Lehigh University

Math 205 Linear Methods [3]

Instructor: Vladimir Dobric

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. Prerequisite: MATH 22 or 32.

Textbook

"Linear Algebra and Differential Equations", by Peterson and Sochacki

References

None

Course Outcomes

Students should master the concepts and techniques listed below under Major Topics Covered in the Course with the ultimate goal of becoming proficient in solving first order systems of differential equations.

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 )

Major Topics Covered in the Course

Basic Linear Algebra: systems of equations, row-reduction, rank, matrices, inverses, determinants.
Vector Spaces: subspaces (mainly n-dimensional Euclidean space and spaces of matrices), span, independence, bases, null-space, dimension, Wronskians.
Differential Equations: modeling and applications. First-order and constant-coefficient second order equations are emphasized. For the former, separable, exact and linear equations are covered, as is Euler's method. Applications include population growth, radioactive decay, mixing problems, heating/cooling, springs, circuits and exponential decay (including resonance and beats).
Linear Transformations, Eigenvalues and Eigenvectors: change of basis, similarity of matrices.
First-order Systems of Linear Diffential Equations and Applications: homogeneous constant-coefficient systems with diagonalizable matrices (the non-diagonalizable case (defective matrices) is not considered in detail), non-homogeneous systems are solved by undetermined coefficients or variation of parameters, applications are to multi-spring or multi-tank mixing problems.

Relationship between Course Outcomes and Program Outcomes

MATH 205 outcomes strongly support the following outcome:

A. An ability to apply knowledge of computing and mathematics appropriate to the discipline

Assessment Plan for the Course

The students take two midterms and a final examination. Homework is collect in each lecture and graded; on occasion, an in-class quiz on the material of the homework assignment may replace a homework grade.

		Math 205 Linear Methods [3] Instructor: Vladimir Dobric 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. Prerequisite: MATH 22 or 32. Textbook "Linear Algebra and Differential Equations", by Peterson and Sochacki References None Course Outcomes Students should master the concepts and techniques listed below under Major Topics Covered in the Course with the ultimate goal of becoming proficient in solving first order systems of differential equations. 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 ) Major Topics Covered in the Course Basic Linear Algebra: systems of equations, row-reduction, rank, matrices, inverses, determinants. Vector Spaces: subspaces (mainly n-dimensional Euclidean space and spaces of matrices), span, independence, bases, null-space, dimension, Wronskians. Differential Equations: modeling and applications. First-order and constant-coefficient second order equations are emphasized. For the former, separable, exact and linear equations are covered, as is Euler's method. Applications include population growth, radioactive decay, mixing problems, heating/cooling, springs, circuits and exponential decay (including resonance and beats). Linear Transformations, Eigenvalues and Eigenvectors: change of basis, similarity of matrices. First-order Systems of Linear Diffential Equations and Applications: homogeneous constant-coefficient systems with diagonalizable matrices (the non-diagonalizable case (defective matrices) is not considered in detail), non-homogeneous systems are solved by undetermined coefficients or variation of parameters, applications are to multi-spring or multi-tank mixing problems. Relationship between Course Outcomes and Program Outcomes MATH 205 outcomes strongly support the following outcome: A. An ability to apply knowledge of computing and mathematics appropriate to the discipline Assessment Plan for the Course The students take two midterms and a final examination. Homework is collect in each lecture and graded; on occasion, an in-class quiz on the material of the homework assignment may replace a homework grade.