Students read through the lesson notes and watch the accompanying videos before class sessions start (you can find the notes and videos inside the Unit links above). I wrote about this duo in detail in an article I published in 2020 in a mathematics education journal, but here are the takeaways: For everyone else, the short story is that this course is structured in a flipped classroom format with a mastery grading scheme for assessments. It details the additional course policies and the course structure. If you are currently enrolled in this course with me then you've received a copy of the course's syllabus. Finally, you will learn how to become a more independent learner. You will also learn how to pinpoint your areas of academic struggles and develop a plan for resolving them. Learning How to Learn: You will learn about the latest research on cognitive science and how it can help you become a better student. Teamwork: You will learn how to engage in and facilitate open dialogue with classmates and others about mathematics, in ways that are respectful of differences and establish equitable learning environments. This course has been designed to achieve the following learning outcomes by the time you complete the course.įoundational Knowledge: You will recognize, understand, and develop intuition for new mathematical concepts rooted in single-variable calculus.Ĭonnecting Content to Real-World Situations: You will recognize how calculus arises from real-world problems and contexts, and be able to interpret the real-world implications of their solutions.Īpplication Skills: You will learn how to create mathematical models involving calculus that describe a variety of real-world phenomena. This will, in turn, be useful for tackling your science courses and social science courses, many of which involve mathematical analyses and/or modeling. This unit will hone that skill and help you start to think more like an applied mathematician. You no doubt have experience doing this in other mathematics courses (e.g., in math word problems). This is the process of translating a real-world problem into mathematics, solving it, and interpreting your solution in the original real-world context that initiated the process. This unit will also introduce, reinforce, and emphasize mathematical modeling. This content includes a review of solving algebraic equations, various area and volume formulas from geometry, and content related to functions, including the definition of a function, its domain and range, how to graph functions, and various properties and transformations of functions. (We'll return to transcendental functions in Unit 6.) We won't be reviewing all the content from those three areas, just the content most relevant to our calculus studies. This unit reviews the algebra, geometry, and precalculus content we'll need for learning single-variable calculus, in the context of only algebraic functions. Unit 1: Review of Relevant Precalculus Content The prerequisite for the course is ideally a precalculus course, though a strong backgr ound in College Algebra should also work. The course's 26 lessons discuss many, many applications of calculus to real-world phenomena, including in the sciences and social sciences. The resulting journey into calculus is one that begins with a review of precalculus concepts (like functions), proceeds to develop the calculus "Big 3" (limits, differentiation, and integration), and then circles back to transcendental functions to study all those topics for that family of functions. This book (and thus this course) covers all the core topics in Calculus 1 in a way that requires no prerequisite knowledge of transcendental functions (e.g., exponential, logarithmic, and trigonometric functions). Both the content and approach I take come from the calculus book I wrote, Calculus Simplified. In terms of content, this course is essentially div ided into five chunks (see the next section). In other words, can we develop mathematics that describes continuous change? (For example, we certainly know how to calculate the average speed of an object between two times, but how do we calculate the instantaneous speed of the object at a particular time?) The answer is: yes! And the resulting mathematics is called calculus. How can we mathematize continuous change ?
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