Penn State University - University Park
MATH 141, Calculus with Analytic Geometry II
Spring 2014
CATALOG DESCRIPTION:
MATH 141
(GQ) Calculus with Analytic Geometry II (4) Derivatives, integrals,
applications; sequences and series; analytic geometry; polar coordinates. Students may take only one course for
credit from MATH 141, 141B, 141E, 141G, and 141H
.
PREREQUISITE:
Math 140,140A, 140E, or 140H, or a score of 4 or 5 on the AP Calculus AB Exam.
TEXT
:
Calculus (Single Variable), Seventh Edition, (OR) Calculus, Seventh Edition, by James Stewart, published
by Thomson (Brooks/Cole).
An electronic version of the text (e-text) is available chapter by chapter through
http://pennstate.ichapterssites.com
.
COURSE FORMAT:
There are four 50-minute lectures each week. The sections covered in lectures are listed at
the end of this syllabus.
MATH 141 LEARNING OBJECTIVES
:
Upon successful completion of Math 141, the student should be able to:
1.
Differentiate exponential, logarithmic, and inverse trigonometric functions.
2.
Integrate exponential, logarithmic, and inverse trigonometric functions.
3.
Recognize integrands for which integration by parts is appropriate.
4.
Use the formula to integrate by parts.
5.
Use techniques for integrals of products of sines and cosines.
6.
Use techniques for integrals of secants and tangents, and for cosecants and cotangents.
7.
Use techniques of trigonometric substitution to integrate various forms of integrands.
8.
Complete the square to express an irreducible quadratic polynomial as a sum or difference of squares.
9.
Perform polynomial long division to reduce an integrand to a more easily integrated form.
10.
Use the technique of partial fraction decomposition to reduce an integrand to a more easily integrated form.
11.
Given a random integration problem, choose the proper method and proceed with integration.
12.
Identify indeterminate limit forms.
13.
Evaluate limits using L’Hospital’s Rule.
14.
Recognize improper integrals and put in proper form for determination.
15.
Determine if an improper integral diverges or converges (and if so, to what?).
16.
Identify and compare different types of sequences.
17.
Determine if a sequence diverges or converges (and if so, to what?).
18.
Recognize famous series in standard and non-standard form.
19.
Apply infinite series tests for convergence and divergence.
20.
Determine the error associated with a partial sum of an alternating series.
21.
Find the interval of convergence and radius of convergence for a given power series.
22.
Generate power series representations of some functions from a geometric series perspective.
23.
Generate power series representations of some functions from a Taylor Series perspective.
24.
Recognize and manipulate important Maclaurin Series (
e
x
, sin
x
, cos
x
, tan
-1
x
, 1/(1-
x
)) by differentiation,
integration, and substitution.