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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.