August 31, 2010

SALEM STATE UNIVERSITY
MATHEMATICS DEPARTMENT
Salem, Massachusetts 01970-5353
COURSE SYLLABUS, Fall 2010
MATH 221     CALCULUS II (4 credits)
Section 2:     MW 2:30 - 3:45 p.m. SB 311;     F 2:30 - 3:20 p.m. SB 311

Instructor:               Dr. Arthur Rosenthal  
E-mail:  arosenthal@salemstate.edu
Office:                     308I Sullivan Bldg. 
Phone:  978-542-6392
Internet home page: http://www.salemstate.edu/~arosenthal/ma221      
Fax:      440-540-6733

Office hours:    Mon. 4:00 – 5:00 p.m.; Wed. 11:00 a.m. – 12:30 p.m.; Fri. 3:30 – 4:30 p.m.
                        Other times by appointment or by chance

Required text:
Thomas' Calculus Early Transcendentals: Part 1
(11th ed.) by Maurice D. Weir, Joel Hass and Frank R. Giordano (Pearson/ Addison Wesley, 2006) (ISBN 0321513398) or
Thomas' Calculus Early Transcendentals (11th ed.) by Maurice D. Weir, Joel Hass and Frank R. Giordano (Pearson/ Addison Wesley, 2006) (ISBN 0321511816)

Chapter coverage:
5. Integration
6. Applications of Definite Integrals

7. Integrals of Transcendental Functions

8. Techniques of Integration
11. Infinite Sequences and Series

Examinations:

2 exams in class of 50 minutes each:     Oct. 8 and Nov. 5
FINAL EXAM:     Monday, Dec. 20     8:00 a.m. - 10:00 a.m.     SB 311


Course and Grading Policies:

Each of the 50 minute exams will count for 20% of the course grade. The final exam will count for 40% of the course grade. Homework assignments (generally done online) and quizzes will count for 20% of the course grade. The number of times you inform me, before I inform the class, of a correct answer to a problem in the chapter currently being covered (according to the schedule of course topics) with an incorrect answer in the back of the text will be added to your overall average. (This means if you correct 5 problems with wrong answers in the back of the text and your overall average would have been 70%, your overall average will become 70%+5%=75%).

All exams are required. Make-ups will be given, no later than 3 pm on Dec. 22, only if you notify me before the exam starts or as soon as possible and supply a reason. Unavoidable conflicts may be resolved by taking parallel exams before the scheduled date, if prior notice of one week is given to the instructor. Assignments submitted late are subject to a 10% penalty if submitted before any students receive their corrected solutions back in class; late assignments receive no credit if submitted after any students receive their corrected solutions back in class.

Most of the homework assignments will be found online in Course Compass. To set up your access to Course Compass, go to http://coursecompass.com and click on "Register" for students. Be sure to type in a valid e-mail address when asked. When asked for your Course ID, enter rosenthal52193 . If you used Course Compass with Thomas' Calculus 11th ed in a previous semester, you may use your log in name and password from the course you took previously. Otherwise, you will need an access code, which is included at no extra charge on a card if you buy a new textbook with ISBN: 0321513398 or 0321511816 . Otherwise, you will need to buy an access code for $75 from this web site. In addition to giving you access to the Course Compass assignments, your access code gives you online access to the full textbook.

It is your responsibility to attend as many classes as possible, to do all homework problems assigned in class, and to complete all course requirements. You are responsible for any topics or problems covered in class (whether or not you are present). Attendance will be spot-checked on at least three occasions.

The Mathematics Department strongly recommends that each student in this course purchase a graphing calculator comparable to the TI 83 or TI 84.

University Policy Statement:
The Salem State University 2010-2012 catalog states, "Salem State University is committed to providing equal access to the educational experience for all students in compliance with Section 504 of the Rehabilitation Act and The Americans with Disabilities Act and to providing all reasonable academic accommodations, aids and adjustments. Any student who has a documented disability requiring an accommodation, aid or adjustment should speak with the instructor immediately. Students with Disabilities who have not previously done so should provide documentation to and schedule an appointment with the
Office for Students with Disabilities (phone 978-542-6217 or e-mail disability-services@salemstate.edu ), and obtain appropriate services."

In the event of a university declared critical emergency, Salem State University reserves the right to alter this course plan. Students should refer to salemstate.edu for further information and updates. The course attendance policy stays in effect until there is a university declared critical emergency. In the event of an emergency, please refer to the alternative educational plans for this course located at http://www.salemstate.edu/~arosenthal/ma221. Students should review the plans and gather all required materials before an emergency is declared.

Last Day to Withdraw from the Course:
The last day on which withdrawal from the course is permitted with a "W" grade is Friday, November 19.


Math/ Computer Lab:

Free tutoring and a variety of mathematics software packages are available in the 
Math/ Computer Lab, SB306. Hours will be posted, and are expected to be from 9 a.m. - 8 p.m. on Monday - Thursday and from 9 a.m. - 4 p.m. on Friday during most of the semester.

Course Description:
This course is a further development of the calculus of functions of one variable. Topics include logarithmic and exponential functions and their derivatives and integrals, exponential growth and decay, inverse trigonometric functions, techniques of integration, numerical integration with error estimates, applications of the integral, indeterminate forms and l'Hôpital's rule, infinite sequences and infinite series with error estimation. Four lecture hours per week.


Prerequisite:

MAT 220.

Global Goals: This course is intended to provide the student with

  1. An understanding of the fundamental principles and theories of integral calculus.
  2. Facility in writing, speaking and using the language of calculus.
  3. An understanding of some applications of integral calculus.
  4. An understanding of error estimation.
  5. An understanding of what it means for sequences and series to converge and an ability to choose which test to use to determine if a series converges.
  6. An exposure to how technology, such as graphing calculators and computers, can be used effectively to help students understand and visualize mathematics.

Learning Objectives: The student will be able to do the following:

  1. Find definite integrals using the Fundamental Theorem of Calculus.
  2. Evaluate appropriate integrals by using substitution, including trigonometric substitution.
  3. Evaluate appropriate integrals using integration by parts.
  4. Evaluate integrals of rational functions by the method of partial fractions.
  5. Recognize the limiting values of certain Riemann sums as integrals.
  6. Use integration for such applications as finding the area between curves, the volume of a solid of revolution, the length of a plane curve and the area of a surface of revolution.
  7. Find derivatives and integrals involving exponential, logarithmic and inverse trigonometric functions.
  8. Use l'Hôpital's rule to find limits involving certain indeterminate forms.
  9. Evaluate integrals using a computer algebra system such as Maple.
  10. Estimate integrals numerically using the Trapezoidal Rule and Simpson's Rule and be able to estimate the errors involved.
  11. Recognize improper integrals, determine whether they converge, and evaluate them if they converge.
  12. Apply Taylor's Theorem to find Taylor polynomial approximations to given functions, and estimate their accuracy.
  13. Determine whether a sequence converges and find its limit if it converges.
  14. Determine the convergence of a series by appropriate tests, including the comparison, ratio, root, alternating series and p- series tests.
  15. Determine whether a series converges absolutely or conditionally and understand the difference between the two types of convergence.
  16. Find the interval of convergence of a power series.
  17. Recognize when differentiating and integrating power series term by term is appropriate and differentiate and differentiate and integrate appropriate power series term by term to perform certain calculations, including modeling with Taylor series.

Course Requirements for Assessment:

Assessment Scheduled Dates Learning Objectives Percent of Grade
Homework Due Dates given online 1-17 20%
Test 1 October 8 1, 2, 5, 6, 7 20%
Test 2 November 5 1, 2, 3, 4, 6, 7, 8, 10, 11 20%
Cumulative Final Exam December 20 1-8, 12-17 40%

Tentative Schedule of Course Topics:

Class Topics Sections in Text
1 Integration: Estimating with finite sums. The definite integral. 5.1 to 5.3
2 The Fundamental Theorem of Calculus; indefinite integrals and the substitution rule; area between curves. 5.4 to 5.6
3 Applications of definite integrals: Volumes of solids of revolution, lengths of plane curves. 6.1 to 6.3
4 Applications of definite integrals: Centers of mass, area of a surface of revolution. 6.4 to 6.5
5 Integrals and transcendental functions: Logarithms and exponential growth and decay. 7.1 to 7.2
6 Relative rates of growth; hyperbolic functions. 7.3 to 7.4
7 Techniques of integration: Basic integration formulas; integration by parts. 8.1 to 8.2
8 Integrating rational functions by partial fractions; trigonometric integrals and substitutions. 8.3 to 8.5
9 Using computer algebra systems to evaluate integrals, numerical integration; improper integrals 8.6 to 8.8
10 Using numerical integration techniques such as Simpson's Rule to approximate integrals; improper integrals. 8.7 to 8.8
11 Infinite sequences and series; using L'Hôpital's rule to find limits of sequences. 11.1 to 11.2
12 Use of the integral, comparison, ratio and root tests to determine convergence of series. 11.3 to 11.5
13 Alternating series; absolute and conditional convergence; Taylor series and power series. 11.6 to 11.8
14 Convergence of Taylor series; error estimates; differentiating and integrating power series; applications of power series. 11.8 to 11.10
15 Final exam  

Bibliography:

  1. Anton, Howard, Irl Bivens and Stephen Davis, Calculus: Early Transcendentals, 8th ed., Wiley, Hoboken, NJ, 2005.
  2. Finney, Ross L., Demana, Waits and Kennedy, Calculus: Graphical, numerical, algebraic, 3rd ed., Pearson Addison Wesley, Boston, Mass., 2007.
  3. Foerster, Paul, Calculus: Concepts and Applications, Key Curriculum Press, Emeryvillle, California, 2004.
  4. Larson, Roland E., Robert P. Hostetler, and Bruce H. Edwards, Calculus: Early Transcendental Functions, 9th ed., Cengage Learning, Belmont, CA, 2009.
  5. Maplesoft web resource, http://www.maplesoft.com (Web site).
  6. Math Archives Calculus page, http://archives.math.utk.edu/topics/calculus.html (Web site).
  7. Math Forum Calculus page, http://mathforum.org/calculus/calculus.html (Web site).
  8. The Math Works, Inc., MATLAB and Simulink Student Version (Release 2010a), available from http://www.mathworks.com/academia/student_version (Web site).
  9. Rogawski, Jon, Single Variable Calculus: Early Transcendentals, W. H. Freeman, New York, 2008.
  10. Stewart, James, Calculus: Concepts and Contexts, 4th ed., Brooks/ Cole Cengage, Belmont, CA, 2009.
  11. Tan, Soo T., Single Variable Calculus: Early Transcendentals, Brooks/ Cole Cengage, Belmont, CA, 2011.
  12. Texas Instruments calculator software, http://education.ti.com/educationportal/sites/US/sectionHome/download.html (Web page).