MAT 180 Calculus & Analytic Geometry I

Exit Skills

1. Demonstrate mastery of algebraic and trigonometric computations.
2. Demonstrate an understanding of limits from a graphical and algebraic perspective and as related to continuity, differentiation and integration.
3. Find derivatives using the basic definition involving limits.
4. Find derivatives using formulas for power rule, product rule, quotient rule, chain rule (basic and formula approach), implicit differentiation and higher order derivatives.
5. Express derivatives in different notations including Leibniz notation and prime notation.
6. Solve related rates problems.
7. Solve problems using differentials.
8. Demonstrate sophisticated graphing skills including use of asymptotes (horizontal, vertical, and oblique), symmetry, maximum and minimum, inflection points and concavity.
9. Analyze a function using inflection points, maximum and minimum.
10. Integrate indefinite integrals (including using substitution), definite integrals and simple differential equations.
11. Apply integrals to problems involving areas in a plane, volumes of revolution (disks, washers, and shells), lengths of plane curves, areas of surfaces of revolution, fluid force, work problems, moments about an axis and center of mass.

Objectives

1. Analyze functions using 1st and 2nd derivatives plus general algebraic analysis to identify the following: maximum, minimum and stationary points, intervals containing increasing, constant and decreasing functions concavity.
2. Find the derivatives of the following functions: polynomial, rational, radical, trigonometric, product and composition of functions.
3. Find the derivative of multivariable relationships involving composition of functions (chain rule), related rates and implicitly defined relations.
4. Evaluate definite and indefinite integrals using algebraic substitution both with and without changing limits.
5. Apply integration to calculate the following: areas, volumes, arc lengths, surface areas, volumes of solids of revolution, force and work.