Math 205 Linear Methods [3]

Instructor: D. L. Johnson

Current Course Catalog Description

Linear differential equations and applications; matrices and systems of linear equations; vector spaces; eigenvalues and applications to linear systems of differential equations.

Textbook     

References  

Course Goals

The students should master the following concepts and techniques, with the ultimate goal of becoming  proficient in solving first order systems of differential equations:  differential equations with an equation on linear equations of first and second order and their applications; basic linear algebra, including matrix algebra, matrix form of systems of linear equations, row reduction, Gaussian elimination, rank, solution of equations, matrix inverses, determinants, vector spaces and subspaces, span, linear independence and dependence, basis and dimension, linear transformations, kernel and range, eigenvalues and eigenvectors.     

Prerequisites by Topic

Mastery of the notions and techniques of single variable calculus as developed in Mathematics 21 and 22 (see Course Descriptions for Mathematics 21 and 22 and their Annotated Syllabus Outlines, appended.

Major Topics Covered in the Course

See above, Catalog Description and Course Goals; see also Annotated Syllabus Outline, appended.

Laboratory projects (specify number of weeks on each)

Estimate CSAB Category Content

CORE   ADVANCED

Data Structures
Computer Organization and Architecture
Algorithms Software Design
Concepts of Programming Languages
 
 
Oral and Written Communications

Every student is required to submit at least  _____  written reports (not including exams, tests, quizzes, or commented programs) of typically  _____  pages and to make  _____  oral presentations of typically  _____  minutes duration. Include only material that is graded for grammar, spelling, style, and so forth, as well as for technical content, completeness, and accuracy.

Social and Ethical Issues

Theoretical Content

Vector spaces, linear transformations, existence of solutions for first order systems of differential equations, reduction of order for higher order systems/equations, variation of parameters. Somewhere between 35 and 40% of lecture time is spent on these topics.

Problem Analysis

Identification of problem types and matching of techniques mastered to problem types.

Solution Design

Devising and carrying out solution strategies to problems from within Mathematics and from a wide range of appplications areas.