MATHS 166: Calculus 2 (4)

MATH 166 Learning Objectives
Students will be able to:
1. Compute exact values for integrals using the following techniques of integration:
a. Integration by parts
b. Trigonometric substitution
c. Partial fractions
2. Compute approximate values for integrals using numerical methods, including the
Midpoint Rule, the Trapezoidal Rule, and Simpson’s Rule.
3. Determine error bounds associated with numerical methods such as the Midpoint
Rule, the Trapezoidal Rule, and Simpson’s Rule.
4. Recognize and solve problems involving applications of the definite integral.
Such applications include:
a. Areas between curves
b. Volumes of solids of revolution
c. Surface areas of surfaces of revolution
d. Work
e. Average value of a function
f. Arc length
g. Hydrostatic force
h. Center of mass
i. Probability
5. Compute exact values for improper integrals.
6. Use the Comparison Test to determine whether an improper integral converges.
7. Define the following:
a. Infinite sequence
b. Convergence of an infinite sequence
c. Infinite series
d. Alternating series
e. Convergence of an infinite series
f. Absolute convergence of an infinite series
8. Compute the sum of a geometric series.
9. Determine whether a positive-termed series converges using various tests,
including:
a. Integral Test
b. Comparison Test
10. Determine whether an alternating series converges using the Alternating Series
Test.
11. Determine absolute convergence using:
a. Ratio Test
b. Root Test
12. Compute the radius of convergence and interval of convergence for a power
series.
13. Compute the Taylor series representation of a smooth function.
14. Recognize a MacLaurin series as a special case of a Taylor series.