Details
Outline
-
Unit 1: Functions, Graphs, and LimitsThis unit begins with a review of functions that should have been learned in a previous course. Specifically, we will examine the relationship between formulas and graphs of functions, as well as general properties of their graphs. After completing the first part of this unit, you should feel comfortable explaining general patterns that occur in certain types of functions, as well as be able to give specific information about a graph given its formula. After studying functions, we will examine the first "big” topic in calculus, the limit. As you will see, much of calculus is based on this concept, so it is important to have a good understanding of its fundamental meaning now. We will study limits as they relate to graphs and formulas, and we will use formal limit notation to explain certain behaviors of graphs that you have studied before (such as continuity), but without the concept of limits. This is a very exciting unit and it is important to understand limits well before moving on to the next part of the course.
-
Unit 2: DerivativesIn this unit, you will learn first the concept of a derivative by explaining it through limits. You will see that the limit definition and computation are drawn out, and often difficult, so you will learn shortcuts to compute derivatives. You will learn to compute derivatives for all different types of functions, as well as for combinations of functions. After you learn how to compute derivatives, you will look at what derivatives tell you specifically at any point in a function, as well as what they tell you about the function as a whole. You will finish this unit by looking at the computation and meaning of second derivatives, as well as real-life applications of derivatives. The main applications to be reviewed in this unit will be related rates problems, optimization problems, and problems involving displacement, velocity, and acceleration.
-
Unit 3: IntegralsIntegrals are the final unit in this course. In a similar way to derivatives, you will approach integrals first by learning their formal definition, then by learning techniques by which to compute them, and then lastly learning about their applications. In this unit, you will also learn the FTC (fundamental theorem of calculus), learn to solve basic differential equations, and also learn some cool approximation techniques. One of the reasons this unit is really interesting is because of all the cool images that can be generated using integrals. You will see what this means very soon!
-
Course Evaluation Survey
Please take a few moments to provide some feedback about this course at the link below. Consider completing the survey whether you have completed the course, you are nearly at that point, or you have just come to study one unit or a few units of this course.
Link: Course Evaluation Survey (HTML)
Your feedback will focus our efforts to continually improve our course design, content, technology, and general ease-of-use. Additionally, your input will be considered alongside our consulting professors' evaluation of the course during its next round of peer review. As always, please report urgent course experience concerns to [email protected] and/or our Discourse forums.
-
Final Exam
Saylor Academy’s mission is to open education to all.
Saylor Academy’s mission is sustained by the continued evolution of an open educational ecosystem, and we are dedicated partners in this movement. Saylor’s commitment to the open education ecosystem is founded not just on open educational resources and open source learning technologies, but also on open access to credentials, and ongoing open learning opportunities.
Guided by these beliefs, Saylor Academy is currently focused on the following projects:
Open Courses: Maintenance and Learner-Centered Improvements
- A commitment to the OER community means that we’ll continue to replace open access materials with openly licensed ones in an effort to make Saylor courseware as reusable and remixable as possible.
- Open courses require more instructional supports for learners, so our current improvements focus on ensuring better and more frequent opportunities for Saylor students to practice what they’re learning.
Open Credentials: Adding New Opportunities and Bolstering Existing Ones
- We’re working on expanding our suite of Saylor Direct credit recommended exams, and we’re also keen on working with university partners to develop innovative and flexible partner degree launching and completion programs. ...
