The course will cover fundamentals of analytical geometry, college-level algebra, elements of trigonometry and elementary calculus. An intuitive introduction to the principal ideas of differential and integral calculus will be covered. Topics include limits, continuity, derivatives, and integrals with applications. As part of this course, students will learn to translate verbal problems into mathematical models and apply appropriate calculus techniques to optimize functions developed in mathematical models. Emphasis will be placed upon the use of calculus in solving problems from various areas including business, economics and natural sciences. Students will be assessed not only on the concepts but also on their ability to successfully apply them.
Student Learning Outcomes
On successful completion of the course, students will be able to
- Apply algebraic concepts in business problems such as calculating monthly payments and interest rates and performing break-even analysis
- Recognize differentiation as a way to calculate instantaneous rate of change and apply those methods to calculate speeds of objects and rate of fluid flow at specific instants.
- Utilize differentiation techniques to determine incremental changes to cost and revenue of an organization
- Demonstrate proficiency in applying optimization techniques to quantities that need to be maximized or minimized like amount of raw material used to fabricate specific shapes or profit margin in a business
- Apply the fundamental theorem of calculus in calculating areas of irregular shapes, centroid of an area and moments of inertia of rotating bodies.
- Identify problems in business, technology, social and life sciences where calculus techniques can be applied.