Math 1512, Honors Calculus II
Fall 2007
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Instructor: Matt Baker
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Time and place: TuTh 9:35 A.M. - 10:55 P.M, Skiles 246
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E-mail: mbaker@math.gatech.edu
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Office: Skiles 212
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New Office Hours: Tuesday 11:00 - 12:00, Tuesday 12:30 - 1:30, and Thursday 1:00 - 2:00
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Course TA: A.J. Friend, office hours Monday 2:00-3:00 and Tuesday 11:00 - 12:00 in Skiles 230
Course survey:
If you haven't done so already, please fill out the
Online course evaluation.
Exam schedule:
- Midterm #1: Wednesday, September 26
- Midterm #2: Wednesday, October 31
- Midterm #3: Wednesday, November 28
- Final exam: Friday, December 14 from 8am - 10:50am in Skiles 246
Handouts and links:
Twelfth homework assignment
(due Thursday, November 29):
Eleventh homework assignment
(due Thursday, November 15):
Tenth homework assignment
(due Thursday, November 8):
Ninth homework assignment
(due Thursday, November 1):
Eighth homework assignment
(due Wednesday, October 24):
Seventh homework assignment
(due Wednesday, October 17):
Sixth homework assignment
(due Thursday, October 4):
Fifth homework assignment
(due Thursday, September 27):
Fourth homework assignment
(due Thursday, September 20):
Third homework assignment
(due Wednesday, September 12):
Second homework assignment
(due Wednesday, September 5):
First homework assignment
(due Wednesday, August 29):
Course texts:
The primary texts for the course will be Linear Algebra by
T. Apostol and Calculus by Salas, Hille, and Etgen
(9th or 10th edition).
We will cover most of Chapters 1 through 6 in the Apostol book,
together with some applications to differential equations from
Chapters 8 and 9. Almost any standard calculus book will be an adequate
reference for the material on infinite series, though we will
attempt to follow the exposition and terminology from Salas, Hille, and Etgen.
Course description:
While Calculus II at Georgia Tech covers several topics in
single-variable calculus which are not covered in Calculus I
(e.g. infinite series and Taylor approximations),
the main emphasis is on linear algebra. In Math 1512, we will assume
familiarity with some of the single-variable calculus topics
covered in Math 1502 (including numerical integration and improper integrals),
and we will cover the linear algebra material in much greater depth.
We will also cover more material from the theory of differential equations than
is typically done in Math 1502.
Roughly speaking, the first 60% of the course will be linear algebra,
followed by 20% on infinite series and 20% on differential equations.
More specifically, the following topics will be covered
(in roughly the order listed):
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Linear algebra:
Systems of linear equations, Gauss-Jordan elimination, vector algebra,
geometry in Euclidean spaces,
vector spaces, linear independence, bases and dimension, the
Gram-Schmidt process, orthogonal projections, the method of least
squares, linear transformations and their matrix representations,
change-of-basis formulas, the rank-nullity theorem, determinants,
eigenvalues and eigenvectors, triangularization and diagonalization,
the characteristic polynomial, the Cayley-Hamilton theorem, and
diagonalization of symmetric operators.
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Series:
Taylor polynomials and Taylor series, convergence tests for infinite series,
power series, L'Hopital's rule, and the exponential of a matrix.
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Differential equations:
Solving systems of linear ODE's via matrix exponentials,
existence and uniqueness theorems, variation of parameters, and power
series solutions.
Homework:
There will be weekly homework assigments in the class.
Homework will be handed out on Thursdays in the lecture
and collected on Wednesdays in the recitation section.
Honor code:
Please review the Georgia Tech Honor Code.
All examinations in this course will be closed book -- no notes of any kind
may be used. You may freely discuss the homework with your
classmates, but you must write up your solutions independently
and the work you turn in must be your own.
Grading Policy:
The two highest midterm exam scores will each count for
25% of your grade, the final will count 35%, and homework will count 15%.
Letter grades will be based on your overall numerical average
at the end of the term.
I have no pre-determined letter grade cut-offs,
but it is guaranteed that 90% or above will be an A, 80% or above will be
at least a B, 70% or above will be at least a C, etc.
Miscellany:
If at any point during the semester you feel
unsatisfied with some aspect of the course, please come talk to me
about it!
Useful links:
This page was last modified on December 6, 2007 by
Matt Baker.