Math 11 Calculus III (Five Units) Section 2841, TTh, 12:45 P.M. - 03:10 P.M. Santa Monica College, Fall 2018 Instructor: Email: Office: Mathlab: Class Location: Sam Soleymani [email protected] MW 10:10 a.m.-10:40 a.m., TTh 10:10 a.m.-11:10 a.m., MC 35 W 2:10 p.m.-3:10 p.m. MC 84 LS 203 Prerequisite: Math 8 with a grade of C or better Course Description: This course is intended for computer science, engineering, mathematics and natural science majors. Topics in this third course include vectors and analytic geometry in two and three dimensions, vector functions with applications, partial derivatives, extrema, LaGrange Multipliers, multiple integrals with applications, vector fields, Green’s Theorem, the Divergence Theorem, and Stokes’ Theorem. Required Text: Stewart, James. Calculus. Eighth edition, Cengage Learning Co., 2016 Entry Skills for Math 11 Prior to enrolling in Math 11 students should be able to: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Apply concepts of limits, continuity and differentiability in two dimensions. Differentiate and integrate exponential and logarithmic functions. Differentiate and integrate transcendental functions and inverses. Perform integral by parts. Perform integration using trigonometric substitution. Perform integration with powers of trigonometric functions. Resolve indeterminate forms using L’Hopital’s Rule. Set up Taylor Series representations of transcendental functions. Use polar and parametric coordinates for plane curves. Find center of mass/centroid. Exit Skills For Math 11: Upon successful completion of this course, the student will be able to: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Perform the basic algebra of vectors including dot and cross products. Write the equations of lines and planes in three dimensions, both in non-vector and vector forms. Sketch planes, cylinders and quadric surfaces. Distinguish between scalar-valued and vector-valued functions. Differentiate and integrate vector-valued funtions. Represent curvilinear motion in vector form both algebraically and geometrically. Find the derivatives of scalar-valued and vector valued functions of two or more independent variables. Find extrema of functions of two of more independent variables both by the Second Derivative Test and by Lagrange Multipliers. Evaluate double and triple integrals. Use multiple integrals to solve various applied problems. Use rectangular, cylindrical and spherical coordinates for graphing and the evaluation of multiple integrals. Set up and evaluate line integrals and surface integrals and apply them to physical applications. Apply Green’s Theorem, Divergence Theorem and Stoke’s Theorem. Apply the concepts of the gradient, divergence and curl. Academic Conduct: As testament to their commitment and readiness to join the Santa Monica College academic community, all students are expected to uphold the Honor Code. Cheating of any kind during exams or quizzes will result in severe consequences such as receiving a failing grade or being dropped from the course as well as being reported to the honors council as academically dishonest. Cheating includes altering graded materials and using external resources such as electronic devices and cheat sheets during exams and quizzes or, copying someone else’s homework and out-ofclass assignments to complete own exam, project, or homework assignments. Requesting special grading consideration due to your transfer plans or other personal situations is inappropriate and may result in disciplinary action. Asking the instructor for “extra credit” is strictly prohibited. Classroom conduct: Classroom is a learning environment for all students enrolled. All need to be courteous of others. If you have a question during lecture then wait for the instructor to finish his/her statement before raising your hand to ask the question. Private conversations with the instructor should be held in office hours, not during class time. See Student Code of Conduct: http://www.smc.edu/StudentServices/StudentJudicialAffairs/Documents/AR4410.pdf Cell phones are a huge source of distraction in the classroom for you and for the others. They must be deactivated while class is in session. This means no sounds or vibrations may occur from an incoming text message or a phone call. Students who use smart devices and mobiles while class is in session will be asked to leave. Anyone who uses a cell phone or any other unapproved electronic devices during an exam receives a failing grade for that exam. Food or drink is strictly prohibited in the Math Complex with the exception of water bottles. Communicating With The Instructor: You must e-mail the instructor via your school e-mail account in case you need to contact the instructor. Any message sent from a personal address such as G-mail or Yahoo may automatically be marked as spam and will not be responded. Include your name and the section number in the message. An e-mail message to the instructor must be written with a professional manner. A message beginning with “Hey” will be completely ignored. Students with Disabilities: Santa Monica College accommodates students with disabilities. If you qualify for any special accommodations due to a disability, you need to officially process your request through the Disabled Students Programs and Services (DSPS) office as close to the beginning of the semester as possible. If you believe you have a learning disability that has not yet been documented, please see me and make an appointment at the DSPS office for assistance. The DSPS office is located in the Admissions/Student Services Complex, Room 101, and the phone numbers are (310) 434-4265 and (310) 434-4273 (TDD). Scheduling of accommodated exams will be arranged on a case-by-case basis. Deadlines Class Census Day: September 10, 2018 Last Day to Withdraw to Receive a Refund: September 09, 2018 Last Day to Withdraw to Avoid a "W": September 09, 2018 Last Day to Withdraw to Guarantee a "W": November 18, 2018 It is the student’s responsibility to be aware of the dates above and to take the appropriate actions. Student Learning Outcomes: 1. Given vector-valued or real-valued functions involving two or more independent variables, identify and use appropriate techniques to analyze the fundamental properties of those functions. Included would be partial and directional derivatives, gradients, differentials, and integrals over lines, surfaces and solid regions. 2. Setup and solve physical applications problems related to all aspects of motion along a curve. Included would be the arclength parametrization of a curve and the use of tangent, velocity, normal and binormal vectors, curvature, and the tangential and normal components of acceleration and their relationship to the osculating plane containing the circle of best fit at a point on the curve. 3. Apply Green's Theorem, Stokes' Theorem, and Gauss' Divergence Theorem with the concepts of divergence and curl and flux. Students will solve problems related to vector fields including magnetic fields, flow fields, and conservative vector fields. Calculators: No calculator of any kind will be used for this course. Attendance is highly advised. Each has a negative impact on your performance. Your third absence may result in an automatic withdrawal from the course. If you miss a session, make sure you update yourself on the material that has been covered on your day of absence. Tardiness: Being tardy twice is equivalent to having one absence. Methods of Evaluation A) Exams: There will be three exams, which are based on suggested homework assignments, class lectures, and discussions. Exams are closed notes and closed book. You must use a pencil to complete each exam. An eraser must be used if necessary. Your grade will be penalized if there are any scratch marks on your exam paper. No make-up exam will be given. All notes, books, cell phones, pencil cases must be out of your reach during all exams. The minimum score of your exams is replaced by the percentage of your final exam score given that your final exam percentage is greater than the minimum of exam scores. B) Quizzes: The date for each quiz will be announced in advance. The number of quizzes varies. C) Final Exam: The final exam is cumulative and is mainly focused on Chapter 18. In order to get a satisfactory grade on the final exam you should frequently review the materials that have been covered previously. Failing to take the final exam will result in a failing grade. Grading Method: Event Exams Quizzes Final Exam Total* Letter grades: Points 100 Vary 150 Total 300 50 150 500 *This is an approximate total number of points. The actual total may be different. A: 90-100%, B: 80-89%, C: 70-79%, D: 60-69%, F: <59% Your average grade is determined by Total points* earned 100% Total In order to succeed in Calculus III You do not to be a math genius. In the past decade that I have taught, I only have encountered a couple of students who are naturally good at math; but, hundreds of my students have earned a grade of A. You must have the knowledge of the items in the entry skills list mentioned earlier as well as having mastered trigonometry, parametric graphs, and the polar coordinate system. You must be dedicated, highly patient, and maintain a highly optimistic attitude. You need to be a critical thinker and avoid fundamental errors. Read, listen to, and properly execute the instructions that are imposed by the instructor. Keep your phone out of your way, out of your sight, and out of your life while you are in class. Read the lecture after class and practice enough problems before the next class meeting. Repeat practicing the same difficult problem until it is not difficult any longer. Be curious about mathematics. You are here because you want to learn. Tentative Schedule (Subject To Change) Date Section and Title Suggested Problems Odd Numbered 08/28 12.1: Three-Dimensional Coordinate System 1-9, 13-41 08/30 12.2: Vectors 12.3: The Dot Product 5-29, 41-48 All 1-53, 61, 62, 63 09/04 12.4: The Cross Product 12.5: Equations of Lines and Planes 12.5: Equations of Lines and Planes 12.6: Cylinders and Quadratic Surfaces 13.1: Vector Functions & Space Curves 13.2: Derivatives and Integrals of Vector Functions 13.3: Arc Length and Curvature 13.4: Motion in Space: Velocity and Acceleration 1-37, 43-51 1-77 1-77 1-37 1-31, 43, 45, 49 1-27, 35-57 1-33, 39, 47, 48, 64 3-27, 09/20 09/25 09/27 10/02 10/04 13.4: Tangential & Normal Components Of Acceleration Catching Up 14.1: Functions of Several Variables Exam 1 14.2: Limits and Continuity 14.3: Partial Derivatives 37-43 10/09 14.5: Chain Rule 14.6: Directional Derivative 14.6: Directional Deriv. (Tan. Planes and Norm.Lines) 14.4: Tangent Planes and Linear Approximations 14.7: Maximum and Minimum Values 14.8: Lagrange Multipliers 09/06 09/11 09/13 09/18 10/11 10/16 10/18 10/23 10/25 10/30 11/01 11/06 11/08 11/13 11/15 11/20 11/22 11/27 11/29 12/04 12/06 12/11 15.1: Double Integrals Over Rectangles Exam 2 15.2: Double Integrals Over General Regions 15.3: Double Integrals in Polar Coordinates 15.4: Applications of Double Integrals 15.5: Surface Area 15.6: Triple Integrals 15.7: Triple Integrals in Cylindrical Coordinates 15.8: Triple Integrals in Spherical Coordinates 16.1: Vector Fields 16.5: Curl and Divergence Exam 3 16.2: Line Integrals 16.3: The Fundamental Theorem of Line Integrals 16.4: Green’s Theorem 16.7: Surface Integrals 16.9: The Divergence Theorem 16.8: Stoke’s Theorem Final Exam 08:00 a.m.- 11:00 a.m. 7-35, 45-53, 67, 69 5-17, 29-35, 39, 41 5, 7, 11, 15-69 Every Other Odd, 71, 75, 79, 81, 83 1-35, 45-49 1, 5-31, 37, 39 1-6 All, 11-21, 31-35 1-6 All, 11-21, 31-35 5-19, 31-37, 41-53 3-13, 21, 23, 33, 35 17-43 1-31, 45-55, 66 1-33, 40, 41 3-15 1-15 1-21, 29-33, 35, 39-47 1-29 1-37, 41, 43, 48 1-17, 21-33 1-35, 38 1-21, 29, 39-43 3-23, 29 1-23 5-31 1-13, 17, 24, 25-30 All 1-17, 20 12:00p.m.-3:00p.m.