Calculus II
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Course: MAT 234 - Calculus II

 Text:   Calculus of A Single Variable, 7th edition by Larson, Hostetler & Edwards; Houghton Mifflin Publishing Company, 2002

 

Instructor: Maureen Woolhouse
                     Office - Room 257, Administration Building
                     508-854-2731
                     mwoolhouse@qcc.mass.edu

 

Course Description:  Calculus II is a typical integration course. All basic techniques of integration are discussed, along with the customary applications (area) volumes, work, fluid force, moments, centroids, arc lengths, and surfaces of revolution. L’Hopital’s Rule and improper integrals are then discussed. This is followed by infinite series with all of the customary convergence tests, and the Power, Taylor, and Maclauren series.

 

Prerequisite:   MAT 233 Calculus I

 

Course Requirements:  A graphing calculator is a requirement for this course. It is recommended that the student purchase a TI-83 or TI-83 plus calculator, since that is the calculator with which the instructor is familiar and which will be used for classroom demonstrations.

Students may use other graphing calculators but they cannot rely upon instructor assistance in their use.

 

Method of Instruction: 

 

Grading:  During the course of the semester there will be:

                    5 - 6 one hour tests

                    6 ten-minute quizzes

                    1 final exam

 

Attendance:  Perfect attendance is possibly the simplest and most effective way for a student to maximize his or her academic performance. Attendance will be taken at the start of each class meeting.

Tardiness:  Late attendance is a source of distraction to both the students and the instructor. Out of mutual courtesy and respect, please be in your seat and prepared to work at the start of our class time.

 

Exams:  Four or five exams will be administered during the semester. No exams will be dropped in the computation of the final grade. Missing tests is a SERIOUS matter. If a student finds it impossible to take a test due to circumstances beyond their control, they should contact the instructor immediately or at the very least, prior to the next class meeting. After this date, there will be no opportunity to make up an exam except through the presentation of a written doctor's certificate establishing a valid medical excuse.

 

Quizzes:  Quizzes will be administered during the first ten minutes of class. If a student is late to class on a quiz day, they will have less than the full time to take the quiz. Quizzes are announced in advance. THERE WILL BE ABSOLUTELY NO MAKE UP ON QUIZZES FOR ANY REASON. A student will receive a grade of zero on a quiz if they miss the quiz or if they leave class after taking the quiz. The five best quizzes out of the six administered will count for twenty points each and be combined to equal one test grade.

 

Homework:  Students should prepare for their tests and quizzes by completing all homework assignments in a timely fashion. Test and quiz questions will be similar to those assigned for homework.

It is commonly expected on most campuses that students will spend two hours of outside preparation and study for each hour of class time.  In this class, it is mandatory that students complete their homework in preparation for the next class meeting.

 

Final Exam:  The final exam will be cumulative and count for two test grades in the computation of the final course mark.

 

Help:  1)  Get to know your classmates. Exchange telephone numbers.  Form study groups. This strategy has worked very well for students who made the effort to try it.

          2)      Purchase a copy of the Student's Solution Manual which accompanies our textbook.  This manual has the worked-out solutions to all odd numbered questions in the textbook.  The Bookstore should have copies.

          3)      Check the hours and days the Math Lab is open and use the free help this facility offers.   

                4)      Meet with me for extra help during my office hours.

            5)      Check the Houghton Mifflin web site for interactive features specific to our textbook:  www.college.hmco.com

 

Calculus II- Course Objectives

The specific content and skill objectives of MAT 234 include the following:

 

bulletDifferentiate the natural logarithmic functions
bulletIntegrate rational functions using the Log Rule
bulletIntegrate all six basic trigonometric functions
bulletFind the derivative of an inverse function
bulletIntegrate and differentiate natural exponential functions and exponential functions with bases other than e
bullet Solve simple differential equations
bulletIntegrate and differentiate inverse trigonometric functions
bulletIntegrate and differentiate hyperbolic functions and inverse hyperbolic functions
bulletDetermine the area of a region between two curves
bulletCompute the volume of a solid of revolution using both the disk, washer and shell methods
bulletFind the arc length of a smooth curve
bulletFind the area of a surface of revolution
bulletSolve applications of integration: work, center of mass, and fluid pressure and force
bulletFind an antiderivative using the following techniques: parts, trigonometric substitution, partial fractions, tables, and powers of trigonometric functions
bulletDetermine when and how to employ L’Hopital’s Rule
bulletEvaluate improper integrals
bulletDetermine if a sequence converges or diverges
bulletDetermine if a series converges or diverges
bulletDetermine the sum of a convergent series
bulletFind a Taylor or Maclaurin series for a function

 

TENTATIVE HOMEWORK ASSIGNMENTS

(Assume odd numbered problems.)

 

Section                        Topic                                            Page            Questions

5.1 The Natural Logarithmic Function :

Differentiation

321 #7 – 69 odd

 

5.2 The Natural Logarithmic Function:

Integration

330 #1 – 35 odd

 

5.3 Inverse Functions 338 #1 – 41, 59-61, 71-81 odd

 

5.4 Exponential Functions: Differentiation &

Integration

347 #1 – 21, odd 25-28 all, 37-57 odd

 87-107 odd

5.5 Bases Other Than e and Applications

 

357 #1 – 17, 41-55, 61-67

 

 

TEST #1

 

 

5.6 Differential Equations: Growth & Decay 366 #1, 11, 21, 25, 33, 35, 49, 65-71 odd
5.7 Differential Equations: Separation of Variables 377 #1, 7, 13, 21, 25, 31, 43, 55-69, 77, 87
5.8 Inverse Trigonometric Functions: Differentiation 386 #5, 13, 17, 21, 31, 41, 71

 

5.9 Inverse Trigonometric Functions:  Integration 393 #1 – 17, 31-39, 51 odd

 

5.10 Hyperbolic Functions 403 #1 – 27, 37, 39-53, 55-61, 67-81 odd

 

 

TEST #2

 

 

6.1 Area of A Region Between Two Curves 418 #1 – 11, 15-27, 41, 53, 71 odd

 

6.2 Volume: The Disk Method

 

428 #1 – 31 odd
6.3 Volume: The Shell Method

 

437 #1 – 23 odd
6.4 Arc Length & Surfaces of Revolution 447 #1 – 19 odd

 

 

 

TEST #3

 

6.5 Work 457 #1 – 15 odd
6.6 Moments, Centers of Mass, and Centroids 467 #1 – 13 odd

 

6.7 Fluid Pressure & Fluid Force 474 #1 – 19 odd

 

 

TEST #3 – part 2

 

7.1 Basic Integration Rules 486 #1 – 41 odd

 

7.2 Integration by Parts 495 #1 – 41 odd

 

7.3 Trigonometric Integrals 503 #3 – 35 odd

 

7.4 Trigonometric Substitution 512 #5 – 39 eoo

 

 

TEST #4

 

7.5 Partial Fractions 522 #1 – 27

 

7.6 Integration by Tables & Other Integration Techniques 528 #1 – 13, 19-47 odd
7.7 Indeterminate Forms & L’Hopital’s Rule 537 #1 – 53 odd

 

7.8 Improper Integrals

 

547 #3 – 75 eoo

 

TEST #5

 

8.1 Sequences 564 #1 – 15, 27 – 41, 47 –77 odd

 

8.2 Series & Convergence 573 #1 – 15, 21 – 25, 33 – 45, 51 - 61

 odd

8.4 Comparison of Series 587 #3 – 13 odd

 

8.5 Alternating Series

 

595 #11 – 23 odd
8.7 Taylor Polynomials & Approximations 613 #13 – 23 eoo

 

 

TEST #6

 

8.10 Taylor & Maclaurin Series 641 #1 - 9

 

CUMULATIVE FINAL EXAM