Calculus I Essentials


Thinkwell's Calculus I Essentials with Professor Edward Burger

This brief course reviews key concepts your student saw their Calculus course at home or in school.  It is not intended to replace a full-year Calculus course.  

This short review course can be completed in less than 40 days. It's a perfect fit for anyone wanting to prepare for high-stakes tests in Calculus like the Calculus AP AB exam, or the Calculus CLEP exam.  It's also a great way to enhance your foundation before taking a calculus class at college. 

Taught by award-winning mathematician and professor Edward Burger with online videos, automatically graded exercises, step-by-step explanations, and sample worked problems, this short-form course has everything your student needs to succeed. 

Course Features

Video Lessons

75+ engaging video lessons
View Sample Video


Auto-Graded Assessments
View Sample Assessment


Notes and Sample Problems
View Sample Notes

Certificate of Completion

Certificate of Completion
View Sample Certificate
What Parents Are Saying...
Thinkwell Math is the most amazing high school level math! I searched for years for a curriculum that would meet the needs of vigorous learning and an understanding of difficult concepts...When shown to a local AP Teacher who was doubtful of our AP Calculus homeschool curriculum she said, "He's good! If they learn from this, they don't need my class!"”
– Mrs B.
"We've used Thinkwell for a number of years now, starting with Pre-Algebra and going up to Algebra 2. We all love watching Professor Burger's video lectures. They are long enough to explain things well, and he is not only a great teacher but also very entertaining, which is a huge benefit when trying to learn topics such as linear functions! The content is very rich. I like how there is a pencil and paper component to each lesson. All in all, a terrific program that we've been very happy to use!”
– Becky
"After reluctantly persevering with a couple of other math programs, we finally found Thinkwell. The humorous lectures are concise, easy to understand and delivered in manageable sizes. We don't have to endure the tedious repetition found in so many other programs. Having lessons online is a win for our family - this medium is so acceptable for the current generation. Doing the exercises online saves us a lot of time because the marking and correction is done immediately. Now that we've found Thinkwell we're staying with it.”
– Judy N.
"We have used Thinkwell for two school years now, 7th and 8th Math, as well as Geometry and Algebra 2. It is the favorite math program with both my son and daughter. They enjoy the teacher and his presentations, and feel they are very clear and complete. The few times we have been stumped and unable to understand, we have sent questions in and received prompt, clear answers. For us, Thinkwell has been a blessing, and we intend to continue to use it for the rest of our math needs. We have also shared this news with our friends, and several have also been won over to the Thinkwell side!”
– DeLena J.
Course Overview

What You Get

  • 3-month, online subscription to our complete Calculus I Essentials course
  • 75 course lessons
  • Automatically graded drill-and-practice exercises with step-by-step answer feedback
  • Downloadable, printable course study notes & sample problems
  • Automatically graded quizzes
  • Skills assessment test with personalized study path feedback
  • Animated interactivities....and more!

How It Works

  • Purchase Thinkwell's Calculus I Essentials through our online store and activate your 3-month subscription when you're ready
  • Take a brief diagnostic that creates a fast-track plan for topics where your student might need work
  • Access your course anytime, anywhere, from any device
  • Your work is automatically tracked and updated in real-time
  • Transcripts, grade reports, and certificates of completion are available upon request
  • Need more info? Download our How This Course Works guide
Learn From Award-Winning Professor and Mathematician, Dr. Edward Burger

It's like having a world-class college professor right by your side.

  • "Global Hero in Education" by Microsoft Corporation
  • "America's Best Math Teacher" by Reader's Digest
  • Robert Foster Cherry Award Winner for Great Teaching
Caculus I Essential Skills Contents
Open All
Close All

Essential Skill Review

Finding Rate of Change over an Interval
One-Sided Limits
The Squeeze Theorem
Continuity and Discontinuity
Evaluating Limits
Limits and Indeterminate Forms
Two Techniques for Evaluating Limits
An Overview of Limits
Finding Instantaneous Velocity
The Derivative
The Slope of a Tangent Line
Instantaneous Rate
The Equation of a Tangent Line


Uses of the Power Rule
The Product Rule
The Quotient Rule
An Introduction to the Chain Rule
Using the Chain Rule
Combining Computational Techniques
The Derivatives of Trigonometric Functions
Derivatives of Exponential Functions
The Derivative of the Natural Log Function
Finding the Derivative Implicitly
Using Implicit Differentiation
Applying Implicit Differentiation

Applications of Differentiation

Acceleration and the Derivative
Solving Word Problems Involving Distance and Velocity
Higher-Order Derivatives and Linear Approximation
Using the Tangent Line Approximation Formula
Newton's Method
The Connection Between Slope and Optimization
The Fence Problem
The Box Problem
The Can Problem
The Wire-Cutting Problem
The Pebble Problem
The Ladder Problem
The Baseball Problem
The Blimp Problem

Derivatives and Curve Sketching

An Introduction to Curve Sketching
Three Big Theorems
Critical Points
Maximum and Minimum
Regions Where a Function Increases or Decreases
The First Derivative Test
Concavity and Inflection Points
Using the Second Derivative to Examine Concavity
The Möbius Band
Cusp Points and the Derivative
Domain-Restricted Functions and the Derivative
The Second Derivative Test
Vertical Asymptotes
Horizontal Asymptotes and Infinite Limits
Functions with Asymptotes and Critical Points


Antiderivatives of Powers of x
Antiderivatives of Trigonometric and Exponential Functions
Undoing the Chain Rule
Integrating Polynomials by Substitution
Integrating Composite Trigonometric Functions by Substitution
Integrating Composite Exponential and Rational Functions by Substitution
More Integrating Trigonometric Functions by Substitution
Choosing Effective Function Decompositions
Approximating Areas of Plane Regions
Areas, Riemann Sums, and Definite Integrals
The Fundamental Theorem of Calculus, Part I
The Fundamental Theorem of Calculus, Part II
Illustrating the Fundamental Theorem of Calculus
Evaluating Definite Integrals

Applications of Integration

Antiderivatives and Motion
Gravity and Vertical Motion
Solving Vertical Motion Problems
The Area between Two Curves
Limits of Integration and Area
Common Mistakes to Avoid When Finding Areas
Regions Bound by Several Curves
Finding Areas by Integrating with Respect to y: Part One
Finding Areas by Integrating with Respect to y: Part Two
Area, Integration by Substitution, and Trigonometry
Frequently Asked Questions

How do Thinkwell "Essentials" courses work?

This short course is designed to ensure your student masters the essential skills of Calculus I. Your student completes an assessment that provides a fast-track plan for the topics they need to complete. Each topic has a 5-10 minute online video lesson with additional exercises and instant correct-answer feedback. With approximately 50 topics in all, the course is self-paced and individualized to each student. Alternatively, you can choose where to start and end or follow the standard table of contents.

When does my 3-month online subscription start?

It begins when you're ready. You can have instant access to your online subscription when you purchase online, or you can buy now and start later.

Does my student get school credit for Thinkwell's Calculus I Essentials?

No, only schools are accredited, and Thinkwell is not a school, though many accredited schools use Thinkwell.

What if my student needs access to the course for more than three months?

We suggest you enroll in Thinkwell's Calculus, which is a 12-month subscription.

Can I share access with more than one student?

The courses are designed and licensed to accommodate one student per username and password; additional students need to purchase online access, which allows parents to keep track of each student's progress and grades.

How long does it take to complete Thinkwell's Calculus I Essentials?

The pace of your course is up to you but should be less than 40 lesson days.

Can I see my grade?

Thinkwell's course software tracks everything your student does. When logged in, your student can click "My Grades" to see their progress.

Can I get a transcript?

You can contact to request a file with your student's grades.

What if I change my mind and want to do a different math course, can I change?

If you discover that you should be in a different course, contact within one week of purchase, and we will move you to the appropriate course.

Can I print the exercises?

Yes, but completing the exercises online provides immediate correct answer feedback and automatic scoring, so we recommend answering the exercises online.

Are exercises multiple choice?

Most of the exercises are multiple choice, and they are automatically graded with correct answer solutions.

Is there a guarantee?

Yes, we offer a full refund within three business days of purchase, no questions asked.

How does my school review this course?

Should your school need to review a Thinkwell course for any reason, have the school contact and we can provide them access to a demo site.

Similar Products