MAT 160 - Applied Calculus I
Designed for students in the Engineering Technologies only, this course covers the mechanics of calculus using application problems from technology fields. Topics include: equations of tangent lines; limits; differentiation and integration of algebraic, logarithmic, exponential, and trigonometric functions; product rule, quotient rule, and chain rule; implicit differentiation; related rates; maxima and minima; differentials; the definite integral and applications to finding area, center of gravity, volume of revolution and work done; numerical integration.
Prerequisite: MAT 130 Applied Algebra and Trigonometry or equivalent
4 Class Hours
Learning Outcomes of the Course:
Upon successful completion of this course the student will be able to:
1. Write the equation of a tangent line.
2. Evaluate limits algebraically.
3. Use limits to find vertical and horizontal asymptotes.
4. Find the points of discontinuity of a function.
5. Differentiate logarithmic, exponential, trigonometric and inverse trigonometric functions.
6. Use the chain rule, product and quotient rules in differentiating.
7. Differentiate implicity.
8. Solve related rate problems.
9. Use differentials to find approximate values.
10. Antidifferentiate logarithmic, exponential, trigonometric and inverse trigonometric functions.
11. Use calculus methods to find area, center of gravity, volume of revolution, work done.
12. Use calculus methods to find maximum and minimum points of functions.
13. Use calculus methods to solve simple circuit and kinematic problems.
14. Approximate integrals using numeric methods.
1. Graphing functions derived from applications to reinforce Calculus solutions.
2. Find limits graphically.
3. Find the slope of a tangent line to a curve at a specified point.
4. Graph a function and the tangent line at a specified point on the function.
5. Explain why the graphing calculator really does not draw a vertical asymptote for functions.
6. Graph a function and its derivative on the same axes.
7. Find relative extrema and inflection points of a function.
8. Evaluate definite integrals.
9. Show and determine the area under a curve.
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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