I. COURSE NUMBER AND TITLE: Math 351 Linear Algebra
II. ACADEMIC CREDIT: Three semester hours.
III. COURSE DESCRIPTION: A study of systems of linear equations, vector spaces, inner product spaces, norms, orthogonality, eigenvalues, eigenvectors, matrices, and linear transformations. Prerequisite: Math 142
IV. PLACE OF THE COURSE IN THE CURRICULUM: This course is required in the engineering program and the mathematics major. It may be used as an elective in the mathematics minor.
V. COURSE OBJECTIVES: This course
A. Encourages the student to identify real world models that can only be represented by systems of equations and to recognize vectors and vector spaces that exist in our real world, enabling him/her to better appreciate and understand the beauty and structure of the world that God created.
B. Enables the student to develop methods of solving systems of equations and to find solutions tin vector spaces.
C. Provides practice for the student in determining when he/she may formulate a problem as a system of equations or as a vector space, reformulate the problem in the proper mathematical context, and then use the algorithms for solving systems of equations or the properties of vector spaces to seek solutions and determine their validity.
D. Provides opportunity for the student to review and understand new mathematical terms and symbols endemic to linear algebra, using them in correct form and with the proper symbols and definitions as understood by the international mathematical community.
E. Provides opportunity for the student to review, refine and use those skills and concepts developed in algebra, trigonometry, and calculus.
F. Introduces the student to the many simple and powerful proofs of the properties of a vector space, including the opportunities to develop some of them on his/her own.
G. Stresses the relation to other areas of mathematics such as algebra, trigonometry, calculus, differential equations, and statistics, as well as to the other disciplines by providing application problems in physics, biology, business, computers, medicine, engineering, chemistry, and history.
VI. STUDENT OUTCOMES: Upon successful completion of this course, a student should be able to
A. Solve systems of linear equations using Gaussian or Gauss-Jordan elimination.
B. Use the addition, subtraction, and multiplication properties of matrices to perform matrix arithmetic.
C. Determine if a matrix is invertible, and if it is, find its inverse.
D. Translate between systems of equations and their matrix form.
E. Solve systems of equations using the properties of invertible matrices.
F. Find the determinant of a matrix.
G. Find the eigenvalues and eigenvectors of a given matrix.
H. Solve systems of equations using Cramer's rule.
I. Use the addition, subtraction and multiplication properties of vectors to perform vector arithmetic.
J. Calculate the dot and cross product of vectors and apply these skills to solving problems involving equations of lines and planes in space, relations between vectors, distances, and volumes.
K. Extend the concepts developed in Euclidean two space and three space to Euclidean n-space.
L. Use projection operators to make linear transformations form two space to three space.
M. Use the properties of a vector space to determine if a set of vectors and their defined operations is a vector space.
N. Determine if a subset of a vector space is a subspace.
O. Determine if a set of vectors can form a basis for a vector space.
P. Determine a basis for the row or column space of a matrix.
Q. Work with inner product spaces in n-space.
R. Use the Gram-Schmidt process to convert an ordinary basis to an orthogonal basis.
S. Use simple orthogonal matrices to change a basis
T. Given a function, determine if it is a linear transformation.
U. Determine the kernel and range of a linear transformation.
V. Determine if a linear transformation can have an inverse.
W. Express simple linear transformations as matrix transformations.
X. Choose a basis for a vector space that makes the matrix of a linear operator on the vector space as simple as possible.
VII. LEARNING RESOURCES: You will need the text: Elementary Linear Algebra Applications Version, 8th edition by Howard Anton and Chris Rorres.
VIII. EVALUATON: Learning will be measured using textbook assignments, exams and an application problem. Textbook assignments will be due on Thursday for assignments given during the previous week. I will pick up and grade your problems, but not necessarily every one. Show and organize your work. Exams will be given on Tuesdays. All exams will be achievement exams. There will be three of them. The first two will each count for 20% of your graade and the final will count for 30%. Textbook assignments will count for 20% and the real world application problem will count for the other 10%.
IX. THE REAL WORLD APPLICATION PROBLEM: Problems from the text which qualify for the project are
A. Electrical Networks
B. Markov Chains
C. Games of Strategy
D. Leontief Economic Models
E. Forest Management
F. Computer Graphics
G. Equilibrium Temperature Distributions
H. Chaos
I. Cryptography
J. Genetics
K. Age-Specific Population Growth
L. Harvesting of Animal Populations
X. ATTENDANCE POLICY: You are expected to be in class. Absences make it very difficult for you to do well in class. Three unexcused absences will drop you from the class. Notify me prior to the class if you must be absent.
XI. GRADING: Grading will be on a percent scale with A's in the 90% range, B's in the 80%, C's in the 70%, D's in the 60%, and failing below 60%.
XII. The instructor reserves the right to modify, amend, or change the syllabus as the curriculum and/or program require(s).
Instructor: Larry Matthews Office: Meyer Hall 314
Email: lmatthews@blc.edu Phone: 344-7587