Distance Calculus @ Roger Williams University is in full operation during COVID-19 Emergency
Winter Break 2020: Distance Calculus in FULL OPERATION for Winter Break Students!
Winter Break 2020: Finish Your Calculus Course Before Spring 2021!

# Precalculus Online Course with Trigonometry for Academic Credit

Precalculus is a catch-all phrase for all of the algebra and trigonometry usually studied in high school. The topics of any standard Precalculus course will include:

• Solving Equations (both easy and more difficult)
• Linear Equations
• Polynomials
• Factoring Polynomials
• Rational Polynomials
• Functions
• Exponential and Logarithmic Functions
• Trigonometry Concepts
• Trigonometric Functions
• Systems of Equations - Linear and More Complicated Equations
• Complex Numbers
• Equations and Inequalities
• Conic Sections

Completion of the Distance Calculus @ Roger Williams University Math 136 - Precalculus course earns 4 academic credit semester hours, earning an official academic transcript from Roger Williams University, in Providence, Rhode Island, USA, which is regionally accredited by the New England Commission of Higher Education (NECHE), facilitating transfer of credits nationwide to other colleges and universities.

## Online Precalculus Course for College Credit Introductory Video

Distance Calculus @ Roger Williams University - Math 136 - Precalculus is a self-paced, asynchronous, live-lecture-free, high-tech, empirical, investigation-driven approach to the traditional topics of high-school (and lower college) Precalculus.

## The Distance Calculus Approach To Precalculus

Our online Precalculus course Math 136 from Distance Calculus @ Roger Williams University has the following educational assumptions and goals:

Distance Calculus is intended for adult students (although we do have advanced High School students in the upper courses like Multivariable Calculus, Differential Equations, Linear Algebra, and Probability Theory), and our Precalculus course is designed for adult learners - especially those looking to continue into our Engineering Calculus sequence.
• Rote Learning Should Be Left in High School
All Distance Calculus students have already gone through high school. Repeating such a high school "rote skills" Precalculus course seems unlikely to produce success to adult learners
• Computer Algebra and Graphing Throughout The Curriculum
As all Distance Calculus courses are based upon curricula written in LiveMath and/or Mathematica - both powerful computer algebra and graphing systems, we extend these tools in the Precalculus course which change the nature of the curriculum, far more than just using a simple graphing calculator as an ancillary tool to a traditional "rote" curriculum
• Empirical Learning
Instead of a "proofs-based" Precalculus course, we use the powerful computer algebra and graphing platform LiveMath to conduct graphical, numerical, and algebraic experiments - like you would in a biology or chemistry or physics laboratory - to empirically investigate the topics of traditional high school precalculus. "Rote" learning is replaced with investigating the topics much more thoroughly using modern technical tools at a much deeper level, because the "Do these 1-99 odd factoring problems" is now replaced with "Use Factor Command" - and then we ask when we can use factoring, what it does for us, and what do we do when we cannot factor!
• Asynchronous Studying
This means that the course happens on your schedule, not at fixed times. You may work as intensely as you wish, take a break for a week or two, and then resume, all on your needs.
• Mastery Learning
The student will learn the current module of material thoroughly before moving on to the next topic. This eliminates the "slippery slope" problem of not mastering a previous topic when faced with a new topic.
• Synchronous Communications
The majority of communcation between the student and the instructors will occur via Chat, so that problems, questions, issues, that come up are solved in real time.
• ChalkTalk Video
Video presentations of problems solved manually, "by hand", providing the basis of the classical study of precalculus topics - we have a balance of 80% Computer Algebra and 20% By Hand Manual Computations split of the problems. There are core problems that all students who complete a Precalculus course should be able to do by hand, which is reinforced by the Computer Algebra assignments.

## Examples of Distance Calculus Unique Approach in Precalculus

Many prospective students will have completed Algebra at some level in high school, perhaps many years ago, and they are looking for a comprehensive course on Precalculus before they start the Engineering Calculus I sequence. Below we list a few topics that demonstrate the enhanced curriculum of our Precalculus course, which studies the same topics as high school Algebra and Trigonometry, but we are able to go to much deeper levels of investigation because of the usage of the computer algebra platform LiveMath.

• Factoring A Polynomial By Graphing Analysis
Factoring is now made rather trivial using LiveMath's Factor command:
You would never attempt to factor such a polynomial in high school algebra class by hand! After we make the standard connection to the x-axis crossings/touches for this polynomial function graphed:
We then ask the question in reverse:
Suppose you are given the graph of a function whose algebraic formula you do not know - can you reconstruct the algebraic formula (assuming it is a polynomial function) from just the graph?

• How Complex Roots Affect A Polynomial Function Graph
Here's what looks to be a degree 4 polynomial function - can we find its algebraic formula?
Only problem is: there are only 2 real x-axis crossings! That function wiggles, but not far enough down to actually cross the x-axis! Turns out this wiggle is the affect of complex roots at work. But we can still analyze this graphically by vertically translating the graph down to force that wiggle to cross the x-axis (and cross at nice roots, too!):
From that translation we can get 4 real roots, create the factorization, and then ... don't forget ... reverse the vertical translation back up, and voila!

• Conic Sections - Parabolas in 3D Animations
Remember parabolas, hyperbolas, ellipses in high school algebra? Well, they never looked this cool in 3D animations on those little TI-83 calculators!
In our Precalculus course, the equations and analytical geometry study of parabolas, hyperbolas, and ellipses takes on a 3D feel, where we study much harder problems: how do we convert these slicing equations into standard form, and rotate everything "just so" to get the standard equations to pop out?

## Other Online Precalculus Courses vs. Distance Calculus

The Distance Calculus Precalculus course was created as a support course for our Calculus I - Engineering Calculus sequence. Many students who need to complete Calculus I or higher in the engineering sequence are often not prepared for starting Calculus I - especially the considerably-different Calculus I course offered via Distance Calculus.

There are many Precalculus courses available around the internet. In almost all cases, these other Precalculus courses are just a re-hash of the high school algebra II and trigonometry experience - more of the same - endless hand-calculation problem sets ("1-99 odd"), perhaps with usage of a graphing calculator (high school Precalculus courses now routinely include the Texas Instrument TI-83 or similar graphing calculators), and probably with a multiple choice engine where your instructor becomes an automated machine checking answers instead of a human being.

These other online Precalculus courses all share the same process: a paper or e-paper textbook is provided to the student, and long problem sets of factoring polynomials, applying the quadratic formula, interpreting word problems into solvable equations, etc.

The Educational term for these courses is: learning by rote - doing a hand-technique over and over again, until the technical process is imprinted in your mind. Many students who go through these types of precalculus courses are so trained that when they see an equation like the following:

x2 + 5x - 8 = 0
They immediately say "Oh, I know the quadratic formula:"

$$\frac {-b\pm\sqrt{b^2 - 4ac}}{2a}$$

But often these students are completely stumped what to do if the equation instead looks like this:

x3 + 5x + 8 = e2x
There often is a disconnect between generally solving equations for (numerical) solutions, and applying (historical) formulas that work only in special cases (purely quadratic equations).

Many students are very successful at "rote" Precalculus courses. As almost all of the other Precalculus courses on the internet are exactly these "rote" courses, if you are looking for such a "plug-and-chug" Precalculus course, you have many options, and Distance Calculus is not for you.

If, on the other hand, diving back into another high-school-like Precalculus "rote" course does not sound appealing to you, then read on about our Distance Calculus online Precalculus course,.

## Roger Williams University Course Catalog Listing - Math 136 - Precalculus

MATH 136: Precalculus [4 credit hours]

Course Description: The focus of this course is on functions, which are of central importance in Calculus. Topics include definitions, properties, and applications of algebraic, inverse, exponential, logarithmic and trigonometric functions.

Prerequisite: High School Algebra

### Precalculus Example Learning Movies

One of the ongoing themes of the Precalculus curriculum is bridging between the classical approach to Precalculus with pen/paper - or chalk on a chalkboard - and using the modern LiveMath computer algebra and graphing platform. Often the video assignments come in pairs, with the same core topic explained in both ChalkTalk format and also in LiveMath format.

## Student Work Assignments

Students will complete a variety of types of homework assignments, including:

• Written Solution Sets
Students will complete written solution sets, take a photo with your phone, and turn them in on-line for grading. These problem sets will be from the classical side of the precalculus curriculum - the "math you need to be able to do by hand."

• Computer Algebra Notebook Solution Sets
Students will complete notebook questions in using LiveMath software dealing with more modern types of questions in Precalculus requiring technological approaches.

• Video Solution Sets
Students will complete some Video Solutions of various problems, and turn these videos in on-line for grading, expanding upon both types of solution sets with more of a "Now You Explain It".

Similar to our Distance Calculus course structure, this course is based upon heavy amounts of communication between the student and the instructional team. All assignments are based upon the mastery learning model, and turned in recursively back-and-forth between student and instructor until 100% mastery is achieved.

This is an excellent course for the computer novice. Even if checking your email is a not a "natural" activity for you, the Distance Precalculus course is an excellent way to simultaneously prepare for Calculus, and conquer whatever computer "phobia" fears you may have.

## Distance Calculus - Student Reviews

Date Posted: Apr 6, 2020
Review by: Paul Simmons
Courses Completed: Multivariable Calculus, Differential Equations
Review: I took Multivariable and Diff Eq during the summer. The DiffEq course was awesome - very useful for my physics and engineering course. I was unsure about Mathematica at first, but I got the hang of it quickly. Thank you Distance Calculus!
Transferred Credits to: University of Oregon

Date Posted: Jan 13, 2020
Review by: Janice Flores
Student Email: jflores35@knights.ucf.edu
Courses Completed: Calculus II
Review: I highly recommend this course! Dr. Curtis is the best teacher and is ALWAYS willing to work with you to make sure you understand the subject. It was definitely a positive experience and the credits were transferred to my University with no problems! I definitely do not regret it and I had doubts in the beginning but if I had to, I would do it all over again!
Transferred Credits to: University of Central Florida

Date Posted: Jun 21, 2020
Review by: Abdul J.
Courses Completed: Applied Calculus
Review: This was the best class! So much more interesting doing the computer math than a boring lecture class. Diane was so responsive and helpful. I recommend this course.
Transferred Credits to: Villanova University