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Graphing and Writing Linear Functions
SOLVING EQUATIONS INVOLVING RATIONAL EXPONENTS
Linear Equations and Graphing
Systems of Linear Equations
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Matrix Equations and Solving Systems of Linear Equations
Introduction Part II and Solving Equations
Linear Algebra
Graphing Linear Inequalities
Using Augmented Matrices to Solve Systems of Linear Equations
Solving Linear Inequalities
Solution of the Equations
Linear Equations
Annotated Bibliography of Linear Algebra Books
Write Linear Equations in Standard Form
Graphing Linear Inequalities
Introduction to Linear Algebra for Engineers
Solving Quadratic Equations
THE HISTORY OF SOLVING QUADRATIC EQUATIONS
Systems of Linear Equations
Review for First Order Differential Equations
Systems of Nonlinear Equations & their solutions
LINEAR LEAST SQUARES FIT MAPPING METHOD FOR INFORMATION RETRIEVAL FROM NATURAL LANGUAGE TEXTS
Quadratic Equations
Syllabus for Differential Equations and Linear Alg
Linear Equations and Matrices
Solving Linear Equations
Slope-intercept form of the equation
Linear Equations
DETAILED SOLUTIONS AND CONCEPTS QUADRATIC EQUATIONS
Linear Equation Problems
Systems of Differential Equations
Linear Algebra Syllabus
Quadratic Equations and Problem Solving
LinearEquations
The Slope-Intercept Form of the Equation
Final Exam for Matrices and Linear Equations
Linear Equations
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Introduction to Linear Algebra for Engineers

Instructor : Yehonathan Hazony, Professor
The course combines linear algebra with analytical geometry in the context of
computer-aided engineering design, analysis and manufacture. Engineeringgeometry
serves to introduce linear algebra. Mathematical abstraction is linked to
practical engineering-graphic applications. Tools of linear algebra are introduced to
facilitate the analysis of engineering designs, as well as for the preparation of design
data for the transformation to computer-controlled manufacture. Eigen Values and
Eigen Vectors are introduced in the context of engineering-problem solving. Over
constraint system and Linear regression analysis.
Cannot be taken in addition to CAS MA142 or MA 242.

Credit: 2 cr.

Textbooks::
Elementary Linear Algebra - Bernard Kolman, and David R. Hill,
8-th Edition, 2004, Pearson/Prentice Hall.
(ISBN 0-13-107678-7; or ISBN 0-13-045787-6)
or 9th Edition, 2008, (ISBN 0-13-229654-3)

Grading: 3 tests (1-hour) – 25 points each (only the better two grades count)
Final Exam (2 hours) – 50 points (to be scheduled by the college)

Topics:
1. Introduction - Linear algebra as a fundamental tool for engineering.
2. Linear Equations and Matrices (Textbook Section 1.1 – 1.6)
 Linear equations in 2- and 3-dimensional spaces.
 Points, lines and planes.
 Normal representation.
3. Scalars, Vectors and Matrices: (Sections 1.2-1.4, 2.1 and 3.1)
 Matrix operations, (Section 1.2)
 Dot-Product and the Inner-Product (Section 1.3, 2.1 and 3.1)
 Outer-Product (Section 1.8 - page 82)
 Matrix equations.
4. Solutions of linear systems of equations (Section 1.5)
 Geometric space,
 Coefficient space,
 Parametric solutions,
 The Gauss Method.

Test #1 – Wed. – Feb. 11, 09

5. The inverse of a matrix: (Sections 1.4 - 1.6)
 An invertible (non-singular) matrix
 A computational definition
 A formal definition.
 LU-decomposition method.
6. Singular (non-invertible) systems (Sections 1.1, 1.4, 1.6, and Chapter 2)
 Span and linear independence (Section 2.4)
 Homogeneous systems (Sections 1.1, 2.3, 2.4, and 2.6)
 Rank of a matrix (Section 2.8 )
 Trivial and nontrivial solutions. (Section 1.1)
 Parametric solutions. (Section 2.3)
7. Determinants: (Chapter 5)
 Definitions and properties (Section 5.1 and 5.2)
 Cofactor expansion and application (Section 5.3)
 A computational point of view (Section 5.6).

Test#2 - Wednesday March 18, 09

8. Vectors in Rn and Inner-Product spaces (Chapter 3)
 n-vectors and dot-product spaces (Sections 3.1 and 3.3)
 Coordinate systems and change of bases (Sections 2.5 and 2.7 )
 Orthogonal and orthonormal bases (Section 3.5)
 The Gram-Schmidt Process (Section 3.4)
9. Linear transformations and Transformation Matrices (Sections 4.1 and 4.3)
10. Quadratic forms and the Eigen-Value problem: (Sections 6.6-6.8)
 Definitions
 Principal Axes
 The Eigen-Value problem
11. Solution methods: (Sections 6.1,6.4)
 Eigen Values
 Eigen Vectors and Orthogonal Transformations

Test #3 Wednesday, April 15, 09

12. Over constraint-systems and Least-mean squares (Section 3.6)

Final Exam - to be scheduled by the College.