MA113 Calculus III Syllabus, Fall 2017

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1 MA113 Calculus III Syllabus, Fall 2017 Overview This syllabus provides information about various aspects of the course including topics covered and course policies. In particular it states the course grading and attendance policies. Although this document is not a contract you should treat it like one. Therefore, YOU ARE RESPONSIBLE FOR KNOWING ITS CONTENT. Also, I reserve the right to make changes to this syllabus during the quarter. If I do make changes you will be notified in a timely fashion. Course Information Course Title and Number: MA113 Calculus III Credit Hours: 5 Course Quarter: Fall Course Format: F2F Course Location: Crapo, G221 Course Meeting Times: section 3: 6th period; section 4: 7th period; MTWThF Course Website: Instructor Information Instructor Name/Title: Mark Inlow, Visiting Associate Professor inlow@rose-hulman.edu Department and Office Location: Mathematics, Olin 216 Website: Office Hours: periods 3, 8, 9, and 10 MTWTh; by appointment Sunday afternoon Short Bio: Course Details Course Description: Vectors and parametric equations in three dimensions. Functions of several variables, partial derivatives, maxima and minima of functions of several variables, multiple integrals, and other coordinate systems. Application of partial derivatives and multiple integrals. Course Text: Thomas Calculus - Early Transcendentals Fourteenth Edition - Hass, Heil, Weir. Course Requirements: Maple 2017 Course Prerequisites: MA112, i.e., mastery of algebra, trigonometry, calculus I, and calculus II

2 Course Objectives: 1. Introduce students to multivariable differential and integral calculus, and more vector techniques, especially in three dimensions; see topics 1, 2, and 3 below in Course Topics for specific topics. 2. Introduce students to the application of multivariable calculus in science and engineering; see topics 2 and 3 below in Course Topics. 3. Develop student mathematical modeling and problem solving skills. 4. Develop student ability to use a computer algebra system (CAS) to aid in the analysis of quantitative problems. 5. Develop student ability to communicate mathematically. 6. Introduce applications of mathematics, especially to science and engineering. Course Topics 1. Vectors in Three Dimensions, Vector-valued functions Space coordinates and vectors in space Dot product and projection Cross products Lines and planes in space Vector-valued functions Differentiation/Integration of vector-valued functions Curvature, arc length, unit tangent and normal vectors,components of acceleration 2. Multivariable Differential Calculus Functions of several variables Partial derivatives Chain rule Directional derivatives, gradients Tangent planes and normal lines Unconstrained extrema Lagrange multipliers 3. Multivariable Integral Calculus Double integrals, evaluation Polar coordinates, change of coordinates Triple integrals, evaluation Cylindrical and spherical coordinates, integration in these coordinate systems 4. Applications Velocity and acceleration problems, projectile motion Unconstrained and constrained multivariable max/min problems Volume, surface area Mass, moments, moment of inertia

3 Text Sections 11. Conic Sections and Polar Coordinates 11.3 Polar Coordinates 11.4 Graphing in Polar Coordinates 11.5 Area and Lengths in Polar Coordinates (optional) 12. Vectors and the Geometry of Space 12.1 Three-Dimensional Coordinate Systems 12.2 Vectors 12.3 The Dot Product 12.4 The Cross Product 12.5 Lines and Planes in Space 12.6 Cylinders and Quadric Surfaces (optional) 13. Vector-Valued Functions and Motion in Space 13.1 Curves in Space and Their Tangents 13.2 Integrals of Vector Functions; Projectile Motion 13.3 Arc Length in Space 13.4 Curvature and Normal Vectors of a Curve 13.5 Tangential and Normal Components of Acceleration 14. Partial Derivatives 14.1 Functions of Several Variables 14.2 Limits and Continuity in Higher Dimensions 14.3 Partial Derivatives 14.4 The Chain Rule 14.5 Directional Derivatives and Gradient Vectors 14.6 Tangent Planes and Differentials 14.7 Extreme Values and Saddle Points 14.8 Lagrange Multipliers 14.9 Taylor s Formula for Two Variables (optional) 15. Multiple Integrals 15.1 Double and Iterated Integrals over Rectangles 15.2 Double Integrals over General Regions 15.3 Area by Double Integration 15.4 Double Integrals in Polar Form 15.5 Triple Integrals in Rectangular Coordinates 15.6 Moments and Centers of Mass 15.7 Triple Integrals in Cylindrical and Spherical Coordinates 15.8 Substitutions in Multiple Integrals (optional)

4 Institute Policies Students with Accessibility Needs: Rose-Hulman is committed to working with students who have special needs or disabilities. Please see the Students with Accessibility Needs link on the course website. Academic Integrity: Your original work will document your own creativity and ability to apply what you have learned here, and you will want your work to be properly acknowledged. Likewise, it is important for you to learn how to properly acknowledge the contributions of others. Rose-Hulman students should abide by our Code of Ethics (see page 51 of the Student Handbook.) Please see the Academic Integrity and Code of Ethics links on the course website. Diversity Statement: Rose-Hulman Institute of Technology strives to make all learning experiences accessible to students. Apparent and non-apparent disabilities can significantly impact a student s academic performance. Impacted students are strongly encouraged to meet with Student Accessibility Services as soon as possible. Contact Patty Eaton, the Director of Student Accessibility Services, for more information at HMU 156, phone , or eaton1@rose-hulman.edu. Please see the Diversity Statement link on the course website. Online Access Requirements: Rose-Hulman welcomes students from around the world, and encourages faculty, staff and students to travel around the world. However, geopolitical conditions and compliance with export law and regulations prevent us from delivering certain kinds of educational experiences and/or using certain kinds of Institute technologies in some locations. For example, students in locations with limited access to the internet in general, or with restricted access to portions of the internet, or which are embargoed (please see Embargo link on course website) by the U.S. Directorate of Defense Trade, may not be able to successfully complete Rose-Hulman online courses. Institutional/Program Outcomes: ABET accredited. Expectations: Absences: You are expected to attend every class. If you miss a class for a valid reason you must me with justification for your absence; verbal notification is not adequate. If you miss for any reason you should see me to discuss what you missed in class that day. If you miss class more than 6 times you will not be ineligible to receive plus grades. Laptops: You will occasionally need your laptops during class for working in Maple. Use of laptops during class for purposes other than MA113 work is prohibited. Cell phones: Use of cell phones or similar devices during class is always prohibited. Academic Misconduct: The Rose-Hulman student handbook states that academic misconduct includes actions such as cheating, plagiarizing, or interfering with the academic progress of other students. In accord with the handbook, I reserve the right to give reduced or no credit for work dishonestly done and to levy further penalties. For more details, see the Academic Integrity links on the course website.

5 Course Grade: I am required to evaluate your performance by giving you a letter grade. I will compute your grade as follows: Homeworks: I plan to assign at least two homeworks a week. Late and/or ed hw s are not accepted. If a valid excuse is provided (in a timely fashion) for a missed hw, your hw average will be computed from the remaining hw s; otherwise the missed hw will be included in the average with a value of zero. Your hw average counts for 10% of your final grade if your average on the midterms and finals is at least 60%. Mini Pop Quizzes: Occasionally I may give unannounced small exercises to be done in class which will then be collected and graded. These will count as one or more hw problems in your hw average. Midterms: There will be three 50-minute midterms. Each midterm will be announced about one week before it is given. Midterms will typically consist of a manual portion and a Maple portion. On the manual portion no laptops, calculators, or other devices may be used. On the Maple portion maple and calculators may be used. Final: The final is a comprehensive exam worth 1.5 exams or 2 exams, whichever gives the higher overall average. Since this there is a common final for all MA113 sections, the final must be taken at the designated time. If you cannot take the final at the specified time for a valid reason, you will be given an incomplete in the course. Formula: Grades will be determined using the usual 90/80/70/60 breakdown: if your overall average is 90 then you will get an A, otherwise if your overall average is 80 you will get a B and so on. Plus grades will be awarded completely at my discretion and are based on class attendance, your overall average, and possibly, other considerations. Extra Credit: No extra credit assignments will be given.

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