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UNF MAC 2313 - Syllabus

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Important Dates:Spring 2010. Syllabus for Calculus III (MAC 2313) Instructor/office/contact info/office hours:Instructor: Ognjen Milatovic Office: Building 14, Room 2733Phone: 620-1745 E-mail: [email protected] Office hours: Monday 3:15 p.m.-5:15 p.m.;Tuesday 10:00 a.m. - 11:00 a.m.;Wednesday 3:15 p.m.- 5:15 p.m.; Or by appointmentInstructor’s Web Page: Prerequisite: MAC 2312–Calculus II. Text: Larson, Hostetler, Edwards, Calculus. Early Transcendental Functions, 4th EditionCalculator: You should have a graphing calculator or a scientific calculator. Course Objectives: To have students understand the concepts of vectors, vector functions, and functions of more than one variable, and their derivatives and integrals, and to enable students to display that understanding through a variety of applications. Specific, measurable manifestations of your understanding that will be tested during the semester include your ability to• algebraically and graphically manipulate vectors, find their components, and determine length and direction• calculate dot products, projections, and angles between vectors• solve physics problems, involving velocity, acceleration, force, and work, by using vectors• differentiate and integrate vector functions• differentiate the position vector function to obtain the tangent, velocity, and acceleration vectors• integrate the acceleration and velocity vector functions to obtain the position vector function• calculate the position, velocity, and acceleration vector functions of a projectile• calculate polar coordinates given Cartesian coordinates, and vice-versa, and draw graphs of polar equations• calculate the cross product of two vectors in 3-dimensional space to find normal vectors to planes• apply the cross product to calculate areas of triangles and parallelograms, and to find the torque vector• produce equations of lines and planes in 3-dimensional space• sketch cylinders and quadric surfaces, and recognize their equations• differentiate dot products and cross products of vector functions• identify the domain of a function of several variables, and produce a rough sketch of the graph• sketch the level curves of a function of several variables• match functions of several variables with their level curves and graphs• calculate partial derivatives of functions of several variables• calculate partial derivatives via the multivariable chain rule• calculate the gradient vector of a function of several variables at a point• calculate the directional derivatives of a function of several variables, and determine the directions of most and least rapid increase of the function, and the directions in which the function remains constant• produce equations of the tangent plane to the graph of a function of several variables at a point• approximate changes in the function by using the tangent plane, the local linearization, and the differential• determine the critical points of a function of several variables, and determine whether they correspond to local maxima, local minima, saddle points, or none of these• sketch the graph and level curves of a function of several variables near local maxima, local minima, and saddle points• determine absolute extreme values on closed, bounded regions• approximate double integrals by using partitions• calculate indefinite and definite double integrals• reverse the order of integration to calculate double integrals• use double integrals to calculate the volume beneath surfaces• calculate double integrals in polar coordinates• calculate triple integrals in rectangular coordinates• calculate the average value of a function of several variables• calculate triple integrals in spherical and cylindrical coordinatesBy the end of the semester, you will extend what you learned in Calculus I and II to functions of several variables learn some important mathematical tools widely used by scientists and engineers strengthen your skills in numerical and symbolic computation, mathematical reasoning, and mathematical modeling gain skills in learning and communicating mathematics Attendance:It is essential that you attend classes regularly. The easiest way for you to learn the material, and to know what material has been covered, is to come to class each day. You are responsible for finding out what material has been covered or what announcements have been made on days that you miss class.Excused Absences or Late Work:In order to turn in assignments late or to take make-up quizzes/tests, you must bring written proof of some emergency situation; notes from doctors or nurses, documents verifying court appearances, receipts from having a car towed are all examples of valid documentation. Notes from family members are not acceptable. If a situation is of a personal nature, discuss the matter with your academic advisor; an e-mailmessage from your advisor saying that he/she believes that you should be allowed to make up work is acceptable. Reading: It is strongly recommended that you read the material from the textbookahead of time. Thus, when you then see the corresponding section covered in class, youwill be able to follow along much more easily (as opposed to seeing the material for thevery first time in class). It is hard to learn multivariable calculus by skimming large quantities of information in the textbook, searching for highlighted text or equation boxes, or by skimming worked examples as you would a novel. A much better way to learn and understand how to apply mathematics is by actively participating in the problem solving process. You can do this by carefully reading and taking notes on the material presented in the text, paying special attention to when various techniques/methods/concepts can be applied. Additionally, instead of just looking at examples in the text, you should try to work through these examples, filling in any missing information and taking note of any questions that you may have. To truly understand worked examples, you should examine them for yourself by working through examples step-by-step, filling in the missing information as needed. You can then use these examples to help you as you work new exercises on your own. As you do this, it is helpful that you take note of differences and similarities in these exercises. Homework: Homework will be

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