Math 1512

Honors Calculus II

Fall 2008

TThu 3:05-4:25, Skiles 202

INSTRUCTOR

• Stavros Garoufalidis
• Room 105, Skiles
• Telephone: 404-894-6614
• stavros@math.gatech.edu
• Office hours: Wed Thu 3:30-4:30 or by appointment.

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TEACHING ASSISTANTS

• Carola Conces MW 3:05-3:55 in Skiles 254, email: cconces@gatech.edu
• Jon Eisen MW 3:05-3:55 in Skiles 271, email: gth732n@mail.gatech.edu

TEXTBOOK

• Tom Apostol, Linear Algebra, Wiley Interscience.
• Michael Spivak, Calculus, Fourth edition.

COURSE DESCRIPTION

The course will cover linear algebra and calculus, presented rigorously with proofs. We will start with Apostol's book on linear algebra, discuss vector spaces, linear transformations, determinants, eigenvalues, eigenvectors, inner products, differential equations and then move on to calculus.

PREREQUISITES

MATH 1501 and some linear algebra.

HOME-PAGE FOR THE COURSE

You can view information about the course here.

HOMEWORK

Homework will be due on Wednesdays during recitation, and will be graded selectively by the teaching assistants. Late homework will not be accepted, unless for documented reason, decided by the instructor. Sample homework problems will be discussed by the teaching assistants. You can download the homework from the home-page of the course. You may discuss homework problems together, however you are required to write the solutions separately . Please staple your homework, and write clearly, each problem on a new page.

MIDTERM-EXAM

There will be two in-class midterm exams on Thursday September 25 and Thursday October 30. No substitutions, please.

FINAL EXAM

The final exam will be on Thursday Dec 11th 11:30 - 2:20 pm in the classroom.

GRADES

The final grade will be calculated according to the following scheme:
• Homework : 15 %
• Midterms : 2 x 20 %
• Final Exam : 45 %
It is expected that an average of around 80% gives an A and an average of below 45% or a final exam grade of less than 40% results in failure.

ACADEMIC HONOR CODE

It is required that the students review and accept the Honor Code of Georgia Tech, which may be found here.
• Calculators, formula sheets, notes or texts are not allowed during midterms and final exams.
• Consultation/collaboration for homework is allowed and encouraged, however the homework should be written separately.
• Identification is required in taking tests.

COURSE SYLLABUS

You may find a course syllabus here .

IMPORTANT DATES

• September 1, School Holiday.
• September 25, Midterm I.
• October 13-14 Fall recess.
• October 10, Last day to withdraw with W.
• October 30, Midterm II.
• November 27-28 School Holiday.
• December 5, Last Day of classes.
• December 11, Final Exam.

WHAT IS A PROOF?

See a note by Chris Heil.

HOMEWORK ASSIGNEMENTS

• Homework 1 Due Wednesday August 27 in the beginning of the recitation. Section 1.8 problems 21,23. Section 1.11 problems 1,9,16,17. One additional problem.

  (a) Let A,B,C be points in R^3 with coordinates (1,0,0), (0,1,0) and (0,0,1) respectively. Find the coordinates of D so that ABCD is a regular tetrahedron (ie a tetrahedron with all sides of equal length).

  (b) Find cos(phi) where phi is the dihedral angle of ABCD. Hint: If E is the midpoint of AB, then phi is the angle of ED, EC. Hint: cos(phi) is a small positive rational number with numerator 1.

• Homework 2 Due Wednesday Sep 3 in the beginning of the recitation. Section 1.15 problems: 10,12,14,15,20. Sec. 1.17: 9.

  Prove by induction that if more than n bees visit n hives, then there exists a hive that is visited by more than one bee.

• Homework 3 Due Wednesday Sep 10 in the beginning of the recitation. Sec. 3.13 problems: 14,16. Sec. 3.17: 2,6,9.