MA 24025, Calculus II
Division of Mathematics and Sciences
Departmental Syllabus
I.
Course Catalog Description
A continuation of Calculus I which includes the following topics: continuation of techniques
of integration, infinite series, conics, polar coordinates and parametric forms, vectors and the
geometry of space.
II.
Course Rationale
Calculus II is the second third of the study of the mathematics of motion and change
III. Course Objectives
At the conclusion of this course, the student will be able to use integration to find the area
between two curves, calculate the volume of a solid of revolution, find the area of a surface of
revolution, and many other applications of integration. Convergence of series will be studied
and this will be used to approximate functions. Plane curves and their properties will be
studied using parametric equations and polar coordinates. Vectors in the plane and threespace will also be studied along with vector-valued functions.
IV.
Course Prerequisites
A student must have a C or above in MA 24015, Calculus I.
V.
Required Texts and Materials
Calculus, Ninth Edition, by Larson and Edwards, published by Brooks/Cole; Graphing
calculator (preferably the TI 84)
VI.
Supplementary (Optional) Texts and Materials
The Student Solutions Guide might be helpful, but is not required.
VII. Grade Dissemination
You can access your assignment grades online by logging on to the portal, myANC, clicking
on Calculus I under “My Courses” and clicking on Assignments (http://myanc.anc.edu). Midtem and final grades can be accessed using Campus Connect on myANC. Please note:
scores assigned at mid-term are unofficial grades. If you need help accessing myANC
contact the ANC Helpdesk by email: ANChelp@smail.anc.edu.
VIII.
Course Policies: Technology and Media
Email: Arkansas Northeastern College has partnered with Google to host email addresses
for ANC students. myANCmail accounts are created for each student enrolled in the current
semester and is the email address your instructor will use to communicate with you.
Access your email account by going to http://mail.google.com/a/smail.anc.edu and using
your first and last names, separated by a period for your username. Your default password
is the last six digits of your Student ID. If you cannot access your student email, contact the
MITS department at 762-1020 ext 1150 or ext 1207 or send an email to
ANChelp@smail.anc.edu.
Internet: This course has a web component on myANC. Grades, class notes, some video
lectures and announcements will all be accessed online. Students should log in daily to
check for new announcements.
Classroom Devices: Scientific graphing calculators should be brought to each class. With
the permission of the instructor, a student may tape the lectures. All cell phones should be
turned off while in class. Students will not be allowed to share calculators or use
calculators on cell phones.
Computer Labs: In addition to general-purpose classrooms, a number of computer
laboratories are provided for instructional and student use. These networked laboratories
are state-of-the-art and fully equipped with computers, printers, Internet connections and
the latest software. The labs are open to students enrolled in one or more credit hours at
the College.
Technology Support: A lab assistant is generally present in the computer lab in B202 for
assistance in using the College computers. These assistants cannot help you with course
assignments; specific questions regarding the technology requirements for each course
should be directed to the instructor of the course. Problems with myANC or College email
accounts should be addressed by email to ANCHelp@smail.anc.edu.
IX.
Course Policies: Student Expectations
Disability Access: Arkansas Northeastern College is committed to providing reasonable
accommodations for all persons with disabilities. This First Day Handout is available in
alternate formats upon request. Students with disabilities who need accommodations in
this course must contact the instructor at the beginning of the semester to discuss needed
accommodations. No accommodations will be provided until the student has met with the
instructor to request accommodations. Students who need accommodations must be
registered with Johnny Moore in Statehouse Hall, 762-3180.
Professionalism Policy: When using email and discussion forums, remember that they are
an all-text medium. Social cues that help bring meaning to normal conversations such as
tone of voice, facial expressions and body language are not present. Clear and careful
writing is especially important. Be careful with wit and humor. Without face-to-face
communications, with and humor maybe viewed as criticism and disrespect
Mobile phones, iPods, etc. must be silenced during all lectures. Those not heeding this
rule will be asked to leave the classroom immediately so as to not disrupt the learning
environment. Please arrive on time for all class meetings.
Academic Integrity Policy:
Academic dishonesty in any form will not be tolerated. If you are uncertain as to what
constitutes academic dishonesty, please consult the Academic Integrity Policy in ANC’s
Student Handbook (http://www.anc.edu/docs/anc_handbook.pdf) for further details.
Students are expected to do their own work. Plagiarism, using the words of others without
express permission or proper citation, will not be tolerated. Any cheating (giving or
receiving) or other dishonest activity will, at a minimum, result in a zero on that test or
assignment and may be referred, at the discretion of the instructor, to the Department
Chair and/or Vice President of Instruction for further action.
Learning Assistance Center: The Learning Assistance Center (LAC) is a free resource for
ANC students. The LAC provides drop-in assistance, computer tutorials and audio/visual
aids to students who need help in academic areas. Learning labs offer individualized
instruction in the areas of mathematics, reading, writing, vocabulary development and
college study methods. Tutorial services are available on an individual basis for those
having difficulty with instructional materials. The LAC also maintains a shelf of free
materials addressing specific problems, such as procedures for writing essays and term
papers, punctuation reviews, and other useful materials. For more information, visit the
LAC website at http://www.anc.edu/LAC or stop by room L104 in the Adams/Vines
Library Complex.
Other Student Support Services: Many departments are ready to assist you reach your
educational goals. Be sure to check with your advisor; the Learning Assistance Center,
Room L104; Student Support Services, Room S145; and Student Success, Room L101 to find
the right type of support for you.
X.
Unit and Instructional Objectives
A. Applications of Integration
Rationale: In this unit, the definite integral is used to find the area between two
curves, the volume of a solid of revolution, the length of a curve, the surface area of
a surface of revolution, work done by a constant force and a variable force, centers
of mass and centroids, and fluid pressure and fluid force.
At the conclusion of this unit, the student should have had the opportunity to do the
following:
1. Sketch the region in the plane bounded by graphs of algebraic functions and then
use integration to find the area of the region.
2. Sketch the region in the plane bounded by graphs of trigonometric functions and
then use integration to find the area of the region.
3. Use the disk method to set up and evaluate the integral that gives the volume of
the solid formed by revolving a region in the plane about the x-axis.
4. Use the disk method to set up and evaluate the integral that gives the volume of
the sold formed by revolving a region in the plane about any horizontal or a
vertical line.
5. Use the shell method to set up and evaluate the integral that gives the volume of
the solid formed by revolving a region in the plane about the y-axis.
6. Use the shell method to set up and evaluate the integral that gives the volume of
the solid formed by revolving a region in the plane about any horizontal or
vertical line.
7. Set up and evaluate the definite integral that gives the arc length of a graph of a
function over an indicated interval.
8. Set up and evaluate the definite integral that gives the area of a surface
generated by revolving a curve about the x or y axes.
9. Calculate the work done by a constant force.
10. Set up and evaluate a definite integral to calculate the work done compressing a
spring, lifting a chain, or emptying a tank of fluid.
11. Find the center of mass in a one-dimensional and in a two-dimensional system.
12. Set up and evaluate the definite integral giving the center of mass or centroid of
a planar lamina.
13. Set up and evaluate the definite integral giving the force exerted by a fluid
against a submerged vertical plane.
B. Integration techniques, L’Hopital’s Rule, and Improper Integrals
Rationale: In this unit, more integration techniques are studied that are used to
evaluate more complicated integrals.
1.
2.
3.
4.
5.
Use integration by parts to evaluate definite and indefinite integrals.
Evaluate integrals involving powers of sine and cosine.
Evaluate integrals involving powers of secant and tangent.
Evaluate integrals involving sine-cosine products with different angles.
Evaluate integrals using trigonometric substitution.
6. Use partial fraction decomposition with linear factors to integrate rational
functions.
7. Use partial fraction decomposition with quadratic factors to integrate rational
functions.
8. Use partial fraction decomposition with repeated quadratic factors to integrate
rational functions.
9. Use partial fraction decomposition with repeated linear factors to integrate
rational functions.
10. Evaluate an indefinite integral using a table of integrals.
0 ∞
11. Evaluate a limit given an indeterminate form of 0 , ∞ , 0 ⨯ ∞, 1∞ , 00 , ∞ − ∞.
12. Use L’Hopital’s Rule, if it applies, to evaluate a limit.
13. Determine whether an improper integral with an infinite limit of integration
converges or diverges. If it converges, evaluate the integral.
14. Determine whether an improper integral with an infinite discontinuity
converges or diverges. If it converges, evaluate the integral.
C. Infinite Series
Rationale: Infinite series can be used to create a polynomial function that can be used to
approximate an elementary function. This polynomial function might then simplify any
computations or calculus operations that are needed.
1.
2.
3.
4.
5.
6.
7.
8.
Find the radius of convergence of a given power series.
Find the interval of convergence of a given power series.
Find the interval of convergence of the derivative of a given power series.
Find a geometric series for a given rational function, centered at a given value of
c, and determine the interval of convergence.
Construct a power series by using series operations and/or differentiation and
integration.
Find a Taylor series centered at c or a Maclaurin series for a given function.
Use the binomial series to find the Maclaurin series fo a given function.
Use the table of power series for elementary functions to find the Maclaurin
series for a given function.
D. Conics, Parametric Equations, and Polar Coordinates
Rationale: Conic sections (parabola, ellipse, hyperbola) and also their reflective
properties are used extensively in physics. Parametric equations are useful when
studying situations in which three variables are used to represent a curve in the plane.
1. Given the General Form of an equation of a conic, write the Standard Form.
Using the Standard Form, find the center, vertex or vertices, focus or foci,
directrix, depending on the conic, and graph it.
2. Given the center, foci, vertices, etc., find the equation of the conic in Standard
Form.
3. Solve applications problems involving conic sections.
4. Given a set of parametric equations, graph the curve and indicate the orientation
of the curve.
5. Given a set of parametric equations, eliminate the parameter and graph the
resulting equation in two variables.
6. Given a curve defined by a set of parametric equation, find the slope and
concavity of the curve at a given point.
7. Given a curve defined by a set of parametric equations, find the area of a surface
of revolution.
8. Given the polar coordinates of a point, graph it, and convert it to rectangular
coordinates.
9. Given the rectangular coordinates of a point, find at least two sets of polar
coordinates for that point.
10. Sketch the graph of an equation given in polar form.
11. Find the slope of a tangent line to a polar graph.
12. Find the area of a region bounded by a polar graph.
13. Find the arc length of a polar graph.
14. Find the area of a surface of revolution of a graph in polar form.