Truman College-Mathematics Department Math 209-ABC: Calculus and Analytic Geometry III Course Syllabus Spring 2012

Transcription

1 Truman College-Mathematics Department Math 209-ABC: Calculus and Analytic Geometry III Course Syllabus Spring 2012 Instructor: Dr. Abdallah Shuaibi Office #: URL: Phone #: (773) Office Hours: DAYS ADVISEMENT OFFICE HOURS WALK-IN OFFICE HOURS Monday 8:30-9:00 AM & 11:30 AM - 12:00 PM 4:30-6:30 PM Wednesday 8:30-9:00 AM & 11:30 AM - 12:00 PM Thursday 2:00-3:00 PM 4:00-6:00 PM MML Website Address: MML Course ID: shuaibi29579 The Truman College Mission Statement: Our Mission dedicates us to deliver high-quality, innovative, affordable, and accessible educational opportunities and services that prepare students for a rapidly changing and diverse global economy. Class Time and Place: Monday & Wednesday 9:00-11:25 AM, Room #: A grade of C or better in Mathematics 208, or consent of department chairperson. Contact & Credit Hours: Five hours per week, for sixteen weeks for five(5) credit hours. The instructor is also available for consultation during conference hours. Length of Course: 16 weeks. Students the Course is Expected to Serve: This course is intended for students who are science and engineering majors and require multivariate calculus and vector analysis for their undergraduate degree. Textbook: Thomas s Calculus, 12th Edition, by George B. Thomas, Maurice D. Weir, and Joel Hass. Addison-Wesley Publishing, Course Description: This is the third course in calculus and analytic geometry. This course covers the following topics: Curves in the plane and in the space, Polar coordinates and parametric equations, Vectors in 2 dimensional and 3 dimensional space, Derivatives of vector valued functions, Partial derivatives, Double and triple integrals, Applications, Line integrals and Greens theorem, Divergence and curl, Surface integrals, Gauss theorem and Stokes theorem. Writing assignments, as appropriate to the discipline, are part of the course. Other materials: Students are required to have a scientific or a graphing calculator. You are not allowed to use a cell phone as a calculator. 1

2 MML & Internet Resources: The textbook used for this course is bundled with MyMathLab (MML) software. MyMathLab is a text-specific, easily customizable online courses for textbooks in Mathematics and Statistics. MyMathLab provides a rich and flexible set of course materials, featuring free-response exercises correlated directly to the textbook that instructors can assign for online homework, quizzes, and tests. These exercises regenerate algorithmically for unlimited practice and mastery, and in homework and practice modes, each exercise is accompanied by an interactive guided solution and sample problem. MyMathLab provides students additional with multimedia resources, such as video lectures, animations, and an ebook, to independently improve their understanding and performance. If you bought your textbook at Beck s Bookstore, you should have automatically received MyMath- Lab access code. If you bought your textbook elsewhere, you may not have MyMathLab access code. You should be able to purchase a code online at The rationale for including MML is to enrich your experience learning statistics both inside and outside of the classroom and to give you every possible opportunity to do well. MML provides you with a wonderful tool to support your learning on a 24/7 basis. It is always there for you no matter what your schedule. It is there to help you to reinforce concepts introduced in the classroom. Consider MML as your virtual tutor. Online class work, homework and quizzes/tests will be assigned throughout this course. You will get immediate feedback on each homework problem, and incorrectly worked problems can be repeated (with a new version of the problem provided by the computer) until a correct solution is obtained. Tips and examples are available online for each problem, in addition to the help available from your instructor and the Tutoring Center. Online Assignments may be done at any location with an internet access. Do not wait till the last hour to start and complete online assignments because a computer glitch may prevent you from accessing your account. Additional MML resources are available such as Video lectures, PowerPoint Presentations, Immediate grading and feedback, Access to tutors (at or tutors@aw.com) and Access to technical assistance (at ). Course Objectives: 1. Understand the properties of vectors and apply vector operations in 2- and 3-dimensional space. 2. Conceptualize graphs of surfaces and curves in 3-dimensional space. 3. Understand the concept of differentiability of a function of several variables, including partial derivatives, the total differential and the Chain Rule. 4. Understand the concept of multiple integrals and their applications. 5. Understand the basic theorems of vector analysis such as the Fundamental Theorem of Line Integrals, Greens, Gauss, and Stokes Theorem. 2

3 Student Learning Outcomes: Upon satisfactory completion of the course, students will be able to: 1. Perform vector operations, including dot product, cross product, and the projection of one vector onto another. 2. Determine the parametric and symmetric equations of a line. 3. Determine the equation of a plane. 4. Analyze the graphs of quadric surfaces. 5. Calculate derivatives of vector-valued functions. 6. Calculate unit tangent, unit normal, curvature, and arc length of a space curve. 7. Apply vector operations to motion problems in space. 8. Determine limits, domains and points of discontinuities of real-valued functions of two variables. 9. Calculate first and second partial derivatives. 10. Apply the Chain Rule to multivariate functions. 11. Determine directional derivatives and gradient vectors. 12. Determine the tangent plane to a surface at a point. 13. Determine local extrema and saddle points for functions of two variables. 14. Calculate double and triple integrals, including the use of Fubinis Theorem. 15. Apply the Jacobian determinant to compute multiple integrals for polar, cylindrical, and spherical substitutions. 16. Compute the divergence and curl of a vector field. 17. Calculate the line integral and apply the Fundamental Theorem of Line Integrals to a gradient field. 18. Apply Greens Theorem to the calculation of a line integral. 19. Evaluate a surface integral of a vector field. 20. Apply Gauss Theorem to the calculation of a line integral. 21. Apply Stokes Theorem to the calculation of a surface integral. 3

4 General Education Goals: This course addresses the following TR General Education Goals: The student performs effectively in the workplace and/or has the ability to work and make effective use of wide variety of current technologies. (Gen. Ed. Goal 2) The student demonstrates the ability to think critically, abstractly, and logically. (Gen. Ed. Goal 4) The student demonstrates the ability to work independently. (Gen. Ed. Goal 6) Class Operation: 1. Homework: Reading the relevant sections in your textbook is always expected. Homework assignments will be collected every week. The quizzes will be based on the homework problems, additional worksheets, and problem sets. Students who keep up the daily work are generally those who do well on quizzes and tests. 2. Blackboard & Website: It is your responsibility to check the Blackboard & My Website regularly for announcements, homework assignments, and other important information regarding the course. 3. Online Assignments: Some of the homework or quizzes are online assignments which are created using MyMathLab software. These assignments are automatically graded. Online homework exercises include guided solutions and sample problems to help students understand and master concepts. 4. Quizzes: Throughout the semester, we will have at least 10 quizzes. Quizzes cannot be made up. There are no exceptions. As a result, I will drop the lowest two quizzes. We will not have quizzes on the weeks an exam is scheduled. 5. Tests: There will be two exams during the semester besides the final exam. The final exam is also cumulative, and it will be given during the last week of the semester. Policies: Participation policy: Class participation is mandatory. You are expected to attend most of the class sessions. If you have any question, be ready to ask it at the beginning of the class. The average student should plan two hours of out of class time for each hour of class. Some students need more time than this. Make-up Policy: No make-up exam is given without prior notification and documented acceptable excuse. The student must contact the instructor by telephone or on the day of the exam if there is a problem. If you know in advance of an unavoidable absence, arrangements can be made to take a test prior to the absence. Attendance Policy: Students must attend most of the class sessions. They are expected to be there ON TIME. Attendance will be taken daily. If you miss a class, it is your responsibility to obtain the assignment and find out what material was covered. 4

5 Mathematics Department Active Pursuit of Course Objectives & ADW Policy: Students are not actively pursuing the course objectives and will be administratively withdrawn (ADW) at midterm if at least two of the following apply: 1. Less than 70% of assignments up to the midterm have been completed. 2. Less than 70% of quizzes and tests up to the midterm have been attempted. 3. Less than 50% of class sessions up to the midterm have been attended. Cell Phones/Beepers policy: Electronic devices cause disruption during class and are not permitted. In order to respect the learning environment, please turn off all such items prior to class. Academic Support & Computer Labs: (Tutoring Center) (Schedule) (Student Services) (Trio Program) Computer Labs: Room 3817; Room 3186; Room 2247; Room L112; Room L933 Students with Disabilities The Disability Access Center (DAC) is located in room 1428 This is the Center, responsible for verifying that students have a disability -related needs for academic, accommodations and for planning appropriates accommodations, in cooperation with the students themselves and their instructors. Students who need academic accommodations should request them from the DAC Center Linda Ford Director Office hours are from 9:00 a.m.- 7:00 p.m. Monday-Thursday & Friday 9:00 a.m. 4:00 p.m. Truman College Academic Integrity Policy: If the alleged violation of the Academic Integrity policy occurs in the classroom, the instructor will determine if a student has committed an act of academic dishonesty. The instructor may take action commensurate with the severity of the act. The instructor may: 1. Assign a grade F or 0 to the assignment or test or appropriate part of the assignment or test. 2. Make a proportional reduction in the grade for an entire assignment, if the assignment is a part of a large assignment. 3. Assign a grade F for the course. See the student Handbook for specifics. Types of Activities: There will be an emphasis on on active and cooperative learning strategies throughout this class. Active Learning is, in short, anything that students do in a classroom other than merely passively listening to an instructor s lecture. This includes everything from listening practices which help students to absorb what they hear, to short writing exercises in which students react to lecture material, to complex group exercises in which students apply course material to real life situations and/or to new problems. Cooperative learning is a successful teaching strategy in which small teams, each with students of different levels of ability, use a variety of learning activities to improve their understanding of a subject. Some of the class Active/Cooperative learning strategies are listed below. Think-Pair-Share, Student Summaries, One-Minute Paper, Roundtable, 5

6 Muddiest Point, Corners and Shared Brainstorming. Weekly Schedule: 1. [Jan 16-Jan 20]: The Conic Sections & Translation and Rotation of Axes(11.6), Conics in Polar Coordinates(11.7)[Optional]. [January 16: Martin Luther King Day - Holiday] 2. [Jan 23-Jan 27]: Three Dimensional Coordinate Systems(12.1), Vectors(12.2), The Dot Product(12.3). 3. [Jan 30-Feb 03]: The Cross Product(12.4), Lines and Planes in Space(12.5). 4. [Feb 06-Feb 10]: Cylinders and Quadric Surfaces(12.6), Curves in Space and Their Tangents(13.1). 5. [Feb 13-Feb 17]: Integrals of Vector Functions: Projectile Motion(13.2), Arc Length in Space(13.3). 6. [Feb 20-Feb 24]: Curvature and Normal Vectors of a Curve(13.4), Tangential and Normal Components of Acceleration(13.5)[Optional]. [February 20: President s Day Holiday] 7. [Feb 27-Mar 02]: Velocity and Acceleration in Polar Coordinates(13.6)[Optional], Functions of Several Variables(14.1). [Review & Exam I] 8. [Mar 05-Mar 09]: Limits and Continuity in Higher Dimensions(14.2), Partial Derivatives(14.3), The Chain Rule(14.4). 9. [Mar 12-Mar 16]: Directional Derivatives and Gradient Vectors(14.5), Tangent Planes and Differentials(14.6). 10. [Mar 19-Mar 23]: Extreme Values and Saddle Points(14.7), Lagrange Multipliers(14.8). 11. [Mar 26-Mar 30]: Doubles and Iterated Integrals over Rectangles(15.1), Double Integrals over General Regions(15.2), Area by Double Integration(15.3). 12. [Apr 02-Apr 06]: [Spring Break - Holiday] 13. [Apr 09-Apr 13]: Double Integrals in Polar Coordinates(15.4), Triple Integrals in Rectangular Coordinates(15.5), Moments and Center of Mass(15.6)[Optional]. 14. [Apr 16-Apr 20]: Triple Integrals in Cylindrical and Spherical Coordinates(15.7). [Review & Exam II] 15. [Apr 23-Apr 27]: Line Integrals(16.1), Vector Fields and Line Integrals: Work, Circulation, and Flux(16.2)[Optional], Path Independence, Conservative Fields, and Potential Functions(16.3), Green s Theorem in Planes(16.4). 16. [Apr 30-May 04]: Surfaces and Area(16.5), Surface Integrals(16.6)[optional], Stoke s Theorem(16.7), The Divergence Theorem and a Unified Theory(16.8). 17. [May 07-May 11]: [Review & Final Exam] 6

7 Grading Policy: Exam I 20 % Exam II 20 % Final Exam 30 % Online Assignments 10 % In-Class Quizzes & Homework Assignments 20 % Grading Scale: A B C D F Extra Help!: Many students find that they need extra help in addition to that available in class. Help is available from the instructor at the times indicated or by appointment. Also, recognize that others in the class can and are willing to help. You are encouraged to keep in touch with classmates who have similar schedules. Tutoring is also available at Truman college. Good Luck Shuaibi, A. 7