- Course Type CLEP
- Subject Science and Mathematics
- Level Introductory
- Length 5 Modules
- Video Length 7h 15m
- Reading Pages 517
- Institution Modern States
ABOUT THIS COURSE
Calculus reviews the core concepts taught in a one-semester college course, including limits, differential calculus, and integral calculus. About sixty percent of the course focuses on limits and differential calculus, while the remaining forty percent addresses integral calculus. A working knowledge of algebraic, trigonometric, exponential, and logarithmic functions is recommended.
This is a free, self-paced Modern States course with no prerequisites. It is aligned to the CLEP® Calculus exam and is designed to prepare you to succeed on the test and earn college credit at no cost.
Modern States originally developed this course in collaboration with James M. Murphy, now at Tufts University, Department of Mathematics. Dywayne A. Nicely, Ph.D. of The Ohio State University–Marion Campus supported course enhancements published in 2025.
Course Overview
Calculus Course Overview - Modern States
| Module | Topic | Video Length | Total pages of required reading |
| Module 1: Limits (10%) 00:55:55 total video length 84 total reading pages |
1: Limits | 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 | |
| 1: Summary | – | – | |
| Module 2: Theory of the Derivative 02:46:04 total video length 161 total reading pages |
2: Theory of the Derivative | 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 | |
| 2: Summary | – | – | |
| Module 3: Applications of the Derivative 01:09:18 total video length 101 total reading pages |
3: Applications of the Derivative | 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 | |
| 3: Summary | – | – | |
| Module 4: Theory of the Integral 01:30:45 total video length 128 total reading pages |
4: Theory of the Integral | 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: Riemann Sums Part I | 0:10:40 | – | |
| 4.3.2: Riemann 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 | |
| 4: Summary | – | – | |
| Module 5: Applications of the Integral 00:52:55 total video length 43 total reading pages |
5: Introduction to Applications of the Integral | 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 | |
| 5: Summary | – | – | |
| Course Conclusion | – | – |
