Math 116: Essentials of Calculus
Essentials of Calculus
(Credit Hours:Lecture Hours:Lab Hours)
Fall (1st and 2nd block), Winter (1st and 2nd block), Spring, Summer
This course gives a brief overview of differential calculus. Topics covered include limits, derivatives, and applications of differentiation to optimization of functions.
Desired Learning Outcomes
- Review of Algebra (4 lectures)
- Determine the graph of a line given two points, a point and a slope, the general form of a line, the slope-intercept form of a line
- Determine the slope of a line given two coordinate points, the equation of a line given the slope and a point, equation of a line given two points, and the x- & y-intercept of a line
- Find the secant line of a function on an interval, and use that to understand the average rate of change of a function
- Approximate the tangent line at a point, and use that to understand the instantaneous rate of change of a function
- Limits and Derivatives (4 lectures)
- Determine the limit of standard functions, e.g., polynomials, rational functions, exponentials, logarithms
- Determine the limits of more complicated functions composed of simpler functions.
- Define the derivative, take derivatives of polynomials using definition
- Derive the differentiation rules for polynomials, exponentials, logarithms
- Product, Quotient, and Chain Rules (2 lectures)
- Derive the product, quotient, and chain rules
- Use the product, quotient, and chain rules to compute complicated derivatives composed of simpler functions
- Optimization and Applications (4 lectures)
- State the derivative rules for local extreme
- Use the derivative rules to find the local extrema of a function on an interval. Then find the global maximum (or minimum) of a function on an interval
- Use the derivative to solve problems in business, e.g., maximize profits, minimize costs, etc.
- Use Newton's method for root finding to locate local extrema.
Minimal learning outcomes
This course will be taught on the block schedule, 2 hours/week for 7 weeks. The grade of pass/fail will be completely determined by the final exam. Students will need to get 80% on the exam to pass. Exams can be retaken weekly in the testing center during the semester and daily during finals (there will be multiple versions of the exam available). The purpose of this class is for the students in the business school to understand the idea of a derivative and how to use it to optimize a function.
Possible textbooks for this course include (but are not limited to):