Northeastern State University

College of Mathematics, Science, and Nursing

Department of Mathematics and Computer Science

Syllabus for Math 2624 Calculus II

PREREQUISITES: Math 2614 - Calculus I

CATALOG DESCRIPTION OF COURSE: Inverse functions, logarithm and exponential functions, hyperbolic functions, techniques of integration, improper integrals, L'Hospital's rule and infinite series.

COURSE PURPOSE: To provide the necessary background, understanding and skills of differentiation and integration for solving problems in science, business and more advanced mathematics.

EXPECTED COURSE OUTCOMES: The student will be expected to achieve the following objectives:

1. Determine the derivatives and integrals of exponential and logarithmic functions.

2. Determine the derivatives and integrals of hyperbolic functions.

3. Apply techniques to find the volumes of solids of revolution, including the use of physical models of the shell and disk methods.

4. Find curve lengths and surface areas of solids of revolution.

5. Understand the idea of integration and apply this reasoning to model real-world phenomena.

6. Communicate a working knowledge of the techniques of integration.

7. Use standard techniques to discuss the convergence of sequences and infinite series.

8. Obtain a familiarity with conic sections.

9. Apply geometric concepts to investigate the calculus of parametrized curves.

10. Investigate the calculus of polar equations.

INSTRUCTIONAL MATERIALS: (Required Textbook) Finney, Ross L and Thomas, George B, Calculus Second Edition : Addison-Wesley Publishing Company 1994.

Recommended: Graphing calculator ( TI - 83 recommended)

INSTRUCTIONAL PROCEDURES: The expected outcomes of this course will be achieved by lecture, classroom discussion, and written exercises.

Calculus II

I. Transcendental Functions (Weeks 1-4)

• Exponential Functions and their Derivatives

• Inverse Functions and their Derivative

• Logarithmic Functions and the derivative of ln x

• Exponential and Logarithmic Integral

• Growth and Decay

• L'Hospital's Rule

• Relative Rates of Growth

• Inverse Trigonometric Function

• Derivatives of Inverse Trigonometric Functions

• Hyperbolic Functions

• First Order Differential Equations

II. Applications of Integration (Weeks 4 - 7)

• Area Between Curves

• Volumes of Solids of Revolution - Disks and Washers

• Cylindrical Shells - An Alternative to Washers

• Curve Length and Surface Area

• Work

• Centers of Mass

III. Techniques of Integration (Weeks 7 -9)

• Basic Integration Formulas

• Integration by Parts

• Partial Fractions

• Trigonometric Substitutions

• Integral Tables

• Improper Integrals

IV. Infinite Series (Weeks 10 - 13)

• Sequences

• Infinite Series

• Series with Nonnegative Terms - Comparison and Integral Tests

• Series with Nonnegative Terms - Ratio and Root Tests

• Alternating Series and Absolute Convergence

• Power Series

• Taylor and Maclaurin Series

• Calculations with Taylor Series

V. Conic Sections, Parametrized Curves, and Polar Coordinates (Weeks 14 - 15)

• Conic Sections and Quadratic Equations

• Parametrizations of Curves

• Calculus with Parametrized Curves

• Polar Coordinates

• Polar Graphs

• Integration in Polar Coordinates

ADA COMPLIANCE: If any member of the class feels that he/she has a disability and needs special accommodations of any nature whatsoever, the instructor will work with you and the University's Office of Student Affairs to provide reasonable accommodations to ensure that you have a fair opportunity to perform in this class. Please advise the instructor of such disability and the desired accommodations at the first class attended.

INCLEMENT WEATHER / DISASTER POLICY: The following are basic premises for the inclement weather policy at Northeastern State University:

1. Classes are expected to be held if at all possible.

2. It is the student's responsibility to receive the information when weather is questionable.

3. Neither students nor faculty are expected to risk life or limb.

4. Faculty members are obligated to hold classes if the University is not closed, unless the faculty member is unable to get to campus.

Policy: During times of inclement weather, decisions concerning day classes will be made by 6:00 a.m. in order for the media to be notified and for students to receive the announcement before they leave home. Decisions concerning night classes will be made by 3:00 p.m.

The following media will be notified regarding closing of the campus:

Radio Stations: Television Stations:

KRMG 740 AM Tulsa KJRH Channel 2 Tulsa

KAYI 107 FM Tulsa KOTV Channel 6 Tulsa

KTLQ 1350 AM Tahlequah KTUL Channel 8 Tulsa

KEOK 102 FM Tahlequah KFSM Channel 5 Fort Smith

KBIX 1490 AM Muskogee Cable Channel 96 Tahlequah

KMMY 97 FM Muskogee

KVOO 1170 AM Tulsa

The automated attendant message on 918-456-5511 will be modified to include information concerning campus operations during inclement weather.