MATH2130 Course Syllabus F2020 A PDF

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University of Manitoba Department of Mathematics, Faculty of Science Course Number and Title: MATH 2130-A01 Engineering Mathematical Analysis Number of Credit Hours: 3 Pre-requisites: Math 1210 and Math 1710 Time: MWF 8:30 am - 9:20 am

Tutorial: R 11:30 am - 12:45 pm

Instructor: Dr. Isam Al-Darabsah

Email: [email protected]

Calendar Description of Course: Multivariable differential and integral calculus up to and including multiple integrals in cylindrical and spherical coordinates. A more Detailed Description of the Course: 1. Vector algebra; three-dimensional geometry including lines, planes, cylinders, and quadratic surfaces; lengths and tangent vectors for space curves 2. Limits, partial derivatives, gradients, chain rules, implicit differentiation, directional derivatives, tangent lines and planes, relative and absolute extrema 3. Double and triple integrals applied to area, volume, centres of mass, moments of inertia, fluid pressure, and surface area, iterated integrals in polar, cylindrical, and spherical coordinates. Goals: The course has four main goals: 1. Represent curves and surfaces in space by vector and scalar equations 2. Differentiate and integrate vector-valued functions of a single variable 3. Introduce aspects of multi-variable calculus including limits, continuity, partial derivatives, gradients, chain rules, implicit differentiation, directional derivatives, relative and absolute extrema 4. Evaluate double and triple integrals and apply them to geometric and physical problems in Cartesian, polar, cylindrical, and spherical coordinates Instructional Objectives: At the completion of the course, the student is expected to be able to: 1. Sketch curves and surfaces in space, and their projections in the coordinate planes 2. Find distances among points, lines, and planes in space 3. Find the derivative and integral of vector-valued functions depending on a single variable 4. Find tangent vectors to, and lengths of, curves in space 1

5. Calculate limits, partial derivatives, gradients, and directional derivatives of functions of more than one variable 6. Develop chain rules for multi-variable composite functions 7. Use Jacobians to calculate partial derivatives of implicitly defined functions 8. Find equations for tangent lines to curves and tangent planes to surfaces 9. Find critical points of functions of multi-variable functions and classify them as giving relative maxima, relative minima, or saddle points for functions of two variables 10. Find absolute maxima and minima of multi-variable functions 11. Evaluate double and triple iterated integrals in Cartesian coordinates 12. Use double integrals to find volumes of solids of revolution, fluid pressure, centres of mass, moments of inertia, and surface area 13. Use triple integrals to calculate volumes in space 14. Evaluate iterated integrals in polar, cylindrical, and spherical coordinates Textbook: Calculus for Engineers by Donald Trim (4th edition) (Pearson/Prentice Hall) Tutorials: Tutorials will be posted on UM Learn. Each Friday, there will be an announcement as to which problems you should attempt to solve before the next tutorial. Evaluation: Three components contribute to the final grade in the course. 1. Three quizzes counting 10% of the final grade will be held in the tutorials on Oct Octob ob ober er 1, Octo ctobe be berr 229 9 , and Dec Decemb emb ember er 3 . 2. Two midterms counting 30% of the final grade will be held in the tutorials on Oct October ober 15 and No November vember 19 . The better of the two will count 20% of the grade, and the lesser will count 10%. 3. A final examination counting 60% of the final grade. There are no make-up quizzes and midterms Since tests and the final examination will be online, notes and books may be used. In other words, quizzes, tests and examination are open book. Grading: The following can be used as a guide in changing numerical grades to letter grades. It is only a guide, however, as fluctuations in grade lines may occur. Numerical Grade 90-100 80-89 74-79 68 -73 61-67 55-60 50-54 0-49

Letter Grade A+ A B+ B C+ C D F

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Voluntary Withdrawal Date: Voluntary withdrawal date is November 23, 2020. Academic Dishonesty: The Department of Mathematics, the Faculty of Science and the University of Manitoba all regard acts of academic dishonesty in quizzes, tests, examinations or assignments as serious offences and may assess a variety of penalties depending on the nature of the offence. Acts of academic dishonesty include bringing unauthorized materials into a test or exam, copying from another student, plagiarism and examination personation. Students are advised to read section 7 (Academic Integrity) and section 4.2.8 (Examinations: Personations) in the General Academic Regulations and Requirements of the current Undergraduate Calendar. Note, in particular, that cell phones and pagers are explicitly listed as unauthorized materials, and hence may not be present during tests or examinations. Penalties for violation include being assigned a grade of zero on a test or assignment, being assigned a grade of "F" in a course, compulsory withdrawal from a course or program, suspension from a course/program/faculty or even expulsion from the University. For specific details about the nature of penalties that may be assessed upon conviction of an act of academic dishonesty, students are referred to University Policy 1202 (Student Discipline Bylaw) and to the Department of Mathematics policy concerning minimum penalties for acts of academic dishonesty. All students are advised to familiarize themselves with the Student Discipline Bylaw, which is printed in its entirety in the Student Guide, and is also available on-line or through the Office of the University Secretary. Minimum penalties assessed by the Department of Mathematics for acts of academic dishonesty are available on the Department of Mathematics web-page. This is what you can expect of me: • • •

make every effort to plan the course and each class so that learning will be maximized be open to suggestions (they can often lead to improvements in a course) treat you as adult learners, with related respect

This is what I expect of you: • complete all requirements of the course. • use university-level, mathematical writing, legible and with correct format. There are many worked examples in the notes and solution manual; these should guide you on how to write solutions to problems on tests. • be honest. Quiz, test and examination submissions must be your own work

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