Course schedule: http://math.utexas.edu/users/henrys/m408mschedule.html

Trigonometric Identities sheet, print out and bring to exams: http://math.utexas.edu/users/henrys/trigident.pdf

Unique numbers: 58615, 58620, 58625

Lecturer: Dr. Henry Segerman

• Email: henrys@REMOVETHISmath.utexas.edu (preferred method of contact)
• Office Phone: (512) 471-8143
• Office: RLM 10.140
• Office hours: MW 10:30 am - 12 noon

Teaching Assistant: Kent Van Vels

• Email: kvanvels(at)math(dot)utexas(dot)edu
• Office Phone: (512) 472-6191
• Office: RLM 13.152
• Office hours: TTH 2 - 3:30 pm

Website: http://math.utexas.edu/users/henrys/m408m.html

Meeting place and time:

• Lectures: CPE 2.208, MWF 1 - 2 pm.
• Discussion, 58615: RLM 5.118, TTH 8:30 - 9:30 am.
• Discussion, 58620: RLM 7.118, TTH 11 am - 12 noon.
• Discussion, 58625: RLM 5.118, TTH 1 - 2 pm.

Text: Calculus by Stewart, Sixth Edition.

Prerequisites: Mathematics 408L or the equivalent with a grade of at least C.

Course description: M408M is one of two first-year calculus courses. It is directed at students in the natural and social sciences and at engineering students. In comparison with M408D, it covers fewer chapters of the text. However, some material is covered in greater depth, and extra time is devoted the development of skills in algebra and problem solving. This is not a course in the theory of calculus. Introduction to the theory and applications of differential and integral calculus of functions of several variables. Includes parametric equations, polar coordinates, vectors, vector calculus, functions of several variables, partial derivatives, gradients, and multiple integrals.

Homework: (10% of your grade) Homework will be assigned regularly via the Web using the UT Quest Learning & Assessment service. See http://cns.utexas.edu/quest/support/student/ for instructions on signing up for and using Quest. All answers and grades will be returned via the Web also using Quest. Assignments will become available before the lectures in which the relevant material is covered. Your lowest 3 homework scores will be dropped. Calculators (particularly graphing calculators) are a useful tool for experimentation and understanding of the material, but may not be used on the homework itself.

Exams: (90% of your grade) There will be three evening midterms, lasting 2 hours and each worth 20% of your grade. There will also be a comprehensive final, lasting 3 hours and worth 30% of your grade. The midterms will consist of at most 20 multiple choice questions and the final will consist of at most 25 questions. All questions will be taken from the same data bank of questions as the homework.

No books, notes or calculators will be allowed in any of the exams. You may bring a printout of the trigonometric identities sheet. Exam dates are:

• Midterm 1: Tuesday Sept 23rd, 7 - 9 pm, SZB 104

• Midterm 2: Wednesday Oct 29th, 7 - 9 pm RLM 4.102

• Midterm 3: Tuesday Nov 25th, 7 - 9 pm RLM 4.102

• Final: Monday Dec 15th, 2 - 5 pm BEL 328

Syllabus: Forty Class Days As:

• 11 Parametric Equations and Polar Coordinates (six days)
  • 11.1 Curves Defined by Parametric Equations
  • 11.2 Calculus with Parametric Curves
  • 11.3 Polar Coordinates
  • 11.4 Areas and Lengths in Polar Coordinates
  • 11.5 Conic Sections
  • 11.6 Conic Sections in Polar Coordinates
• 13 Vectors and the Geometry of Space (eight days)
  • 13.1 Three-Dimensional Coordinate Systems
  • 13.2 Vectors
  • 13.3 The Dot Product
  • 13.4 The Cross Product
  • 13.5 Equations of Lines and Planes
  • 13.6 Cylinders and Quadric Surfaces
• 14 Vector Functions (four days)
  • 14.1 Vector Functions and Space Curves
  • 14.2 Derivatives and Integrals of Vector Functions
  • 14.3 Arc Length and Curvature
  • 14.4 Motion in Space: Velocity and Acceleration
• 15 Partial Derivatives (ten days)
  • 15.1 Functions of Several Variables
  • 15.2 Limits and Continuity
  • 15.3 Partial Derivatives
  • 15.4 Tangent Planes and Linear Approximations
  • 15.5 The Chain Rule
  • 15.6 Directional Derivatives and the Gradient Vector
  • 15.7 Maximum and Minimum Values
  • 15.8 Lagrange Multipliers
• 16 Multiple Integrals (ten days)
  • 16.1 Double Integrals over Rectangles (review of first three sections)
  • 16.2 Iterated Integrals
  • 16.3 Double Integrals over General Regions
  • 16.4 Double Integrals in Polar Coordinates
  • 16.5 Applications of Double Integrals (optional)
  • 16.9 Change of Variables in Multiple Integrals (if time permits)

Students with Disabilities: The University of Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471- 6259, 471-6441 TTY.

Some general information:

• Take advantage of office hours! Seek out help before problems get too large to tackle. You will find that I have a lot of patience with people who are genuinely interested in learning, and decreasingly less for those who regularly skip class/homework/etc. Don't hesistate to ask me, the TA or others in the class if you have questions or are having trouble. We can also schedule appointments outside of office hours as needed.
• If a student will be absent from a test and wishes to be given a make-up test, then he or she must formally request this with a properly documented excuse at least 48 hours in advance. If you are the least bit uncertain as to the validity of an excuse based on some previously scheduled, upcoming event, then seek approval for a make-up before the exam in question, not after the fact.
• Do not take an exam when you are ill, a subpar performance will likely affect your grade. Do not take an exam while under the influence of medication that could affect your concentration or ability to think clearly. If you become ill during an exam, inform your teacher about the nature of the problem then go straight to a doctor or the health center. Any claim made after the end of an exam that illness or other factors affected performance on the exam will be discounted.
• The UT Learning Center offers a number of refresher mini-courses in early September that may be useful.