Examines the basics of calculus. Topics include the differential calculus computations and applications to graphing and finding maxima-minima, the integral calculus substitution and applications to area and probability, and the Fundamental Theorem of Calculus.
Demonstrate how to form and use functions.
Find the limit of a function, continuous function, and discontinuous function using graphs, tables, and limit properties.
Use the average rate of change and instantaneous rate to find the tangent or secant line to the graph.
Use the sum and difference rules and the product, quotient, and chain rules to find derivatives.
Find where functions are increasing and decreasing, the relative extrema, concavity, and inflection points using first and second derivative tests and consolidate all information onto a graph.
Find absolute maxima/minima and relative minima/maxima using derivatives.
Find antiderivatives.
Apply the Fundamental Theorem of Calculus to evaluate definite integrals.
Find the area under a curve and between two curves.
Evaluate improper integrals by identifying when an integral is convergent or divergent.
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Textbook(s)
Publisher: Pearson (2012)
Author: Lial, M. L., Greenwell, R. N., & Ritchey, N. P.
ISBN: 978-0-321-74900-0
* Disclaimer: Textbooks listed are based on the last open revision of the course. Prior revisions and future revisions may use different textbooks. To verify textbook information, view the course syllabus or contact the AU Bookstore at [email protected]