This course is an introduction to the concepts of differential calculus. Topics include the calculation of limits and the differentiation of functions including trigonometric, inverse trigonometric, exponential, logarithmic functions, chain rule, and implicit differentiation. Further topics include Rolle's theorem, the mean value theorem, differentials, antiderivatives, partial differentiation, as well as the application of differentiation to related rates, maxima and minima, curve sketching, Newton's method. Emphasis on applications is provided for all topics.
Hours: 60 (Lecture Hours: 3; Laboratory Hours: 1)
Total Weeks: 15
One of Math 100, Math 105, Math 110, “C+” or higher in Principles of Mathematics 12, “C+” or higher in Pre-calculus 12, or C+ or higher in Math 050; alternatively, completion of the Calculus Readiness Assessment.
- Functions and Models
- Limits and Rates of Change
- Inverse Functions
- Applications of Differentiation
- Review some topics in algebra and analytic geometry such as functions and their graphs.
- Study of limits: how they arise as slopes of tangents and rates of change; properties of limits; continuity.
- Study of differentiation: how to calculate derivatives and how to use them to solve problems involving rates of changes
- Statement and applications of the Mean Value Theorem: How to find maximum and minimum values, points of inflection, asymptotes,
and how to use the above information to sketch curves. How to solve maximum and minimum values.
- Use the L'Hospital's Rule to evaluate difficult limits.
- A brief introduction to integral calculus: motivation and definition of definite integrals, use the Fundamental Theorem to evaluate definite integrals, use the Substitution Rule to evaluate indefinite/definite integrals. Use integrals to solve some area problems.
Grading System: Letters
Passing Grade: D (50%)
Percentage of Individual Work: 100
Textbooks are subject to change. Please contact the bookstore at your local campus for current book lists.