Math 233H: Honors Multivariate Calculus

Instructor: Professor Markos Katsoulakis, LGRT 1423G, E-mail: markos [at] math umass edu

Lectures: Tuesdays, Thursdays, 9:30AM-10:45AM, Hasbrouck 242.

Office Hours: Tuesdays, Thursdays, 11AM-12noon and by appt.

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Textbook

• Calculus, Early Transcendentals 7th ed, UMass Custom Edition, by James Stewart.

  See below for the class material listed by Section (helpful if you use an older edition of the same book)

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Grading

• Final Exam 30%, Exam 1 and Exam 2 each 20%, Homework 30%.
• The final exam will be cumulative, with more emphasis on topics covered after Exam 2.
• Date for Exam 1: February 28 (in class), Date for Exam 2: April 10, 6-8PM LGRT0202. Sections covered on these exams will be announced before the exam date.
• The date and time of the final exam will be scheduled by the university.
• Make-up exams will only be given in the case of family or medical emergency. Both situations will require official documentation. No make-up exams will be given for any other reason.

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Homework

There will be (almost) weekly homework assigned that is to be done using webwork.

You can login into your account on Webwork from here: webwork. Your user name is the part of your UMass email address appearing before the '@' symbol (usually your NetID). Your default password is your student ID number. Please make sure you change your password once you login for the fi\ rst time. Write-up/Print your solutions, and keep them, say in a binder, so that you may easily reference that when you are stud\ ying for an exam.

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Announcements

• Exam 2: April 10, 6-8PM LGRT0202. Material: Chapter 14.

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Class Material by Section

• 12.1 Three-dimensional coordinate systems
• 12.2 Vectors
• 12.3 The dot product
• 12.4 The cross product
• 12.5 Equations of lines and planes
• 12.6 Cylinders and quadric surfaces
• 10.1 Curves defined by parametric equations
• 13.1 Vector functions and space curves
• 13.2 Derivatives and integrals of vector functions
• 13.3 Arc length
• 13.4 Motion in space velocity and acceleration
• 14.1 Functions of several variables
• 14.2 Limits and continuity
• 14.3 Partial derivatives
• 14.4 Tangent planes and linear approximations
• 14.5 The chain rule
• 14.6 Directional derivatives and the gradient vector
• 14.7 Maximum and minimum values
• 14.8 Lagrange multipliers
• 15.1 Double integrals over rectangles
• 15.2 Iterated integrals
• 15.3 Double integrals over general regions
• 10.3 Polar coordinates
• 15.4 Double integrals in polar coordinates
• 15.5 Applications of double integrals
• 15.6 Triple Integrals
• 15.7 Triple Intehrals in Cylindrical and Spherical Coordinates
• 16.1 Vector fields
• 16.2 Line integrals
• 16.3 The fundamental theorem for line integrals
• 16.4 Green's theorem
• 16.5 Curl and Divergence
• 16.8 Stokes Theorem
• 16.9 The divergence Theorem
• 17 Applications to Differential Equations