NORTHWEST-SHOALS COMMUNITY COLLEGE

GENERAL COURSE SYLLABUS

TITLE OF COURSE: Calculus II (MTH 126)

DIVISION: Mathematics, Science, and Technology

COURSE DESCRIPTION: This is the second of three courses in the basic calculus sequence. Topics include vectors in the plane and in space, lines and planes in space, applications of integration (such as volume, arc length, work and average value), techniques of integration, infinite series, polar coordinates, and parametric equations.

HOURS:

Credit: 4 Contact: 4

Lecture: 4 Clinical: 0

Lab: 0

PREREQUISITE(S): MTH 125

COREQUISITE(S): None

REQUIRED TEXTBOOK(S): Calculus, Eighth Edition, by Larson, Hostetler, and Edwards, Houghton-Mifflin Co., 2006.

SUPPLIES: Rectangular and Polar Graphing Paper, Graphing Calculator.

GENERAL EDUCATION OBJECTIVE: All associate degree graduates should be able to use the mathematical concepts, notations, and manipulations needed in their field of study or occupation. (3)

COURSE OBJECTIVE(S): Upon successfully completing Calculus II, the student should be able to:

1. Apply integration methods to find the volume of a solid of revolution and to solve other application problems involving arc length, surface area, work, or average value.

2. Find antiderivatives using integration by parts, a table of integrals, trigonometric identities, trigonometric substitutions, partial fractions, and other algebraic techniques.

3. Evaluate improper integrals using limits, including those requiring L’Hopital’s Rule.

4. Determine convergence or divergence for sequences and series, and use series to represent certain functions.

5. Convert between rectangular, parametric, and polar forms and find derivatives for parametric and polar equations.

6. Perform operations with vectors, and write equations of lines and planes in space.

METHODS OF EVALUATION:

1. Course Grade Evaluation: (Minimum of 4 measurements)

A comprehensive final exam will be given and counted toward the student’s final average. Make-up examinations, as such, will not generally be given.

2. Evaluation of General Educational Objectives: Student success on the General Educational Objective (3) is measured by student performance on each of the course objectives, which require use of mathematical concepts, notations, and manipulations. Performance on each course objective will be evaluated using appropriate problems from the final exam. Results will be tallied for each course objective.

3. Use of Findings: Instructors will analyze data gathered from the assessment(s) for each course objective and changes will be made based on identified weaknesses. The math department will meet once every three years to discuss findings and implement strategies to improve department and student performance.
   
   

OUTLINE OF COURSE TOPICS:

I. Applications of Integration

A. The Average Value of a Function

B. Area Between Two Curves

C. Volume: The Disc Method

D. Volume: The Shell Method

E. Arc Length and Surfaces of Revolution

F. Work

II. Integration Techniques, L'Hopital's Rule, and Improper Integrals

A. Basic Integration Rules

B. Integration by Parts

C. Trigonometric Integrals

D. Trigonometric Substitution

E. Partial Fractions

F. Integration by Tables and Other Techniques

G. Indeterminate Forms and L'Hopital's Rule

H. Improper Integrals

III. Infinite Series

A. Sequences

B. Series and Convergence

C. The Integral Test and p-Series

D. Comparisons of Series

E. Alternating Series

F. The Ratio and Root Tests

G. Taylor Polynomials and Approximations

H. Power Series

I. Representation of Functions by Power Series

J. Taylor and Maclaurin Series

IV. Conics, Parametric Equations, and Polar Coordinates

A. Conics and Calculus

B. Plane Curves & Parametric Equations

C. Parametric Equations and Calculus

D. Polar Equations and Polar Graphs

V. Vectors and the Geometry of Space

A. Vectors in the Plane

B. Space Coordinates and Vectors in Space

C. The Dot Product of Two Vectors

D. The Cross Product of Two Vectors in Space

E. Lines and Planes in Space

AMERICANS WITH DISABILITIES ACT POLICY: It is the policy of Northwest-Shoals Community College to comply with the Americans with Disabilities (ADA) Act. Any student covered under this act needing and desiring reasonable accommodations for this class should notify Linda Waide at 331-5321. See NWSCC catalog for additional details.

ATTENDANCE POLICY: Because class attendance is considered to be essential to the accomplishment of course objectives, excessive absences are discouraged. At no time should a student miss more than 20% of the class meetings for a course. These absences also include any absences accrued during late registration. Failure to adhere to the 20% policy may result in a failing grade based on academic performance. Students should discuss with the instructor what is considered “excessive” for a particular course. Any variation of this policy must be approved through the Chief Instructional Officer. A student who is absent due to required participation in a school activity must be allowed to make up work, according to guidelines issued by individual instructors.

WITHDRAWAL POLICY: A student who is unable to complete a course is expected to withdraw from that course by the end of 60% of class meetings. A student who withdraws by the date published in the schedule will receive a grade of “W” for the course. This withdrawal is done only by student request. The grade of “W” is allowed regardless of the student’s grades to the point of withdrawal.

After the designated date of class withdrawal, the approval of the Chief Instructional Officer is required prior to allowing a student to withdraw. The determination of “WP” (withdrawal passing) or “WF” (withdrawal failing) will be made by the instructor for the course and is based on the student’s grades to the point of withdrawal.