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Syllabus for Elements of Linear Algebra


Catalog Description:

This course is a study of matrices, systems of linear equations ,
determinants, vectors, vector spaces, eigenvalues, eigenvectors,
and other selected topics.
 

Credit Hours:
3 sem hrs
Contact Hours: 3 hrs/wk
Lab Hours: 0
 

Prerequisite(s):
MATH 1910
 

Required
Elementary
 
Text(s): Linear Algebra
Title
Howard Anton
Author(s)
9th/2005
Edition/Date
John Wiley & Sons
Publisher


 


Required Supplies/Material(s):

Graphics Calculator --TI-86 is preferred , but any
calculator which will perform matrix operations
will be acceptable
 


Recommended Supplementary Material(s):
 

Student Group for Whom Course is Required/Intended:

This course is required for
students selecting pre-engineering option and is recommended as an elective for
students who select from the fol lowing options : computer science, mathematics, and
physics.
 

GOALS

 

The goals of instruction of MATH 2010 are :
1. to teach the skills needed to solve systems of equations using various matrix methods ,
2. to teach skills needed to evaluate determinants,
3. to teach the skills necessary to use vectors in other areas,
4. to teach the student how to change bases and construct orthogonal bases,
5. to teach the skills necessary to perform linear transformations,
6. to teach the student how to find eigenvectors, and
7. to make the student familiar with certain applications of matrix
theory.
 

OBJECTIVES
 

Through the study of MATH 2010, the student should be able to do the following.
1. Solve systems of linear equations using Gaussian elimination.
2. To perform matrix operations.
3. To use matrix ope rations to find the inverse of a matrix.
4. To evaluate determinants.
5. To use properties of de terminants to solve problems.
6. To find the norm of a vector and do vector arithmetic.
7. To find dot products.
8. To find the cross product of two vectors .
9. To do vector operations in N -dimensional space.
10. To study orthogonality of a matrix and vectors.
11. To understand and use general vector spaces, subspaces, and spanning sets.
12. To find the dimension and basis of a vector space.
13. To determine the linear independence or dependence of sets of vectors.
14. To determine the rank of a matrix and the uses of the rank.
15. To construct an orthonormal basis using the Gram-Schmidt process.
16. To understand linear transformations and to perform them.
17. To construct the matrices of linear transformations.
18. To find the eigen values and eigenvectors of certain matrices.
19. To diagonalize matrices.
20. To do orthogonal diagonalizations.
 

SUGGESTED EVALUATION PLAN

TASK WEIGHT OBJECTIVES
Test 1

Test 2

Test 3

Test 4

Test 5

Test 6 - Final Exam

100 points

100 points

100 points

100 points

100 points

100 points

1-3

4-5

9, 11, 12, 13, 14

5, 6, 7, 8, 15

16, 17

1-20

FINAL GRADING PLAN
Based Upon Percentages

A = 90-100
B = 80-89
C = 70-79
D = 60-69
F = Below 60

Additional Comments :

INSTRUCTIONAL SCHEDULE
for

MATH 2010 - Elements of Linear Algebra
Course Number and Name

Week Objective
Numbers
Content to be Covered Student As signments /
Supplementary Material(s)
I.
 
1
 
Introduction to Systems of Linear
Equations
Exercises 1.1
 
  1
 
Gaussian Elimination and Gauss -
Jordan Elimination
Exercises 1.2
 
  1
 
Applications of Systems of Linear
Equations
Exercises 1.3
 
       
II. Operations with Matrices Exercises 2.1
  Properties of Matrix Operations Exercises 2.2
  The Inverse of a Matric Exercises 2.3
       
III.   Review for Test  
  1-3
 
Test 1 (Chapter 1 and
Chapter 2 sections 1-3)
 
    Elementary Matrices Exercises 2.4
       
IV. Applications of Matrix Operations Exercises 2.5
    The Determinant of a Matrix Exercises 3.1
  4
 
Evaluating of a Determinant Using
Elementary Operations
Exercises 3.2
 
       
V. Properties of Determinant Exercises 3.3
    Applications of Determinants Exercises 3.4
    Review for Test 2 Review
       
VI.
 
4-5
 
Test 2 (Chapter 2 Sections 4 & 5
and Chapter 3)
 
    Vectores in Rn Exercises 4.1
    Vector Spaces Exercises 4.2
       
VII. 11 Subspaces of Vector Spaces Exercises 4.3
  11, 13
 
Spanning Sets and Linear
Independence
Exercises 4.4
 
  12 Basic and Dimension Exercises 4.5
       
VIII.
 
14
 
Rank of a Matrix and Systems of
Linear Equations
Exercises 4.6
 
    Coordinates and Change of Basis Exercises 4.7
    Applications of Vector Spaces Exercises 4.8
       
IX.   Review for Test 3  
  9,11,12,
13,14
Test 3 (Chapter 4)
 
 
  5, 6, 7 Length and Dot product in Rn Exercises 5.1
       
X. 6 Inner Product Spaces Exercises 5.2
  15
 
Othonormal Bases; Gram-Schmidt
Process
Exercises 5.3
  8 Applications of Inner Product Spaces Exercises 5.5
       
XI.   Review for Test 4  
  5,6,7,8,
15
Test 4 (Ch. 5 Sections 1,2,3,5)
 
 
    Introductions to Linear Exercises 6.1
  16 Transformations  
       
XII.
 
16
 
The Kennel and Range of a Linear
Transformation
Exercises 6.2
 
  17 Matrices for Linear Transformation Exercises 6.3
    Transitions Matrices and Similarity Exercises 6.4
       
XIII.   Applications of Linear
Transformations
Exercises 6.5
 
    Review for Test 5  
  16,17 Test 5 (Chapter 6)  
       
IV. 18 Eigenvalues and Eigenvectors Exercises 7.1
  19 Diagonalization Exercises 7.2
  10, 20
 
Symmetric Matrices and
Orthogonal Diagonalization;
Exercises 7.3
 
       
XV.   Induction Appendix A - Induction
    Review for final  
       
XVI. 1-20 Final Exam  
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