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Homework

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Exams

Instructor's Contact Information

Course Information

Textbooks

Prerequisites

MATH 1B or equivalent. In particular, you should be familiar with techniques of integration such as substitution and integration by parts, Taylor series, and solving second-order linear homogeneous differential equations with constant coefficients. Topics from high school mathematics that you may want to review include row reduction of matrices, solving systems of linear equations, determinants, and the factorization of polynomials in one variable, up to degree 4. Topics from MATH 1A that you may want to review include odd and even functions; basic properties of continuity, differentiation, and integration; and the Fundamental Theorem of Calculus. Some prior knowledge of the complex numbers is also helpful. If you've taken MATH 53 before, it may help to review the dot product and its basic properties.

Important Dates

Event Date
Last day to cancel registration Friday, June 22
First day of class Monday, June 25
Last day to withdraw or drop with refund Friday, June 29
Independence Day (no class) Wednesday, July 4
Last day to register for MATH 54 Friday, July 6
First midterm exam Friday, July 13
Second midterm exam Wednesday, August 1
Last day to withdraw, drop, or change grading option Friday, August 3
Final exam Thursday, August 16 and Friday, August 17

Schedule

Week of Monday Tuesday Wednesday Thursday Friday
June 25 complex arithmetic; systems of linear equations; augmented matrices; lecture notes 1 matrix arithmetic; elementary matrices; matrix inverses; lecture notes 2 more elementary matrices and matrix inverses; examples; Quiz 1; lecture notes 3 more with inverses; transposes and symmetric matrices; lectures notes 4 vector spaces; linear combinations; Quiz 2; lecture notes 5
July 2 more vector spaces; subspaces; lecture notes 6 null spaces; Quiz 3; lecture notes 7 Holiday linear independence; bases fundamental subspaces and rank; Quiz 4; lecture notes 8
July 9 coordinate vectors; lecture notes 9 transition matrices; rank; Quiz 5; lecture notes 10 linear transformations Review Midterm 1
July 16 inner product spaces; lecture notes 11 least squares; lecture notes 12 Gram-Schmidt; projections; Quiz 6; lecture notes 13 and accompanying graphs orthogonal matrices; linear transformations relative to given bases; similarity of matrices; lecture notes 14 determinants; eigenvalues and eigenvectors; Quiz 7; lecture notes 15
July 23 diagonalization; lecture notes 16 Spectral Theorem; lecture notes 17 linear recurrence relations; Quiz 8; lecture notes 18 Jordan canonical form; lecture notes 19 Jordan canonical form; Quiz 9
July 30 Jordan canonical form; Review Euler's Formula; intro to differential equations; Review; lecture notes 20 Midterm 2   existence and uniqueness theorem; the Wronskian; Quiz 10; lecture notes 21
August 6 Abel's Theorem; systems of linear first-order differential equations; lecture notes 22 matrix exponentiation; lecture notes 23 sources, sinks, etc.; Quiz 11; lecture notes 24 eigenvalues and eigenfunctions of boundary value problems; lecture notes 25 Fourier series; Quiz 12; lecture notes 26
August 13 solving PDEs using separation of variables nonhomogeneous PDEs; wave equation; computations for heat equation and wave equation examples Review Final Exam Final exam

Grading

The breakdown of points in the class will be as follows:

There will be a curve, but that curve will be no harsher than 90 for A-, 80 for B-, 70 for C-, and 60 for D-. That is, if your overall score at the end of the class is 90% or higher, then your grade will be at least an A-, it will be at least a B- if your score is 80% or higher, and so on.

Your two lowest homework scores and three lowest quiz scores will be dropped. Homework will generally be due on each quiz day. Late homework will not be accepted, and there will be no makeup quizzes.

Links

Some Mathematica functions that might be helpful:

Also see the general documentation on working with matrices in Mathematica.

A short guide to linear algebra on the TI-89.