Mercer County Community College                                               Liberal Arts Division

 

MAT 112                                                            Calculus 2

 

TENTATIVE COURSE OUTLINE

 

Catalog Description:

A continuation of MAT111.  This is the second course in the standard integrated calculus sequence.  Topics include definitions of the indefinite and definite integrals of algebraic, logarithmic, exponential, and trigonometric functions, techniques and applications of integration, improper integrals; infinite sequences and series; analytic geometry and polar coordinates.

 

Prerequisites:            MAT111 with minimum C grade

 

Required Materials:

            Text:    Calculus

                        Howard Anton, 7th edition

 

A graphing calculator is required.  TI – 83 or 86  will be used by the instructor and is therefore strongly recommended for the student

 

 

Instructor:  Richard Porter     

 

E-mail: porterr@mcc.ecu 

 

Web Page:    http://www.mcc.edu/~porterr

 

Office: LA 114  Extension 3826

 

Office Hours:  See Web Page

 

Grading:

 

Quizzes and Homework:      40%

Midterm:                                 20%

Final:                                       40%

 

Grade Scale:

90%-100%........A

80%-89.5%.......B

70%-79.5%.......C

60%-69.5%.......D

<59.5%.............F

1

1/22/2003

M

6.1,6.2

2

1/27/2003

W

6.2,6.3

3

1/29/2003

M

6.3,6.4

4

2/3/2003

W

6.4,6.5

5

2/5/2003

M

6.6,6.7

6

2/10/2003

W

6.8,6.9

7

2/12/2003

M

Review

8

2/17/2003

W

7.1-7.3

9

2/19/2003

M

7.4-7.6

10

2/24/2003

W

7.7,7.8

11

2/26/2003

M

8.1,8.2

12

3/3/2003

W

8.3,8.4

13

3/5/2003

M

8.5

14

3/10/2003

W

8.6

15

3/12/2003

M

8.7,8.8

16

3/24/2003

W

Review

17

3/29/2003

M

Midterm

18

3/31/2003

W

10.1,10.2

19

4/5/2003

M

10.3

20

4/7/2003

W

10.4,10.5

21

4/12/2003

M

10.6

22

4/14/2003

W

10.7

23

4/19/2003

M

10.8

24

4/21/2003

W

10.9

25

4/26/2003

M

10.1

26

4/28/2003

W

Review

27

5/3/2003

M

11.1,11.2

28

5/5/2003

W

11.3,11.4

29

5/10/2003

M

11.5,11.6

30

5/12/2003

W

Review

 

 

 

UNIT I            (Chapter 6)      Integration

Classes 1-6

1.         Associate the process of integration with finding the area under a curve.

2.         Find the infinite integral for polynomial, trigonometric, logarithmic and exponential function by reversing the derivative formulas.

3.         Use a u – substitution to find an indefinite integral and when given conditions evaluate the constant of integration.

4.                  Interpret and use the properties of sigma notation to evaluate sigma notated problems.

5.                  Use the left end point, right end point, and mid point approximations and the properties of limit to determine exact areas under a curve.

6.                  Use the theorems and properties to evaluate and rewrite definite integrals.

7.                  State and use the First Fundamental Theorem of Calculus, the Mean Value Theorem for Integrals, and the Second Fundamental Theorem of Calculus.

8.                  Use integration techniques to determine velocity and position functions when given an acceleration function, and to find the average value of a continuous function over a closed interval.

9.                  Use u – substitution to rewrite the integrals and redefine its bounds to evaluate composite function integrals.

10.              Define the natural logarithm as an integral and use the definition and the properties of limits to aid in evaluating limits of exponential and logarithmic functions.

UNIT II  (Chapter 7) Applications of the Definite Integral

Classes 7-10

1.         Find the area bounded by several functions using x or y as the independent variable of integration.

2.         Find the volume generated by revolving an area bounded by several functions about the x axis or y axis by using the disk-washer or cylindrical shells methods.

3.                  Use integrals to find the length of a plane curve.

4.         Use integrals to find the surface of revolution.

5.         Define the hyperbolic functions and their inverses.

6.         Find derivatives and integrals involving the hyperbolic functions and their inverses.

UNIT III (Chapter 8)  Principles of Integral Evaluation

Classes 11-17

1.         Apply the appropriate integration formulas previously presented in this course.

2.         Recognize when to use and perform integration by parts as many times as needed to evaluate an integral.

3.         Use trigonometric identities to integrate powers of trigonometric functions.

4.         Use trigonometric substitution where applicable to evaluate integrals.

5.         Use partial fraction decomposition when needed to integrate rational functions.

6.         Use integral tables to evaluate integrals.

7.         Use the trapezoid rule or Simpson’s rule to approximate definite integrals.

8.         Determine whether an integral is improper, and if so, determine if it converges or diverges and be able to find what it converges to if it converges.

UNIT IV (Chapter 10) Infinite Series (18 lecture hours)

Classes 18-26

1.         Define an infinite sequence, write several of its terms, write its general term and determine whether it converges to a limit or diverges.

2.         Use the difference, ratio or derivative method to determine if a sequence is eventually monotonic or neither, if sequence is bounded and if it is bounded its limit.

3.         For a given infinite series determine which convergence test (divergence test, integral test, comparison test, limit comparison test, ratio test, root test, alternating series test) to use to determine absolute convergence, conditional convergence or divergence, apply the test and if possible determine the limit.

4.         Write an nth degree Maclaurin or Taylor polynomial for a given function and determine the related Maclaurin or Taylor series.

5.         Find the radius of convergence and interval of convergence for a given power series.

6.         Use the Remainder Estimation Theorem to estimate the error in using a polynomial of nth degree to approximate a function.

7.         Perform algebraic and calculus manipulations of power series.

 

UNIT V (Chapter 11) Analytic Geometry in Calculus

Classes 27-30

1.         For given points or equations in rectangular form convert them to polar form and vice versa.

2.         Graph equations and points using the polar coordinate system and polar symmetry tests.

3.         Determine the polar equation for a given graph.

4.         Find slopes of tangent lines, equations of tangent lines and length of parametric and polar curves.

5.         Find areas of regions that are bounded by polar curves.

6.         Find vertices, foci, centers, asymptotes, directrix, where applicable of conic sections given in rectangular form and use this information to solve application problems.

7.         For a given polar equation of a conic section find its eccentricity, foci, the distance from the pole to the directrix or vertices in order to graph the conic section.

8.         Find the polar equation of a conic section for given conditions.

 

It is essential that the student, throughout the semester, devote at least eight hours per week in homework effort.