Calculus II

CVCC Course number - MATH 174 - 4 credit hours
INSTRUCTOR: Mr. Howard        ROOM: 205
TIME: MWTh  7:30 - 8:20, 8:25 – 9:15

COURSE DESCRIPTION: A college level study of integral calculus, this course includes the study of Riemann Sums, antiderivative, definite and indefinite integrals, integration techniques, applications of integration, solving differential equations, convergence of sequences and series, and Taylor Series.  Upon completion of the course the students earn 4 semester hours from the Central Virginia Community College.

COURSE CONTENT: At the end of the semester, the student will be able to:

• interpret the definite integral
• perform integration using u-substitution, integration by parts, partial fractions, trigonometric substitution, power reduction of integrals involving trig functions and table look-up
• approximate the definite integral using Riemann Sums, Trapezoidal Rule (with error) and Simpson’s Rule with error
• apply L’Hopital’s Rule when evaluating limits
• evaluate improper integrals
• apply the definite integral (position-velocity-acceleration, growth and decay, work, force-pressure, economics, probability distributions, volumes by slicing, arc length and surface area), using rectangular and polar functions
• solve separable differential equations using tables, slope fields, numerical techniques including Euler’s Method and algebraic techniques
• solve logistic and preditor/prey population models
• Determine convergence/divergence of infinite sequences
• Determine convergence/divergence of geometric series
• Apply integral, comparison, alternating series, absolute convergence, and ratio tests to determine series convergence/divergence
• determine radius of convergence of power series
• find Taylor and MacLaurin polynomials and Taylor and MacLaurin series with error term

COURSE OBJECTIVES: At the end of the semester, students will have an understanding of the concepts and techniques listed above.  This understanding will be enhanced, when appropriate, through directed group and individual computer exercises and group and individual projects. 

CLASS METHODOLOGY: A small amount of time at the beginning of most class periods will be used to answer questions on the material that is due for that day.  The rest of the class period will consist of a variety of activities which will include lecture (usually by me, but you may get a turn before the year is gone), group problem solving and exploration of questions and concepts using selected software.  Periodically we will have question and answer days (see course calendar for details).  Your math/tech time will also provide ample opportunity for these ventures, along with allotted time to take your online quizzes.  It is strongly advised (shall we say required) that you prepare for each class meeting by reading the material AND by working the problems for the next class meeting.  It is solely your responsibility to prepare for class.

GRADING: The semester grade will be determined as follows:

             The mean (average) of all tests (3 tests + S³). - 60%
             Pledged problems/quizzes/Online homewok. - 15%
             Final exam (comprehensive) . - 25%

Pledged problems are problems/exercises which shall be turned in and graded.   Ilrn problems are web-based problem sets which will be graded.  You will be asked to present problems to the class and participate in group discussions. 

The grading scale is a ten point scale.

Six week grades should be viewed as a progress report for the entire semester.  All 6 week grades will be cumulative from the beginning of the semester!

ABSENCES/TARDINESS: If a student is absent (excused) for only one class meeting, then upon return, he/she is expected to have completed the work which was due on the day of absence.  If a test was missed, then the student is expected to take the test on the day of return.  If a student misses two or more consecutive class meetings, then he/she should talk to the instructor to devise a game plan to catch up.  Absences for any other reason need to be discussed with the instructor in advance.  Failure to do so will result in an unexcused absence.  Work missed because of an unexcused absence cannot be made up.  If a test is missed because of an unexcused absence, then that test grade will be lowered by 10 points for each day late.  You are expected to be in class on time.  You will be allowed one and only one tardy "on the house".  After that you will pay 1/2 a point off your semester grade for any additional tardies!

HONOR CODE: Students are required to pledge all work that they turn in for a grade.  Refer to CVGS Student Handbook for complete requirements.

Tentative Schedule:  

Chapter 8 - Integration Techniques

Chapter 8 - Integration Techniques Homework Assignments

Sec 8.2 page 531: 11-19 odd, 27, 33, 35, 90, 92

Sec 8.3 page 540: 5-17 odd, 25-41 odd

Sec 8.4 page 549: 5-15 odd, 21-35 odd, 43

Sec 8.5 page 559: 7-25 odd, 41, 48

Sec 8.6 page 565: 15-41 odd, 51, 53, 55

Sec 8.7 page 574: 11-19 odd, 37-53 odd, 85

Sec 8.8 page 585: 15-35 odd

Applets for Chapter 8 topics

1. L'Hopital's Rule
2. Improper Integrals

Chapter 7 - Applications of Integration

Chapter 7 - Applications of Integration Homework Assignments

Sec 7.1 page 452: 13, 14, 17-31 odd

Sec 7.2 page 463: 5, 9, 11, 13, 19, 21, 27, 31, 47, 49, 53

Sec 7.3 page 472: 1, 3, 13, 19, 21, 23, 28, 43

Sec 7.4 page 483: 3, 5, 9, 11, 35, 39, 41, 51, 55

Sec 7.5 page 493: 9, 11, 17, 20, 21, 23, 29, 31, 33

Sec 7.6 page 504: 1, 3, 13-19 odd, 33, 36, 45

Sec 7.7 page 511: 3, 7, 9, 17, 25, 26

Sec 8.8 page 585: 77

Sec 10.5 page 745: 5, 7, 8, 11, 13

Applets for Chapter 7 topics

Applications of Integration

1. Areas by Slicing
2. Volumes of Revolution
3. Volumes of Known Cross Section
4. Arc Length
5. Area of Polar Curve

Chapter 9 - Sequences and Series

Chapter 9 - Sequences and Series Homework Assignments

Sec 9.1 page 602: 1, 3, 11, 25, 37, 39, 47, 49, 51, 69, 73, 75

Sec 9.2 page 612: 7-16, 51, 53, 57, 59, 61, 63, 99

Sec 9.3 page 620: 1-17 odd, 25, 27

Sec 9.5 page 636: 11-19 odd, 47-57 odd

Sec 9.6 page 645: 13-27 odd

Sec 9.7 page 656: 13, 17, 25, 29, 31, 32

Sec 9.8 page 666: 11, 15

Sec 9.9 page 674: 21

Sec 9.10 page 685: 1, 3, 5, 6, 11, verify Taylor Series for 1/x, ln x, sin x

Applets for Chapter 9 topics

Sequences and Series

1. Sequences
2. Series
3. Integral Test
4. Comparison Test
5. Limit Comparison Test
6. Ratio Test
7. Alternating Series and Absolute Convergence
8. Power Series & Interval of Convergence
9. Taylor Series & Polynomials

Chapter 6 - Differential equations

Chapter 6 - Differential equations Homework Assignments

Sec 6.2 page 400: 1-9 odd, 17, 41, 42, 71, 72

Sec 6.3    page 465: 1, 3, 8, 19, 20, 22, 77, 78

Sec 6.5 page 431: 39, 40, 43

Applets for Chapter 6 topics

Differential Equations

1. Slope Fields
2. Euler's Method
3. Separation of Variables
4. Growth, Decay and the Logistic Equation

Senior Science Scenario