- Course Type CLEP
- Subject Science and Mathematics
- Level Introductory
- Length 10 Modules
- Effort 6 Hours/Module
- Institution Modern States
ABOUT THIS COURSE
It reviews the fundamentals taught in a one-semester college course in calculus. Our lessons are aligned to the content of the CLEP exam, which covers approximately 60% limits and differential calculus and 40% integral calculus. Our goal as creators of this course is to prepare you to pass the College Board’s CLEP examination and obtain college credit for free.
“Now more than ever, mathematics is a subject that opens doors-doors to new career opportunities and new intellectual worlds” explains Dr. James Murphy, professor at Tufts University, and instructor of this course.
“Calculus” is a completely self-paced course. It has no prerequisites and it is offered entirely for free.
Instructors
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James Murphy, Ph.D.Professor, Tufts University
Course Overview
Calculus Course Overview - Modern States
| Module | Topic | Video Length | Reading Pages |
| Module 1: Limits (10%) 00:55:55 total video length 84 total reading pages |
1.0 Introduction | 0:02:01 | – |
| 1.1 Definition of a Limit | 0:11:10 | 19 | |
| 1.2 Computing Basic Limits | 0:18:18 | 44 | |
| 1.3 Continuity | 0:15:32 | 15 | |
| 1.4 Squeeze Theorem | 0:08:54 | 6 | |
| Module 2: Theory of the Derivative 02:46:04 total video length 161 total reading pages |
2.0 Introduction | 0:02:21 | – |
| 2.1 Tangent Lines | 0:08:34 | 18 | |
| 2.2 Definition of Derivative | 0:16:14 | 15 | |
| 2.3 Rates of Change | 0:13:55 | 12 | |
| 2.4 Derivative Rules | 0:01:59 | – | |
| 2.4.1 Fundamental Derivative Rules | 0:16:44 | 19 | |
| 2.4.2 Chain Rule | 0:16:02 | 12 | |
| 2.4.3 Derivatives of Exponential and Logarithmic Functions | 0:13:03 | 15 | |
| 2.4.4 Trigonometric Derivatives | 0:13:17 | 10 | |
| 2.4.5 Derivatives of Inverse Trigonometric Functions | 0:08:19 | 4 | |
| 2.5 Higher Order Derivatives | 0:12:58 | 2 | |
| 2.6 Implicit Differentiation | 0:15:41 | 10 | |
| 2.7 L’Hôpital’s Rule | 0:12:59 | 18 | |
| 2.8 Some Classic Theoretical Results | 0:06:48 | 16 | |
| 2.9 Derivatives of Inverse Functions | 0:07:10 | 10 | |
| Module 3: Applications of the Derivative 01:09:18 total video length 101 total reading pages |
3.0 Introduction | 0:02:14 | – |
| 3.1 Plotting with Derivatives | 0:01:22 | – | |
| 3.1.1 Increasing and Decreasing Functions | 0:15:57 | 32 | |
| 3.1.2 Extrema | 0:15:49 | 13 | |
| 3.1.3 Concavity | 0:10:52 | 17 | |
| 3.2 Rate of Change | 0:12:00 | 25 | |
| 3.3 Some Physics Problems | 0:11:04 | 14 | |
| Module 4: Theory of the Integral 01:30:45 total video length 128 total reading pages |
4.0 Introduction | 0:02:14 | – |
| 4.1 Antidifferentiation | 0:09:37 | 21 | |
| 4.2 Definite Integral | 0:09:28 | 20 | |
| 4.3 Riemann Sums | 0:00:45 | 21 | |
| 4.3.1 Riemman Sums Part I | 0:10:40 | – | |
| 4.3.2 Riemman Sums Part II | 0:06:02 | – | |
| 4.4 The Fundamental Theorem of Calculus | 0:14:43 | 17 | |
| 4.5 Basic Integral Rules | 0:01:08 | 18 | |
| 4.5.1 Basic Integral Rules I | 0:09:09 | 12 | |
| 4.5.2 Basic Integral Rules II | 0:11:22 | 8 | |
| 4.6 U-Substitutions | 0:15:37 | 11 | |
| Module 5: Applications of the Integral 00:52:55 total video length 43 total reading pages |
5.0 Introduction | 0:01:59 | – |
| 5.1 Area Under Curves | 0:01:37 | 12 | |
| 5.1.1 Area Under Curves Part I | 0:08:02 | – | |
| 5.1.2 Area Under Curves Part II | 0:11:10 | – | |
| 5.2 Average Value | 0:08:14 | 2 | |
| 5.3 Growth and Decay Models | 0:10:40 | 11 | |
| 5.4 Return to Physics | 0:11:13 | 18 |
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Student Stories
“It was totally free. I got college credit for all of the CLEP exams and passed all of them on the first try. I loved being able to learn at my own pace. Modern States is amazing.”
“I'm using Modern States to complete my engineering degree in the shortest amount of time possible”
“I can trust Modern States.”
“For 15 credit hours I’ve essentially paid nothing … which has been awesome!”
“All of my undergraduate courses, which I can CLEP out of, will go towards my nursing degree and probably save me close to $15,000.”
“Modern States made it possible to do a five-year degree in four years. It's helping dreams come true.”
“I'd like to thank Modern States for even making this possible to students.”
“It doesn't matter how old you are. You can go back [to school] with the help of Modern States.”
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