# Linear Algebra

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## Presentation Description

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## Presentation Transcript

### Slide 1:

Linear Algebra Lecture 1

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12 18 24 30 36 42

### Slide 3:

12 18 24 30 36 42

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[12 18 24 30 36 42]

### Slide 5:

12 18 24 30 36 42

What is Algebra?

### Slide 8:

What is Linear Algebra?

### Applications :

Applications Computer Graphics, Electronics, Chemistry, Biology, Differential Equations, Economics,

### Applications :

Applications Business, Psychology, Engineering, Analytic Geometry, Chaos Theory, Cryptography,

### Applications :

Applications Differential Equations, Fractal Geometry, Game Theory, Graph Theory, Linear Programming, Operations Research

### Why Use Lin Algebra? :

Why Use Lin Algebra? Formalizing Structuring Organizing Presenting Manipulating

### Using Linear Algebra :

Using Linear Algebra The solutions of systems of linear equations The vectors of physics, such as force, acceleration. Binary code, an example of a vector space, has applications in computer Sciences

### Using Linear Algebra :

Using Linear Algebra Solutions to specific systems of differential equations Statistics uses linear algebra. Signal processing uses linear algebra.

### Using Linear Algebra :

Using Linear Algebra Linear Algebra is part of and motivates much abstract algebra. Vector spaces form the basis from which the important algebraic notion of module has been abstracted.

### Using Linear Algebra :

Using Linear Algebra Vector spaces appear in the study of differential geometry through the tangent bundle of a manifold.

### Using Linear Algebra :

Using Linear Algebra Many mathematical models, especially discrete ones, use matrices to represent critical relationships and processes.

### Using Linear Algebra :

Using Linear Algebra This is especially true in engineering as well as in economics and other social sciences.

### Course Segments :

Course Segments Linear Equations (8) Matrix Algebra (6) Determinants (3) Vector spaces (8) Eigenvalues & Eigenvectors (8) Orthogonality (7)….+2+3

### Course Objectives :

Course Objectives To master techniques for solving systems of linear equations To introduce matrix algebra as a generalization of the single variable algebra of high school.

### Course Objectives :

Course Objectives To build on the background in Euclidean space and formalize it with vector space theory. To develop an appreciation for using linear methods in a variety of applications.

### Course Objectives :

Course Objectives To relate linear methods to other areas of mathematics such as calculus and, differential equations.

### Recommended Books :

Recommended Books Linear Algebra and its Applications (3rd Edition) by David C. Lay Contemporary Linear Algebra by H. Anton and R. C. Busby

### Recommended Books :

Recommended Books Introductory Linear Algebra (8th Edition) by H. Anton and C. Rorres Introduction to Linear Algebra (3rd Edition) by L. W. Johnson, R.D. Riess and J.T. Arnold

### Recommended Books :

Recommended Books Linear Algebra (3rd Edition) by S. H. Friedberg, A.J. Insel and L.E. Spence Introductory Linear Algebra with Applications (6th Edition) by B. Kolman

### Some useful Web sites :

Some useful Web sites www.laylinalgebra.com www.wiley.com/college/anton

### Slide 27:

Linear Algebra Lecture 1