2011-2012 Official General Catalog [Archived Catalog]
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MAT 181 - Calculus I
A university parallel calculus course covering functions, limits and continuity. Differentiation and integration of polynomial, rational, trigonometric, logarithmic, exponential functions using computational, intuitive and technology assisted methods. Applications including curve sketching, rectilinear motion, related rates, maxima and minima. Summation, integration and the Fundamental Theorem of Calculus, and applications of the definite integral. Emphasis will be placed on analyzing problems using technology assisted methods.
NOTE: Students may not use more than one of the following to meet graduation requirements: MAT 146, MAT 160, MAT 181.
Prerequisite- Corequisite
Prerequisite: MAT 156 Algebra & Trigonometry for Calculus or equivalent
Credits: 4
Hours
4 Class Hours
Course Profile
Learning Outcomes of the Course:
Upon successful completion of this course the student will be able to:
1. Find limits using computational, intuitive and technology assisted methods.
2. Understand the formal definition of a limit.
3. Determine continuity of functions.
4. Find the derivative of a function using the limit definition.
5. Graph, differentiate and integrate polynomial, rational, trigonometric, logarithmic, and exponential functions, using computational, intuitive, and technology assisted methods.
6. Find derivatives by the chain rule.
7. Find implicit derivatives.
8. Understand differentials and linear approximations and their relation to the derivative.
9. Understand the Mean Value Theorem and Rolle’s Theorem.
10. Set up and solve maxima and minima problems and related rate problems.
11. Use the first and second derivatives as aids in sketching curves.
12. Find antiderivatives.
13. Understand sigma notation and know that a definite integral is the limit of a Riemann sum.
14. Understand the Fundamental Theorem of Calculus.
15. Integrate by Substitution.
16. Apply the definite integral to problems involving volume, curve length, and surface area.
17. Understand and solve elementary differential equations.
18. Integrate using approximation techniques.
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