Math 116: Essentials of Calculus
Essentials of Calculus
(Credit Hours:Lecture Hours:Lab Hours)
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
Possible textbooks for this course include (but are not limited to):