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. TopicsPREREQUISITES:
MATH 141 and one MATH/STAT course for which MATH 141 is a prerequisite.
Linear Algebra with Applications, Sixth Edition, by Steven Leon , Prentice Hall, 2001. (The 5th Edition may also be used.)
ISBN 0-13-849308-1
Based on total points as follows:Exams : 100 points each
Homework percentage (if applicable): 75 points Homework to be handed in
Matlab percentage (if applicable): 75 points
Final exam: 200 points
Each exam will be curved immediately after it is graded. The homework will be curved 90, 80, 70, 60. The exam and homework curves will be added to produce a curve for the entire course.
ACADEMIC INTEGRITY:
Students are subject to the University's Code of Academic Integrity as approved by the Campus Senate.
HOMEWORK ASSIGNMENTS (SIXTH EDITION):
SECTION EXERCISES3.1 1, 5-7, 9, 10, 16
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), 11, 14, 15
1.3 1-4, 5(c), 10-12, 13(a), 16, 19-22, 24, 25
1.4 1-5, 7(a,d), 9(c,e,h), 13, 15, 162.1 2-4, 6, 11
2.2 1-7, 10-13
2.3 1, 2, 14
4.1
1, 4-8, 10, 13, 15
4.2
1(c), 2(c), 4, 5(a), 6, 12-14
4.3
7, 9, 11-13
5.1
1(a), 2(a), 3(c), 13, 14
5.2
1(a,c), 2, 7, 14
5.3
1-3, 6, 7, 8, 9(a), 10(a)
5.4
7, 9
5.5
1-3, 8, 9, 14, 15, 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
6.6
1, 3(a,d)
6.7
1, 3, 4, 5, 7, 9
HOMEWORK ASSIGNMENTS (FIFTH EDITION):
SECTION EXERCISES3.1 1, 5-7, 9, 10, 16
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(c), 10-12, 13(a), 16, 19-21, 23, 24 (Also Ex.19 from the 6th Edition)
1.4 1-5, 7(a,d), 9(c,e,h), 13-152.1 2-4, 6, 11
2.2 1-7, 10-13
2.3 1, 2, 14
4.1
1, 4-8, 10, 13, 15
4.2
1(c), 2(c), 4, 5(a), 6, 12-14
4.3
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, 18[a,b(ii)], 24(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
Mon., Sept. 10
Section 1.2 Ex. 5(e,g); Section 1.3 Ex. 1(a), 13(a,b)
Fri., Sept. 14
Section 1.4 Ex. 6, 9(a)
Mon., Sept. 17
Section 1.4 Ex.. 13, 14
Wed., Sept. 19
MATLAB Ex. 2 for Chapter 1
Wed., Sept. 26
Section 2.3 Ex. 2(c); Section 3.1 Ex. 9(a)
Fri., Sept. 28
Section 3.2 Ex. 1(a,b), 3(b), 5(a)
Mon., Oct. 1
Section 3.2 Ex. 10(a,d), 13, 14(a)
Wed., Oct. 2
EXAM (Up to the end of Section 3.2)
Fri., Sept. 4
Section 3.3 Ex. 2(a,b), 6(b,c)
Wed., Oct. 31 EXAM (Up to the end of Section 5.2)
Fri., Nov. 9 MATLAB Ex. 4 for Chapter 3
Wed., Nov. 28 MATLAB Ex. 3 for Chapter 5
Mon., Dec. 3 EXAM (Up to the end of page 308 in the 5th Edition or 343 in the 6th Edition)
Wed., Dec. 19
FINAL EXAM 10:30-12:30
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.
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)