Calculus I – mth280 (4 credits)
This course is an introduction to differential calculus. Students explore limits and continuity. They examine the basic concept of differentiation and practice differentiation techniques. Students develop competence applying differentiation to solve problems. Students also examine simple antiderivatives.
- Find the derivative of the sum and difference of two functions.
- Find the derivative of the ratio and the product of two functions.
- Recognize derivatives as rates of change.
- Compute the derivative of trigonometric functions.
- Compute the derivatives of linear, quadratic, and polynomial functions.
Chain Rule and Related Rates
- Find the derivative of the composition of two functions.
- Calculate the derivative of multivariable expressions, implicit differentiation.
- Derive rates of change from related known rates of change.
- Approximate derivatives using linearization.
Graphing and Applications
- Use the Mean Value Theorem to find the derivative of a continuous function.
- Determine critical points and points of inflection of functions with derivatives.
- Use derivatives to find extreme values of functions.
- Find local extrema using the first derivative of a monotonic function.
More Applications of Derivatives
- Solve applied optimization problems.
- Approximate a solution to an equation using Newton’s method.
- Recover the antiderivative of simple polynomial and trigonometric functions.
Calculus I Concept Review
- Apply the concepts presented in this course.
Functions and Rates of Change
- Use limit laws to find limits of functions.
- Recognize mathematical functions from graphs.
- Determine the effects of operations on a graph.
- Graph trigonometric functions.
- Calculate slopes of tangent lines at given points.
Limits and Continuity
- Calculate one-sided limits.
- Calculate limits of functions.
- Determine the continuity of functions at given points.
- Identify asymptotes of graphs.
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