MATHS 166: Calculus 2 (4)

MATH 166: Calculus 2 (4 hours)
Syllabus
1. Prerequisite: C- or better in MATH 165 or permission of the department chairperson.
2. Course Description: Standard techniques of integration, applications of the integral, numerical
integration, sequences and series. Includes the use of graphing calculators and computer software. Core
Transfer Library: Mathematics (IMA 1603)
3. Course Objectives: This course continues the study of calculus, which begins in MATH 165. Additional
theory, techniques, and applications support the new mathematical concepts developed in this course.
Applications to a wide variety of fields will be stressed to enhance the student’s appreciation and ability
to apply the techniques of calculus to solve problems in the real world.
4. Course Rationale: This course continues the study of calculus, which begins in MATH 165. Students
planning to major in mathematics, engineering, physics, chemistry, or a related subject need this
sequence.
5. Course Content: The topics to be covered are listed in the course description. They constitute the
standard second semester calculus course offered by nearly every college and university. The students
are expected to attend class regularly and to study the material and examples in the text as well as those
presented in class.
It is expected that the student will master and utilize a graphing calculator and the computer algebra
system Mathematica. Relevant portions of the Departmental Mathematica Tutorial will be incorporated
into the course. Additional applications of Mathematica will be included. The program Mathematica, as
well as the Departmental Mathematica Tutorial and sample Mathematica labs, are available on any
Departmental lab computer.
6. Course Format: The standard modes of instruction will include individual and group projects, including
three required group computer projects common to every section of the course.
7. Methods of Evaluating Student Performance: Course grades are determined primarily by student
performance on tests, quizzes, and projects, as well as possibly homework and class participation. The
evaluation and weight of these various components are at the discretion of the individual instructor.
8. Evaluation of the Course: The instruction in the course is evaluated by departmental student evaluations
and peer evaluations. The course is periodically reviewed, evaluated, and revised by the Departmental
Undergraduate Programs Committee.

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.

15. Use Taylor’s Theorem to:
a. Show that the natural exponential function, the trigonometric functions,
and polynomials are real analytic.
b. Approximate functions using polynomials.
16. Recognize and solve separable differential equations.
17. Solve problems involving applications of separable differential equations, such as
population growth.
18. For curves defined by parametric equations, compute:
a. Slopes of tangents
b. Arc length
c. Surface area of surfaces of revolution
d. Volumes of solids of revolution
19. Plot curves in polar coordinates.
20. Convert between polar and rectangular coordinates.
21. For curves defined by polar coordinates, compute:
a. Arc length
b. Area between curves
[Fall 2005, M. Karls; December 2009, Assessment Committee, R. Bremigan, Chair;
December 2008, M. Begum & J. Lorch; Oct 2012, UPC, R. Pierce Chair; Fall 2014,
UPC, R. Pierce, Chair]