CALCULUS III (MATH 2415)

Houston Community College Spring 2014 Northwest College CRN: 81469 Math Department Math 2415: Calculus III Alief-Hayes Campus - Room: B213 Jan 13 to May 11 Instructor: Hung Q. Dam MW: 11:00 am to 1:00 pm COURSE SYLLABUS Audience: This course is intended basically for students who are pursuing degrees in mathematical sciences and engineering and who are required by the nature of their respective curricula to enroll in the 3-semester calculus series. Students enrolled in other areas not requiring calculus may wish to take this course as an elective to broaden their mathematical background, provided the following necessary prerequisites have been met. Prerequisites: Math 2414. Pass with a “C” or better. Course Intent: This course provides a detailed study of: (a) Vectors and the Geometry of Space (b) Vector-Valued Functions (c) Functions of Several variables (d) Multiple Integration (e) Vector Analysis Course Objectives: Upon completion of this course, a student should be able to: (1) Apply calculus to vectors and vector-valued functions (2) Describe and use partial differentiation (3) Apply Lagrange multipliers to solve problems (4) Solve multiple integrals (5) Find the Jacobian using determinant notation (6) Apply Green’s theorem to evaluate line integrals around a bounded area (7) Apply the Divergence theorem and Stokes' theorem to specific problems Text Book:. CALCULUS by Larson & Edwards, 10th edition, Brooks/Cole, Cengage Learning, 2010 Resource Materials: Any student enrolled in Math 2415 at HCCS has access to the Academic Support Center where they may get additional help in understanding the theory or in improving their skills. The Center is staffed with mathematics faculty and student assistants, and offers tutorial help, video tapes and computer assisted drills. Also available is a Student’s Solutions Manual which may be obtained from the Bookstore. Suggested Methods: Students are encouraged to work the review exercises at the end of each chapter. Also, they are encouraged to visit the Academic Support Center at their respective college. Attendance : Regular attendance is extremely important in mathematics classes. You may be dropped for excessive absence (more than 12.5% of the class time, or 2 weeks or the equivalent). Veterans with excessive absence will be dropped with an official drop form by the last drop day. If you should decide to withdraw from the course, initiate a student drop in the office. Should your name remain on the roll at the end of the term, you must receive a grade. Major Exams: There will be 3 major exams. Each major exam score will count for 25% of the final course average. Final Exam: The final exam will cover all the course material. The final exam score will count for 25% of the final course average. Grading Formula: The grading formula is : Co Course average = ( T1 + T2 + T3 + F ) ( 0.25 ) where T1, T2, T3 are the 3 major exam scores, and F the final exam score. Americans With Disabilities Act (ADA): Persons needing accommodations due to a documented disability should contact the ADA counselor for their college as soon as possible. Departmental Policies: 1. The final exam is comprehensive and questions on it can deal with any of the course objectives. 2. Each student should receive a copy of the syllabus for the course on the first day of class. 3. A comprehensive final examination must be given. The final examination must be taken by all students. 4. All major exams should be announced clearly in advance in the course syllabus. 5. The final exam must count for at least 25% and at most 40% of the final grade. 6. The final course average will be used in the usual manner. Grades will be assigned as follows: Course average : Grade : 90 - 100 A 80 - 89 B 70 - 79 C 60 - 69 D Below 60 F 7.Either an open book or a take-home major exam may be given at the discretion of the instructor. 8. Review sheets (if any) should be comprehensive and the student should not feel that classroom notes, homeworks and major exams may be ignored in favor of the review sheets for examinations. 2014 SPRING COURSE CALENDAR, CAL III SESSION DATE TOPICS SECTIONS WEEK # 1 M Jan 13, 2014 Vectors in the plane Space coordinates and Vectors in Space 11.1 11.2 W Jan 15 The dot product of 2 vectors 11.3 WEEK # 2 M Jan 20 MLK Holiday W Jan 22 The cross product of 2 vectors in Space Lines & planes in Space 11.4 11.5 WEEK # 3 M Jan 27 Surfaces in Space Cylindrical & Spherical Coordinates 11.6 11.7 W Jan 29 Vector Valued Functions (VVF) Differentiation & Integration of VVF 12.1 12.2 WEEK # 4 M Feb 03 Major Exam # 1 Sections 11.1 – 11.7 W Feb 05 Velocity & Acceleration 12.3 2014 SPRING COURSE CALENDAR, CAL III WEEK # 5 M Feb 10, 2013 Tangent vectors & Normal vectors Arc length & Curvature 12.4 12.5 W Feb 12 Functions of several variables Limits & Continuity 13.1 13.2 WEEK # 6 M Feb 17 Presidents’ Holiday W Feb 19 Partial Derivatives 13.3 WEEK # 7 M Feb 24 Differentials Chain Rules for functions of Several Variables 13.4 13.5 W Feb 26 Directional Derivatives & Gradients 13.6 WEEK # 8 M Mar 03 Major Exam # 2 W Mar 05 Tangent planes & Normal lines Extrema of functions of 2 variables 13.7 13.8 SPRING BREAK: From March 07 thru March 17 2014 SPRING COURSE CALENDAR, CAL III WEEK # 9 M Mar 17 Applications of Extrema of Funct. of 2 Variables Lagrange Multipliers 13.9 13.10 W Mar 19 Iterated Integrals & Area in the plane 14.1 WEEK # 10 M Mar 24 Double Integrals & Volume Change of Variables. Polar Coordinates 14.2 14.3 W Mar 26 Center of Mass & Moments of Inertia 14.4 WEEK # 11 M Mar 31 Surface Area Triple Integrals &Applications 14.5 14.6 W Apr 02 Triple Integrals in Cylindrical & spherical Coordinates. Change of Variables: Jacobians 14.7 14.8 WEEK # 12 M Apr 07 Major Exam # 3 Sections 13.7 – 14.6 W Apr 09 Vector Fields Line Integrals 15.1 15.2 2014 SPRING COURSE CALENDAR, CAL III M Apr 14 Conservative fields & Independence of Path 15.3 W Apr 16 Green’s Theorem Parametric Surfaces 15.4 15.5 WEEK # 14 M Apr 21 Surface Integrals 15.6 W Apr 23 Divergence Theorem Stokes’s Theorem 15.7 15.8 WEEK # 15 M Apr 28 Review for Final Exam W Apr 30 No meeting WEEK # 16 M May 05 No meeting W May 07 Final Exam from 11:00 am to 1:00 pm 2014 SPRING SEMESTER ENDS Calculus III Spring Syllabus