabilities of the software make these ideas come to life.

Courseware: Vector Calculus

## Differential Equations

Intended for engineering students and others who require a working knowledge of differential equations; included are techniques and applications of ordinary differential equations and an introduction to partial differential equations. Topics include: exponential differential equations; oscillators, Laplace Transforms and Fourier approximations; first order differential equations; system flow; linear systems; non-linear systems; linearization of systems; heat and wave equations.

Courseware: Differential Equations

## Linear Algebra

A graphically oriented introductory linear algebra course with a focus is on matrix action, the geometry of matrix action, and the underlying reasons for what we see, how we solve, and what makes it all work. The foundation is the singular value decomposition of matrices. Topics include: perpendicular frames; 2D, 3D and beyond 3D matrices; ill-conditioned matrices and round-off; subspaces; span; dimension; eigenvalues; eigenvectors, diagonalization; Spectral Theorem; function spaces; and RMS approximation.

Courseware: Matrices & Geometry

## Probability & Statistics

Introduction to the study of statistics and probability, but based upon the usage of Calculus to study both discrete and continuous aspects of the subject. A thorough and advanced investigation of the subject matter. The usage of the powerful computer algebra and graphing system Mathematica™ allows for a unique exploration of distributions – both discrete and continuous – and their application to the cornerstone of the subject – the data set from a real-world situation. Includes the calculus of probability, combinatorial analysis, random variables, expectation, distribution functions, moment-generating functions, and central limit theorem. Students should have completed the prerequisite of multivariable calculus before attempting this course.

Courseware: Probability & Statistics