Course Description
Students will use the derivative to understand the behavior of functions and will discuss the limit, the derivative, and the antiderivative, both conceptually and computationally, culminating in the Fundamental Theorem of Calculus. Students will use calculus concepts to model and solve problems in science and engineering, with emphasis on graphs, optimization, and basic integration.
Athena Title
Calculus I for Sci and Eng
Equivalent Courses
Not open to students with credit in MATH 2250
Non-Traditional Format
This course will be taught 95% or more online.
Prerequisite
MATH 1113 or permission of department
Semester Course Offered
Offered summer semester every year.
Grading System
A - F (Traditional)
Course Objectives
At the end of the semester, a successful student will be able to: 1. Calculate and interpret basic trends, rate, and accumulation using the limit, the derivative, and the integral, respectively. 2. Use a function’s graph to: a. Identify increasing/decreasing behavior and critical numbers of the first or second derivative of the function b. Identify extrema c. Determine limits d. Identify points of continuity/discontinuity e. Identify asymptotes f. Identify points where the function is/is not differentiable 3. Use information (a formula or table and/or first or second derivative, etc.) about a function to predict: a. Behavior of the function and/or its first or second derivative b. Extrema c. Limits d. Points of continuity/discontinuity e. Asymptotes f. Points where function is/is not differentiable g. Area under the curve, net area under the curve, or area/net area between two curves 4. Apply calculus to solve an application problem by selecting an appropriate model, identifying an appropriate calculus technique, using the calculus technique on the model to solve the problem, and interpreting the solution in context. 5. Effectively communicate mathematics, in writing and orally, with their peers and with the course instructor.
Topical Outline
1. Rates of Change and Tangents to Curves 2. Limit of a Function/Limit Laws 3. One-Sided Limits 4. Continuity 5. Limits Involving Infinity/Asymptotes 6. Tangents and the Derivative at a Point 7. The Derivative as a Function 8. Differentiation Rules 9. Derivative as Rate of Change 10. Derivatives of Trig Functions 11. The Chain Rule 12. Implicit Differentiation 13. Derivatives of Inverse Functions, Logs 14. Derivatives of Inverse Trig Functions 15. Related Rates 16. Linearization and Differentials 17. Extreme Values 18. Mean Value Theorem 19. Monotonic Functions and the First Derivative Test 20. Concavity and Curve Sketching 21. Indeterminate Forms and L'Hopital's Rule 22. Curve Sketching 23. Applied Optimization 24. Antiderivatives 25. Areas/Finite Sum Estimates, Sigma Notation, Limits of Finite Sums 26. The Definite Integral 27. The Fundamental Theorem of Calculus 28. Indefinite Integrals and Substitution 29. Substitution and Areas Between Curves
General Education Core
CORE I: FoundationSyllabus