SYLLABUS
Embry-Riddle Aeronautical University
College Of Career Education
**Last Updated 12/16/00**
Course Number: MA 112
Course Title: College Mathematics for Aviation II
(03 Semester Hours)
Course Texts:
Washington, A. J.(2000). Basic technical mathematics with calculus (7th ed.). Menlo Park,
CA: Addison Wesley.
Supplementary Materials:
1. A scientific calculator. (Required)
2. Martin, John R. Student Solutions Manual for the Allyn J. Washington Series in Basic Technical Mathematics with Calculus, 7th Ed., Addison Wesley Pub. (Optional)
3. World Wide Web Sites: Jack R. Hunt Library on-line resources: http://amelia.db.erau.edu/ec/index.html http://amelia.db.erau.edu/cgi-bin/library_links.pl
http://www.comlab.ox.ac.uk/oucl/users/jonathan.bowen/algebra/algebra.html
http://www.sisweb.com/math/tables.htm
http://www.geom.umn.edu/apps/gallery.html
http://www.math.psu.edu/dna/graphics.html
http://www.interdigm.com/mwarner/MA112 (class website and bulletin board)
Student Resources:
Resident Center Riddle Aviation Collection (RAC). Available at the Resident Center.
Extended Campus Videotape Library. Available at the Resident Center.
Guide to Library Resources (Area Libraries). Available at the Resident Center.
Extended Campus Student Handbook: [On-line]. Available:
http://www.ec.erau.edu/cce/faculty/studhndbk.shtml
Resident Center computer(s) for academic support. Available at the Resident Center.
Course Description:
Basic calculus designed for the student of aviation. Differentiation and integration of algebraic functions; applications to velocity, accelerations, area, curve sketching and computation of extreme values. Prerequisite: MA111
Goals:
This course is designed to provide the Aeronautical Science, Aircraft Maintenance and Professional Aeronautics students with an understanding of basic differential and integral calculus as a mathematics foundation for further work in their degree program. It is also intended that the student gain insight into some of the problem-solving techniques used in modern science and technology.
Learning Outcomes:
Upon course completion, students will be able to:
1. Identify basic functions from their graphs and evaluate limits from graphs and from algebraic expressions.
2. Find the derivative of a product, a quotient, a composite and an implicit function.
3. Use the derivative to find tangent lines and interpret tangent slope as a rate of change. Apply rate-of-change concepts to problems involving straight line motion.
4. Use calculus to solve applied optimization problems.
5. Analyze graphs of polynomial functions using the derivative as a tool.
6. Find the antiderivative of a function. Use these techniques to manipulate indefinite integrals.
7. Compute the area under a curve using approximate and exact methods. Interpret area for various functions arising in the field of Aeronautical Science.
8. Using integration, derive the equations of motion. Given initial conditions find velocity and displacement equations.
9. Demonstrate increased cogent abilities to write, speak, and think in mathematical terms relevant to the concepts of this course as enhanced with computer technologies.
Grading:
Class Participation and Involvement |
40 PTS |
10 % |
Topic Report/Presentation (30% Style, 70% Content) |
40 PTS |
10 % |
Homework |
60 PTS |
15 % |
Tests/Quizzes |
160 PTS |
40 % |
Final Exam |
100 PTS |
25 % |
Total: |
400 PTS |
100 % |
Grade Points |
Grade |
Percentages |
400 - 360 PTS |
A (Superior) |
100-90 % |
356 - 320 PTS |
B (Above Average) |
89-80 % |
316 - 280 PTS |
C (Average) |
79-70 % |
276 - 240 PTS |
D (Below Average) |
69-60 % |
236 - 000 PTS |
F (Failure) |
59-00 % |
Teaching Methods:
Class meetings will be comprised of lectures and discussions of assigned material, sample solutions to representative problems, board work, graphing calculator and computer lab demonstrations, and testing for understanding. Class participation is expected with emphasis on aviation related applications.
Class Policies:
Assignments: All students are expected to bring their text, calculator, paper and pencil to each scheduled class where academic honesty is the required mode of behavior. Assignments contained herein, and as augmented at instructor's discretion, shall be completed prior to the next scheduled class session and will not be accepted beyond that date without prior instructor approval. Assignments constitute minimum coverage of the required lessons and the student is encouraged to complete additional exercise problems contained within each assigned chapter to promote mastery of the objectives. Course content may vary from this syllabus to meet the needs of this particular class composition
Guidelines for Project: The Project Report will be done individually. Each student will select a problem or project from suggested topics list posted on the class website. By the third weekend of class, each student will deliver the Project Outline, a one-page outline (bullets) of the Project Report. It is a formative exercise, preferably delivered by E-Mail, so the student can obtain early feedback on the expectations for the report. The final four-page Project Report and 10-minute Oral Presentation are due the last week of class.
Make-Up of Classes/Examinations: The faculty of Embry-Riddle Aeronautical University affirms the importance of prompt and regular attendance on the part of all students. Quality instruction clearly depends upon active student participation in the classroom or its equivalent learning environment. Your participation is particularly important in this course, since each class constitutes a significant percentage of the total course. All absences, regardless of reason, require a make-up assignment, mutually arranged between the instructor and the student. If an absence is anticipated, the student should notify the instructor, preferably in advance. Students are encouraged to assist each other with access to class notes for missed classes.
Academic Honesty And Integrity: Academic honesty is the expected mode of behavior. All honesty violations will be treated seriously as prescribed by the University. Plagiarism is perhaps the most common and misunderstood form of academic dishonesty. It involves the taking of ideas, writings, etc. from another and passing them off as one's own. Plagiarism includes the use of any source to complete academic assignments without proper acknowledgment of the source.
Proprietary Information: While the University’s teaching/learning model emphasizes the sharing of professional experiences in the context of analyzing relevant course materials, it is against the policy of Embry-Riddle Aeronautical University for students and/or faculty members to share information about present or past employers that would be considered to be "proprietary," "confidential," "company sensitive," or "trade secret."
Harassment and Unethical Behavior: All employees and students have a right to an environment free of discrimination, including freedom from sexual harassment. It is the policy of Embry-Riddle Aeronautical University that no employee or student may sexually harass another. The intent of this policy is not to create a climate of discomfort but to foster responsible behavior in an academic and working environment free of discrimination. The University sexual harassment policy can be found in ERAU Administrative Policies and Procedures Manual (APPM) section 8.3.4 at http://www.db.erau.edu/appm/policy/8-3-4.html
Student Preparation and Participation: As a MINIMUM, all students are EXPECTED to have READ and thought about the information provided in the assigned chapters BEFORE class commences! This is a professional responsibility to yourself and your classmates. Active participation in class discussions is an important element of a collegiate program; it is evaluated by instructors and is reflected in the assignment of course grades. Participation includes the quantity and quality of comments and class discussions, lively fellowship, positive contributions to group assignments, ability to respond to questions by classmates and the instructor and ability to work as a member of a group. Students are expected to synthesize, analyze and integrate all reading assignments. It is obvious that consistent attendance and being on time is an essential ingredient of participation.
Computing, Critical Thinking, Speaking and Writing Across the Curriculum:
In addition to the specific content of this course, there will a concentration on the development of the students’ computing, critical thinking, speaking and writing skills:
(1) Computing: Students will be expected to use computer technology in this course. Use of word-processing to compose and edit course papers, PowerPoint or HTML to make class presentations, and E-mail to communicate with other students and the instructor is the recommended class standard,
(2) Critical Thinking: Students will be encouraged to form their own opinions and analysis of the relevant course topics and information. Throughout the course, they will be encouraged to use clear, logical thinking. The ability to analyze situations using sound, scientific reasoning will be emphasized,
(3) Speaking: Students will be expected throughout this course to express themselves orally. Their opinions will always be sought on a voluntary basis. Each student will have an opportunity to make a presentation in the course, and
(4) Writing: The required report is recommended to be written in ERAU Graduate Research Project (GRP) format and style, using the GRP Guidelines and the American Psychological Association (APA) format. The GRP/APA format uses citations in the text, when citing another author’s work, and a reference list at the end with all the sources. GRP/APA is very formal, third person, uses no contractions and has a very specific style. Development of writing skills is considered an essential element of this course.
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Session #1:
Topic: Course Overview, Review of The Straight Line and Limits, and Intro to Derivatives
Objectives:
1. The student will know the scope and concept of the course to include the classroom procedures, homework requirements, examinations and grading policy.
2. The student will be able to compute the slope and intercepts of a straight line from its equation and write the equation of a line in slope-intercept and general forms.
3. The student will be able to compute the limits of a variety of algebraic functions.
4. The student will be able to state the definition of the derivative of a function, use the definition to compute the derivatives of simple algebraic functions; find the slope of a tangent line to a curve using the delta process; and use the derivative to find the velocity and acceleration of an object in linear motion.
Assignment: Read/review sections 5-2, 21-2, and 23-1 thru 23-4. Do assigned problems from assignment sheet handout.
Session #2:
Topic: Computation of Derivatives
Objectives:
1. The student will be able to compute the derivative of a polynomial, to use the product rule, the quotient rule, the power formula and implicit differentiation, and to compute the derivative of various algebraic functions.
2. Test over material covered during week #1.
Assignment: Read sections 23-5 thru 23-9. Do problems as assigned.
Sessions #3:
Topic: Tangent, Normal Lines and Curvilinear Motion
Objectives:
1. The student will be able to write the equation of the tangent line and normal line to a point on a curve.
2. Be able to find approximate roots for f(x) = 0 according to Newton"s Method.
3. The student will be able to find the velocity and acceleration vectors of an object in curvilinear motion.
Assignment: Read sections 24-1 thru 24-3. Do problems as assigned.
Session #4:
Topic: Related Rates and Curve Sketching
Objectives:
1. The student will be able to find the time rate of change of a physical quantity using related rates.
2. The student will be able to sketch the graph of a function by finding the intervals where the function is increasing or decreasing and to find the relative maxima and minima.
3. Test over week #2 and #3 material.
Assignment: Read section 24-4 and 24-5. Do problems as assigned.
Session #5:
Topic: More Curve Sketching and Maximum and Minimum Problems
Objectives:
1. The student will be able to use intercepts, symmetries, asymptotes, and vertices in sketching functions.
2. The student will be able to use the first and second derivatives to find the maximum and minimum of a physical quantity.
3. The student will be able to find differentials and linear approximations of a function.
Assignment: Read section 24-6 thru 24-8. Do problems as assigned.
Session #6:
Topic: Differentials, Antiderivatives and Indefinite Integrals
Objectives:
1. The student will be able to use differentials to find absolute and relative errors in functional change.
2. The student will be able to find the indefinite integral of simple algebraic functions.
3. Test over week #4 and #5 material.
Assignment: Read section 25-1 thru 25-3. Do problems as assigned.
Session #7:
Topic: Area Under a Curve, the Definite Integral, and Numerical Integration
Objectives:
1. The student will be able to approximate the area under a curve using the rectangular method and to calculate the exact area using integration.
2. The student will be able to evaluate the definite integral of various algebraic functions.
3. The student will be able to evaluate the definite integral using the Trapezoidal Rule and Simpson’s Rule.
Assignment: Read section 25-4 thru 25-7. Do problems as assigned.
Session #8:
Topic: Applications of the Indefinite Integral, Area Computation and Final Exam Review
Objectives:
1. The student will be able to compute such quantities as distance, velocity, voltage, current, etc., by using the indefinite integral.
2. The student will be able to use the definite integral to compute the area bounded by two or more curves.
3. Practice Final Examination.
4. Test over week #6 and #7.
Assignment: Read section 26-1 and 26-2. Do problems as assigned.
Session #9
Topic: Final Exam
Objective:
1. Assess student comprehension of materials covered in this course.
2. Oral presentations of Project Reports.
For questions contact Instructor: E-mail.
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