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Approved by Faculty Senate

 

University Studies Course Approval Proposal
Flag Requirements – Mathematics/Statistics Flag

 

The Department of Mathematics and Statistics proposes the following course for inclusion in University Studies as a course satisfying the requirements for a Mathematics/Statistics Flag. This was approved by the full department on Thursday, February 1, 2001.

 

Course: Differential Equations and Linear Algebra (MATH 270), 4 s.h.

 

Catalog Description: Solution techniques for ordinary differential equations including boundary/initial value problems and systems of first-order equations. Topics include linear homogeneous and non-homogeneous differential equations and the Laplace transform. Methods of linear algebra are studied as they apply to the solution of differential equations. Prerequisite: MATH 165.

 

This is an existing course, previously approved by A2C2.

 

Department Contact Person for this Course:

Name: Barry A. Peratt

Title: Assistant Professor of Mathematics and Statistics

Email: bperatt@winona.edu

 

General Discussion of University Studies – the Mathematics/Statistics Flag

in relation to MATH 270

 

University Studies: Mathematics/Statistics Flag

 

Flagged courses will normally be in the student’s major or minor program. Departments will need to demonstrate to the University Studies Subcommittee that the courses in question merit the flags. All flagged courses must require the relevant basic skills course(s) as prerequisites (e.g., the "College Reading and Writing" Basic Skill course is a prerequisite for Writing Flag courses), although departments and programs may require additional prerequisites for flagged courses. The University Studies Subcommittee recognizes that it cannot veto department designation of flagged courses.

 

The purpose of the Mathematics/Statistics Flag course requirement is to reinforce the outcomes specified for the basic skills area of mathematics/statistics. These courses are intended to provide students with significant practice in applying prerequisite mathematical or statistical knowledge.

 

Courses can merit the Mathematics/Statistics Flag if students will be required to make essential use throughout the semester of mathematical or statistical models appropriate to their prerequisite knowledge of those areas, and if the correct use of techniques based on such models will comprise a significant portion of a student’s final grade. It is understood that mere rote computations, algebraic manipulations, or graphical design without inferential content would not merit a Mathematics/Statistics Flag.

 

These courses must include requirements and learning activities that promote students’ abilities to:

  1. practice the correct application of mathematical or statistical models that are appropriate to their prerequisite knowledge of those areas; and
    2.

    Differential Equations are powerful mathematical tools used to most type of physical phenomena that involve change: fluid flow, celestial motion, population dynamics, etc. To be successful in this course, the student must demonstrate an ability to accurately model physical phenomena using Differential Equations. Additionally, the student must demonstrate an ability to accurately analyze those mathematical models using the techniques of calculus and linear algebra.

     

  2. make proper use of modern mathematical or statistical methods appropriate to their level of prerequisite knowledge, to include, if statistics is used in a substantive way, the use of a statistical package with graphics capability when appropriate.

The successful student will employ the use of computational and graphical aids (e.g. Mathematica, Matlab, TI-89, MathCad, and Derive) along with several modern qualitative, algebraic, and numerical methods to analyze Differential Equations.

 

 

Winona State University

Department of Mathematics and Statistics

Course Outline—M270

 

Course Title: Differential Equations and Linear Algebra

Number of Credits: 4 s.h.

Prerequisite: Calculus II (M165)

Grading: Grade only for all majors, minors, options, concentrations and licensures within the Department of Mathematics and Statistics. The P/NC option is available to others.

Course Description: A study of ordinary differential equations and systems. Methods of linear algebra are studied as they relate to the solution of differential equations. Emphasis is on modeling and on the qualitative and numerical study of differential equations. Topics include linear and nonlinear systems of equations and the method of LaPlace transforms.

Statement of Major Focus and Objectives of the Course: The major focus of this course is to introduce students differential equations as tools for modeling physical phenomena that involve change, and to various qualitative, algebraic, and numerical methods for analyzing those differential equations.

Possible Texts: Except for Bugl, which includes linear algebra topics, all differential equations texts listed must be supplemented by a linear algebra text such as Schaum's. The other two DE texts provide a more modern treatment of the discipline than does Bugl. The IDE software is a only a supplement to the course and is available on the computers in the Mathlab.

bulletAn Introduction to Differential Equations: Order and Chaos by Diacu.
bulletDifferential Equations by Blanchard, Devaney, and Hall.
bulletLinear Algebra and Differential Equations using Matlab by Golubitsky & Dellnitz.
bulletDifferential Equations: A Modeling Perspective by Borrelli and Coleman.
bulletDifferential Equations: Graphics, Models, Data by Lomen and Lovelock.
bulletSchaum's Outline Series: Linear Algebra by Lipschutz.
bulletDifferential Equations: Matrices and Models by Bugl.
bulletInteractive Differential Equations software by West, Strogatz, McDill, Cantwell, and Hohn.

Methods of Instruction: Lecture, Discussion, Projects (possibly cooperative).

Course Requirements: Recommended software includes Student version of Matlab or Mathematica IDE software.

Evaluation Process: Tests, Quizzes, Projects.

University Studies: Mathematics/Statistics Flag

Flagged courses will normally be in the student’s major or minor program. Departments will need to demonstrate to the University Studies Subcommittee that the courses in question merit the flags. All flagged courses must require the relevant basic skills course(s) as prerequisites (e.g., the "College Reading and Writing" Basic Skill course is a prerequisite for Writing Flag courses), although departments and programs may require additional prerequisites for flagged courses. The University Studies Subcommittee recognizes that it cannot veto department designation of flagged courses.

 

The purpose of the Mathematics/Statistics Flag course requirement is to reinforce the outcomes specified for the basic skills area of mathematics/statistics. These courses are intended to provide students with significant practice in applying prerequisite mathematical or statistical knowledge.

 

Courses can merit the Mathematics/Statistics Flag if students will be required to make essential use throughout the semester of mathematical or statistical models appropriate to their prerequisite knowledge of those areas, and if the correct use of techniques based on such models will comprise a significant portion of a student’s final grade. It is understood that mere rote computations, algebraic manipulations, or graphical design without inferential content would not merit a Mathematics/Statistics Flag.

 

These courses must include requirements and learning activities that promote students’ abilities to:

    1. practice the correct application of mathematical or statistical models that are appropriate to their prerequisite knowledge of those areas; and
    2. make proper use of modern mathematical or statistical methods appropriate to their level of prerequisite knowledge, to include, if statistics is used in a substantive way, the use of a statistical package with graphics capability when appropriate.

 

Topics below which include such requirements and learning activities are indicated below using lowercase, boldface letters a.-b. corresponding to these requirements.

 

Course Outline of the Major Topics and Subtopics:

bulletWhat is a differential equation and why are they necessary?
bulletStatic vs. Dynamic models. a.-b.
bulletElementary DEs of the form from calculus; rate of change problems. a.-b.
bulletMain types of analysis: qualitative (for global asymptotic behavior) and quantitative (analytical and numerical). a.-b.
bulletModeling natural phenomena with differential equations.
bulletMalthusian Population Model. a.-b.
bulletLogistic Population Model. a.-b.
bulletTorcelli's Law. a.-b.
bulletNewton's Law of Cooling. a.-b.
bulletSHM with Damping. a.-b.
bulletCompeting species models, predator-prey, harvesting. a.-b.
bulletFirst-Order Differential Equations
bulletType of equations: autonomous, non-autonomous, linear, non-linear, separable. a.-b.
bulletTechniques for analyzing: existence/uniqueness theorem, slope fields, phase plots, numerical integration, separation of variables, integrating factors. a.-b.
bulletBifurcations a.-b.
bulletLinear Algebra
bulletSolving simultaneous linear equations. a.-b.
bulletThe inverse of a matrix and reduced row-echelon form. a.-b.
bulletVector spaces, linear independence, spanning, bases. a.-b.
bulletLinear Transformations a.-b.
bulletEigenvalues and Jordan-Canonical Form. a.-b.
bulletFirst Order Systems of Differential Equations
bulletModeling with systems. a.-b.
bulletEuler's Method with systems. a.-b.
bulletLinear systems and eigenvalue analysis. a.-b.
bulletConverting second order equations to systems. a.-b.
bulletForcing and non-autonomous systems. a.-b.
bulletNon-linear systems, linearization, series solutions. a.-b.
bulletLaPlace Transforms a.-b.

 

 

Approval/Disapproval Recommendations

 

 

Department Recommendation: Approved Disapproved Date

 

 

Chairperson Signature Date

 

 

Dean’s Recommendation: Approved Disapproved Date

 

 

Dean’s Signature Date

*In the case of a Dean’s recommendation to disapprove a proposal, a written rationale for the recommendation

to disapprove shall be provided to USS.

 

 

USS Recommendation: Approved Disapproved Date

 

 

University Studies Director’s Signature Date

 

 

A2C2 Recommendation: Approved Disapproved Date

 

 

A2C2 Chairperson Signature Date

 

 

Faculty Senate Recommendation: Approved Disapproved Date

 

 

FA President’s Signature Date

 

 

Academic VP’s Recommendation: Approved Disapproved Date

 

 

VP’s Signature Date

 

 

President’s Decision: Approved Disapproved Date

 

 

President’s Signature Date