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. These discussions, however, are in separate sections that can be skipped for instructors who prefer to wait until the integral definitions are given before teaching the calculus derivations of exponentials and logarithms.How can we mathematize continuous change ? Differentiation and integration of these functions is covered in Modules 3–5 for instructors who want to include them with other types of functions. Exponential and logarithmic functions are introduced informally in Module 1 and presented in more rigorous terms in Module 6. Important note: Calculus 1 is designed to accommodate both Early and Late Transcendental approaches to calculus. Calculus 3 (coming soon) covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integrations, and second-order differential equations.Calculus 2 (coming soon) covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.Calculus 1 covers functions, limits, derivatives, and integration.This course is designed to be used as part one of a three-part calculus sequence: Together these measures reduce uncertainty for instructors as they work through the impact of COVID-19 on course design and instruction. Careful attention to content and platform accessibility ensures the course works well for individuals with varying abilities. The course can also be used in terms or semesters of various lengths. Thoughtful, evidence-based learning design and a digital-first flexible format make OHM course materials effective in any modality (e.g. OHM for Calculus I is a great option for the many institutions and faculty who have shifted towards remote instruction. All content is constructed around the goal of helping students master the learning outcomes for this course. Faculty can adapt and use these materials in a variety of ways depending on their class structure and institutional requirements. Keeping student engagement in mind, we have created a full suite of thought-provoking assignments: discussion prompts, Desmos interactives, application-based assignments (in relation to economics, computer science, biology, physics, and engineering), flipped classroom options, and a capstone project. The course includes embedded algorithmically generated practice questions, worked-example videos, and a complete set of outcome-aligned online assessments in OHM.įor even more practice opportunities, there are problem sets for each section and an activity for each module. Additionally, just-in-time reviews of essential math concepts appear throughout the text to help those students who need further learning support. Each module begins with a prerequisite material review section, in which critical skills from Precalculus and College Algebra are revisited. Lumen has curated, designed, and built additional resources to enhance both the teaching and learning experience. The primary text for this course is Calculus Volume 1 from OpenStax.
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