JEFFERSON COLLEGE
COURSE SYLLABUS
MTH 185
CALCULUS II
5 Credit Hours
Prepared by:
Lynn S. Cunningham
Revised: November 2006
by
Skyler Ross
Arts & Science Education
Dr. Mindy Selsor, Dean
MTH185 CALCULUS II
I.
CATALOG DESCRIPTION
Prerequisite: MTH180 Calculus I with minimum grade of C
Calculus II is a continuation of Calculus I. The student will study transcendental
functions, techniques and applications of integration, infinite series, and conic
sections. A graphing calculator is required. (F,S)
II.
GENERAL COURSE OBJECTIVES
Upon completion of this course the student should be able to:
A. Solve equations containing natural logs and exponential expressions.
B. Differentiate functions containing natural logs and exponential expressions.
C. Evaluate integrals of the form
1
∫ u du
and ∫ e u du where u is a function of x.
D. Evaluate integrals using inverse trigonometric functions.
E. Use L’Hopital’s Rule to find limits of indeterminate form.
F. Use a table of integrals to evaluate integrals
G. Use integration by parts to evaluate an integral.
H. Evaluate integrals of the form ∫ sin m x cos n x dx and ∫ sec m x tan n x dx
I. Use the method of partial fractions to evaluate an integral of a rational whose
denominator is a product of linear factors, some of which are repeated.
J. Determine if an improper integral is convergent or divergent. Evaluate the
integral if it is convergent.
K. Approximate definite integrals by using the midpoint rule, trapezoidal rule,
and Simpson’s rule.
L. Find the centroid of a region bounded by curves.
M. Find the length of an arc of a given function over a specified interval.
N. Find the area of the surface formed by revolving a given arc about a
horizontal or vertical axis.
O. Determine the probability of events in a normal distribution.
P. Graph parametric functions.
Q. Find extrema of, and tangent lines to, parametric functions.
R. Find the length of an arc of a given parametric function over a specified
interval.
S. Translate points and functions from Cartesian form to polar form, and vice
versa.
T. Find the area of a region bounded by one or more curves in polar form.
U. Find the length of an arc of a given polar curve over a specified interval
V. Graph conic sections in Cartesian and polar coordinates, indicating their
important parts and attributes (shape, eccentricity, vertices, foci, asymptotes,
and directrix)
W. Provide the equation of a conic, in Cartesian and polar coordinates, given
sufficient information.
X. Be conversant with sequence and series notation
Y. Determine if a sequence is convergent or divergent. If it is convergent, find
the limit.
Z. Find the sum of convergent geometric series.
AA. Use the integral test, the comparison tests, and ratio test to classify series as
conditionally convergent, absolutely convergent, or divergent.
BB. Given a power series, find the radius of convergence and the interval of
convergence.
CC. Find power series for functions and use them to integrate functions
DD. Find the Taylor, Maclaurin, and binomial series expansion of a given function
These objectives will be assessed on the final examination.
III.
IV.
COURSE OUTLINE
A.
Exponential, Logarithmic, and Inverse Trigonometric Functions
B.
Techniques of Integration
C.
Applications of Integration
D.
Parametric Equations and Polar Coordinates
E.
Infinite Sequences and Series
UNIT OUTLINE
A.
Exponential, Logarithmic, and Inverse Trigonometric Functions
1.
Inverse Functions
2.
Exponential Functions and their Derivatives
3.
Logarithmic Functions
4.
Derivatives of Logarithmic Functions
5.
Inverse Trigonometric Functions
6.
Hyperbolic Functions
7.
Indeterminate Forms and l’Hopital’s Rule
B.
Techniques of Integration
1.
Integration by Parts
2.
Trigonometric Integrals
3.
Trigonometric Substitution
4.
Integration of Rational Functions by Partial Fractions
5.
Strategies for Integration
6.
Integration Using Tables
7.
Approximate Integration
8.
Improper Integrals
C.
Applications of Integration
1.
Arc Length
2.
Area of a Surface of Revolution
3.
Applications to Physics and Engineering
4.
Probability
D.
Parametric Equations and Polar Coordinates
1.
Curves Defined by Parametric Equations
2.
Tangents and Areas with Parametric Curves
3.
Polar Coordinates
4.
Areas and Lengths in Polar Coordinates
5.
Conic Sections
6.
Conic Sections in Polar Coordinate
E.
V.
VI.
Infinite Sequences and Series
1.
Sequences
2.
Series
3.
The Integral Test and Estimates of Sums
4.
The Comparison Tests
5.
Alternating Series
6.
Absolute Convergence and the Ratio and Root Tests
7.
Strategy for Testing Series
8.
Power Series
9.
Representation of Functions as Power Series
10.
Taylor and Maclaurin Series
11.
The Binomial Series
12.
Applications of Taylor Polynomials
METHOD OF INSTRUCTION
A.
Lectures
B.
Class Discussion
C.
Textbook
REQUIRED TEXTBOOK(S) (WITH PUBLICATION INFORMATION)
Stewart, Calculus, 5th Ed, Brooks/Cole
VII.
REQUIRED MATERIALS (STUDENT)
Graphics Calculator
VIII.
SUPPLEMENTAL REFERENCES
None
IX.
METHOD OF EVALUATION (STUDENT)
A.
Tests
B.
Quizzes
C.
Homework
D.
Projects
E.
Final Exam