MATH 221 - Calculus for Technology I

1. Understand basic properties of circles, ellipses, and parabolas.
2. Define and determine limits. Use the limit theorems to find limits, including limits at infinity.
3. Definite and determine continuity of a function.
4. Find the derivative of a function from the limit definition.
5. Find derivatives of polynomial and radical functions using the Power Rule and other differentiation rules.
6. Interpret the derivative as a rate of change.
7. Find derivatives of products, quotients, and composite functions.
8. Find equations of tangent and normal lines to curves.
9. Review and differentiate trigonometric functions.
10. Find related rates and solve related rates problems.
11. Use the first and second derivatives to find local and absolute extrema, determine concavity and inflection points, and find intervals on which a function is increasing or decreasing.
12. Solve applied optimization problems.
13. Find instantaneous velocity and acceleration of an object.
14. Define and use differentials.
15. Determine area under a curve by limits of finite sums.
16. Evaluate definite integrals using the Fundamental Theorem of Calculus, and find areas under a curve or between curves using definite integrals.
17. Find indefinite integrals using the basic integration formulas and by substitution.
18. Find volumes of revolution using the disk, washer, and shell methods.
19. Find centroids, and do applied problems in work and fluid pressure.
20. Find the mean value and the root mean square of a function on an interval.

• Limits
• Continuity and discontinuity
• Derivatives
• Applications of derivatives
• Integrals
• Applications of integrals

 
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Course Addendum - Syllabus (Click to expand)