MATHEMATICS 461: LINEAR ALGEBRA FOR SCIENTISTS AND ENGINEERS


Professor Robert Ellis
4417 Mathematics Building
(301) 405-5118
rle@math.umd.edu

            The following information is available at   http://www.wam.umd.edu/~rle/webpage_461.html and http://www.math.umd.edu.
 

COURSE DESCRIPTION

TOPICS

HOMEWORK ASSIGNMENTS

TEXT:

Linear Algebra with Applications,  Sixth Edition, by  Steven Leon , Prentice Hall, 1998.  ISBN 0-13-033781-1

GRADING:

Based on total points as follows:
   Exams :  100 points each
   Final exam:  200 points
   MATLAB projects:  75 points
   Total:   575 points
Each exam will be curved immediately after it is graded.   The curve for the MATLAB projects will be 67, 60, 53, 46. The curves for the exams and MATLAB will be added to produce a curve for the total.

FINAL EXAMINATION:

          Section 0201 (11:00):  Monday, May 19, 8:00 - 10:00 in our regular classroom.
          Section 0301 (1:00):  Saturday, May 17, 1:30-3:30 in our regular classroom.

PUBLIC POSTING OF GRADES:

            If  you give written consent, your grades will be posted  on the web under a number chosen by you at www.math.umd.edu/grades/MATH461.****.html ,where **** must be replaced by your section number (0201 or 0301).

ACADEMIC  INTEGRITY:

 Students are subject to the University's Code of Academic Integrity as approved by the Campus Senate.


LEARNING ASSISTANCE:http://www.inform.umd.edu/LASRV

         If you  are experiencing difficulties in keeping up with the academic standards of this course, you may wish to contact the Learning Assistance Service, 2201 Shoemaker Building, 301-314-7693.  Their educational counselors may be able to help with time management, reading, notetaking and exam preparation skills.
 

RELIGIOUS OBSERVANCES:
            If your religion dictates that you cannot take an exam or hand in assigned work on a particular date, then contact me at the beginning of the semester to discuss alternatives. You are responsible for making these arrangements at the beginning of the semester

HOMEWORK  ASSIGNMENTS:

        SECTION                                     EXERCISES
               1.1                               1,2,4(b,d), 5(b), 6(f,h), 7-11
               1.2                               1-3, 5(a,b,c,e,g,j), 6(d), 10,13,14
               1.3                               1-4, 5©, 10-12, 13(a), 16, 19-21,23,24
               1.4                               1-5, 7(a,d), 9(c,e,h), 13-15
                             2.1                               2-4, 6, 11
                             2.2                               1-7, 10-13, 16, 17
                             2.3                               1, 2, 14

                             3.1                               1, 5-7, 9, 10, 16
                             3.2                               1-3, 4(a,d), 5,6, 9(b), 10(b), 11, 12-14, 19, 20
                             3.3                               1,2(a,b,c), 4-8, 14-16
                             3.4                               2(a,b,c), 4,5,10,11,13-15,17
                             3.5                               1(a), 2(a), 5(a), 9, 10
                             3.6                               1,3,4-6,8,13

                             4.1                               1, 4-8, 10, 13, 15
                             4.2                               1(c), 2(c), 4, 5(a), 6, 12-14
                             4.3                               2, 4-7, 9, 11-13

                             5.1                               1(a), 2(a), 3(c), 13, 15
                             5.2                               1(a,c), 2, 7, 14
                             5.3                               7,9
                             5.4                               1-3, 6,7,8,9(a), 10(a)
                             5.5                               1-3, 7,8,13,14,19[a,b(ii)],25(a-c)
                             5.6                               5,6,8

                             6.1                               1(a,f,g,I), 2-4, 8, 11,23
                             6.2                               1(a,b), 2(b,c), 4,6
                             6.3                               1(a,d), 2(a,d), 4(a), 6, 23(b), 25(b)
                             6.4                               4(a,b,e,f), 5(c,e), 6,10
                             6.5                               1,3(a,d)
                             6.6                               1,3,4,5,7,9
 

COURSE DESCRIPTION:

The course provides an introduction to linear algebra and matrix theory.  It is intended primarily for engineering students.  This course cannot be used toward the upper level math requirements for MATH/STAT majors.  Credit will be granted for only one of the following: MATH 240, MATH 400, MATH 461.  Topics include systems of linear equations, matrices, vector spaces,  linear transformations, scalar products and orthogonality, eigenvalues, and various applications.


TOPICS:

                                     Systems of Linear Equations
                                          Gaussian elimination
                                          Echelon forms
                                          Existence and uniqueness of solutions
                                          Homogeneous systems
                                     Matrices
                                          Addition, scalar multiplication, multiplication of matrices
                                          Elementary matrices and inversion
                                          LU decomposition
                                          Systems of linear equations as matrix equations
                                          Partitioned matrices
                                          Determinants and their properties
                                          Cramer's rule
                                     Vector Spaces
                                          Definition and examples
                                          Subspaces and spanning sets
                                          Linear independence
                                          Basis and dimension
                                          Row space
                                          Column space
                                          Rank of a matrix
                                          Null space of a matrix
                                     Linear Transformations
                                          Definition and examples
                                          Kernel and range
                                          Matrix representation
                                          Change of basis and similarity of matrices
                                     Scalar Products and Orthogonality
                                          Definitions and examples
                                          Cauchy-Schwarz inequality
                                          Triangle inequality
                                          Pythagorean theorem
                                          Orthogonal projection
                                          Least squares problems
                                          Orthonormal sets and orthogonal matrices
                                          Gram-Schmidt process and QR factorization
                                          Orthogonal polynomials (optional)
                                     Eigenvalues
                                          Definitions and examples
                                          Diagonalization of matrices
                                          Spectral theorem for hermitian matrices
                                          Quadratic forms
                                          Positive definite matrices
                                          Nonnegative matrices (optional)