Slide 1: Linear Algebra
Lecture 1
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: 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