# Math 116: Essentials of Calculus

### Title

Essentials of Calculus

(1:1:0)

Fall, Winter

Math 110

### Description

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

1. 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
2. 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
3. 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
4. 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.

Math 110

### Textbooks

Possible textbooks for this course include (but are not limited to):