Specific information about this course and its requirements can be found below. For more general information about taking Saylor Academy courses, including information about Community and Academic Codes of Conduct, please read the Student Handbook.
Get a detailed introduction to functions, graphs, limits, continuity, and derivatives, and explore the relationship between derivatives and graphs.
Calculus can be thought of as the mathematics of change. Because everything in the world is changing, calculus helps us track those changes. Algebra, by contrast, can be thought of as dealing with a large set of numbers that are inherently constant. Solving an algebra problem, like, merely produces a pairing of two predetermined numbers, although an infinite set of pairs. Algebra is even useful in rate problems, such as calculating how the money in your savings account increases because of the interest rate , such as , where is elapsed time and is the initial deposit. With compound interest, things get complicated for algebra, as the rate is itself a function of time with . Now we have a rate of change which itself is changing. Calculus came to the rescue, as Isaac Newton introduced the world to mathematics specifically designed to handle those things that change.
Calculus is among the most important and useful developments of human thought. Even though it is over 300 years old, it is still considered the beginning and cornerstone of modern mathematics. It is a wonderful, beautiful, and useful set of ideas and techniques. You will see the fundamental ideas of this course over and over again in future courses in mathematics as well as in all of the sciences (like physics, biology, social sciences, economics, and engineering). However, calculus is an intellectual step up from your previous mathematics courses. Many of the ideas you will gain in this course are more carefully defined and have both a functional and a graphical meaning. Some of the algorithms are quite complicated, and in many cases, you will need to make a decision as to which appropriate algorithm to use. Calculus offers a huge variety of applications and many of them will be saved for courses you might take in the future.
This course is divided into five learning sections, or units, plus a reference section, or appendix. The course begins with a unit that provides a review of algebra specifically designed to help and prepare you for the study of calculus. The second unit discusses functions, graphs, limits, and continuity. Understanding limits could not be more important, as that topic really begins the study of calculus. The third unit introduces and explains derivatives. With derivatives, we are now ready to handle all of those things that change mentioned above. The fourth unit makes visual sense of derivatives by discussing derivatives and graphs. The fifth unit introduces and explains antiderivatives and definite integrals. Finally, the reference section provides a large collection of reference facts, geometry, and trigonometry that will assist you in solving calculus problems long after the course is over.
This course includes the following units:
Upon successful completion of this course, you will be able to:
Throughout this course, you will also see learning outcomes in each unit. You can use those learning outcomes to help organize your studies and gauge your progress.
The primary learning materials for this course are articles, lectures, and videos.
All course materials are free to access and can be found in each unit of the course. Pay close attention to the notes that accompany these course materials, as they will tell you what to focus on in each resource, and will help you to understand how the learning materials fit into the course as a whole. You can also see a list of all the learning materials in this course by clicking on Resources in the navigation bar.
Only the final exam is considered when awarding you a grade for this course. In order to pass this course, you will need to earn a 70% or higher on the final exam. Your score on the exam will be calculated as soon as you complete it. If you do not pass the exam on your first try, you may take it again as many times as you want, with a 7-day waiting period between each attempt. Once you have successfully passed the final exam you will be awarded a free Course Completion Certificate.
There are also problem sets and other assessments in this course. These are designed to help you study, and do not factor into your final course grade. You can take these as many times as you want until you understand the concepts and material covered. You can see all of these assessments by clicking on Quizzes in the course's navigation bar.
This course is eligible for college credit via Saylor Academy's Direct Credit Program. If you want to earn college credit, you must take and pass the Direct Credit final exam. That exam will be password protected and requires a proctor. If you pass the Direct Credit exam, you will receive a Proctor Verified Course Certificate and be eligible to earn an official transcript. For more information about applying for college credit, review the guide to college credit opportunities. Be sure to check the section on proctoring for details like fees and technical requirements.
There is a 14-day waiting period between attempts of the Direct Credit final exam. There is no waiting period between attempts for the not-for-credit exam and the Direct Credit exam. You may only attempt each Direct Credit final exam a maximum of 3 times. Be sure to study in between each attempt!
MA005: Calculus I is a self-paced course, which means that you can decide when you will start and when you will complete the course. There is no instructor or an assigned schedule to follow. We estimate that the "average" student will take 122 hours to complete this course. We recommend that you work through the course at a pace that is comfortable for you and allows you to make regular progress. It's a good idea to also schedule your study time in advance and try as best as you can to stick to that schedule.
Learning new material can be challenging, so we've compiled a few study strategies to help you succeed:
This course is delivered entirely online. You will be required to have access to a computer or web-capable mobile device and have consistent access to the internet to either view or download the necessary course resources and to attempt any auto-graded course assessments and the final exam.
For additional guidance, check out Saylor Academy's FAQ.
This course is entirely free to enroll in and to access. Everything linked in the course, including textbooks, videos, webpages, and activities, is available for no charge. This course also contains a free final exam and course completion certificate.
This course also has an optional final exam that can give you an opportunity to earn college credit. This exam requires the use of a proctoring service for identity verification purposes. The cost for proctoring for this optional exam is $25 per session.