COURSE: Differential Equations with Linear Algebra, M427J #54010, Fall 2016
------ Class: TTh 12:30pm - 2:00pm, CPE 2.214, attendance is mandatory!
TA sessions: MW 5:00pm - 6:00pm, PAI 2.48
PREREQUISITES: M408D or M408L or M408S, with a grade of at least C-
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TEXT: M. Braun, "Differential Equations and Their Applications", 4th ed
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SYLLABUS: Ch. 1. First order ODEs (2 lectures)
-------- Ch. 2. Second order linear ODEs (5 lectures)
Ch. 3. Systems of linear ODEs, matrices (5 lectures)
L. Linear algebra (8 lectures)
Ch. 5. PDEs, sep of variables, Fourier series (4 lectures)
INSTRUCTOR: Hans Koch, RLM 12.152, Office Hours Tue Thu Fri 4:00-5:00 pm
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TA: Rustam Antia-Riedel, RLM 10.106, Office Hours Mon 4-5, Wed 3-5.
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GRADING: Letter grades (A,A-,B+,...,D-,F) will be given for | 93 -100 A
------- each exam, but number grades (100,99,..,2,1,0) will | 89 - 92 A-
be kept for averaging. The course grade is obtained | 85 - 88 B+
by averaging the number grades of the 4 exams and of | 81 - 84 B
the quizzes. Each student may replace the grade of | 77 - 80 B-
ONE exam by the grade of one of the following exams. | 73 - 76 C+
| 69 - 72 C
HOMEWORK problems will be posted on Wednesdays. | 65 - 68 C-
-------- Homework is NOT graded or even collected, but ... | 61 - 64 D+
QUIZZES are given in the TA sessions, roughly every 4 weeks, | 57 - 60 D
------- consisting of slightly modified homework problems. | 53 - 56 D-
The quizzes contribute 10% to the class grade. | 0 - 52 F
EXAMS: Three 70 minute in-class (Exams 1,2,3) | Exam 1 (Tu Sep 20) 21%
----- and a 120 minute Final (Exam 4, 9-11 am) | Exam 2 (Th Oct 13) 22%
The exams are mostly on new material. | Exam 3 (Th Nov 3) 23%
Books, calculators, or notes are not | Exam 4 (Th Dec 8) 24%
allowed. No make-up exams will be given. | Quizzes 10%
DROP deadline: November 1, Tuesday. Last day an undergraduate student may,
---- with the dean's approval, withdraw from the University or drop a class
except for urgent and substantiated, nonacademic reasons.
SSD: UT provides upon request appropriate academic accommodations for
--- qualified students with disabilities. For more information, contact
Services for Students with Disabilities (SSD) at 512-471-6259 (voice)
or 1-866-329-3986 (video phone).
MORE INFO: See the class web page http://www.ma.utexas.edu/users/koch/M427J/
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More detailed syllabus:
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1.2,4 | linear, separable ODEs
1.9 | exact equations, integrating factors
1.10,2.1 | Picard iteration, linear 2nd order ...
2.1,2 | superposition, reduction of order
2.2 | constant coefficients
2.3,4 | nonhomogeneous, variation of parameters
2.5 | undetermined coefficients
2.8 | power series, series solutions, ordinary points
3.A | systems, matrices
3.B | functions of matrices, inverse
3.C | fundamental matrix exp(tA)
3.D | eigenvalues and eigenvectors
3.E,F | complex roots, repeated roots
L.1 | simultaneous linear equations
L.2 | matrices again, span, lin indep, matrix inverse
L.3 | determinants
L.4 | vector spaces and subspaces
L.5 | bases and dimension
L.6,7 | linear transformations, coordinates
L.8 | inner products
L.9 | Hermitian operators
5.1 | two-point boundary value problems
5.3 | heat equation, separation of variables
5.4,5 | Fourier series, even/odd functions
5.6 | solution of the heat equation