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 and intuitive 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.
NOTE: Students may not use more than one of the following to meet graduation requirements: MAT 146, MAT 160, MAT 181.
Prerequisite: MAT 156 Algebra & Trigonometry for Calculus or equivalent
4 Class Hours
Learning Outcomes of the Course:
Upon successful completion of this course the student will be able to:
1. Find limits using computational and intuitive 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 and intuitive 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 area under a curve and area between curves.
17. Apply the definite integral to problems involving volume, curve length, and surface area.
18. Understand and solve elementary differential equations.
This course prepares students to meet the Mathematics General Education requirement.
In the context of the course objectives listed above, upon successful completion of this course the student will be able to:
1. Interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics.
2. Represent mathematical information symbolically, visually, numerically and verbally.
3. Employ quantitative methods such as arithmetic, algebra, geometry, or statistics to solve problems.
4. Estimate and check mathematical results for reasonableness.
5. Recognize the limitations of mathematical and statistical methods.
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