LSU
Mathematics

Math 2090

Current catalog description:

Math 2090 Elementary Differential Equations And Linear Algebra (4) F,S,Su Prereq.: MATH 1552. Credit will be given for only one of the following: MATH 2065, 2070, 2090. Credit will not be given for both this course and MATH 2085 or 2086. Introduction to first order differential equations, linear differential equations with constant coefficients, and systems of differential equations; vector spaces, linear transformations, matrices, determinants, linear dependence, bases, systems of equations, eigenvalues, eigenvectors, Laplace transforms, and Fourier series.

The Undergraduate Studies Committee recommends the following two changes:

1. Drop the mention of Math 2070 (last fall, the department voted to drop Math 2070 from the catalog).

2. Drop "Fourier series" from the list of topics covered in Math 2090.

Regarding (2) above: In the 1998-1999 catalog, and in many earlier catalogs, the description of Math 2090 did not mention Laplace transforms or Fourier series; then, as now, Math 2090 was a 4-hour course. Then, in the 1999-2000 catalog, Laplace and Fourier were added, but Math 2090 still remained a 4-hour course; the only gesture of a corresponding reduction of other material to be covered was to replace the topic "first order differential equations" with "introduction to first order differential equations." The result has been an overloaded syllabus since 2000, requiring the teacher either to race through the course and leave the students far behind, or to skip one or more topics—most commonly Fourier series, and occasionally even Laplace transforms as well. Our understanding is that the College of Engineering does not want Math 2090 to be increased to a 5-hour course. Last year a committee of five recent teachers of Math 2090 developed a list of topics to be covered in Math 2090, which we reproduce below. Fourier series are not on that list. We are not aware of any other university offering a 4-hour course that purports to cover all the topics that our Math 2090 currently purports to cover (though we have not checked too many other universities). Furthermore, Math 2090 is supposed to be a 4-hour equivalent to the (3 + 3 = 6)-hour combination of Math 2065 (Elementary Differential Equations) and Math 2085 (Linear Algebra); and neither Math 2065 nor Math 2085 mention Fourier series. If we don’t have time for Fourier in either Math 2065 or 2085, then why should we try to cover Fourier in a 4-hour equivalent course?

Text currently being used in Math 2090: Stephen W. Goode and Scott A. Annin, Differential Equations and Linear Algebra, Third Edition. Detailed list of topics and sections from this textbook that the committee recommends covering in Math 2090:

First-Order Differential Equations
1.2 Basic Ideas and terminology
1.4 Separable Differential Equations
1.6 First Order Linear Differential Equations
1.9 Exact Differential Equations

Matrices and Systems of Linear Equations
2.1 Matrices: Definitions and Notations

2.2 Matrix Algebra
2.4 Elementary Row Operations and Row-Echelon Matrices
2.5 Gaussian Elimination
2.6 Inverse of a Square Matrix

Determinants
3.1 The definition of the Determinant
3.2 Properties of the Determinant
3.3 Cofactor Expansions

Vector Spaces
4.2 Definition of a Vector Space
4.3 Subspaces
4.4 Spanning Sets
4.5 Linear Dependence and Linear Dependence
4.6 Bases and Dimension

Linear Transformations
5.1 Definition of a Linear Transformation
5.3 The Kernel and Range of a Linear Transformation
5.6 The Eigenvalue/Eigenvector Problem
5.7 General Results for Eigenvalues and Eigenvectors

Linear Differential Equations of Order n
6.1 General Theory for Linear Differential Equations
6.2 Constant-Coefficient Homogeneous Linear Differential Equations
6.3 The Method of Undetermined Coefficients. Annihilators
6.7 The Variation of Parameters

Systems of Differential Equations
7.1 First-Order Linear Systems
7.2 Vector Formulation
7.3 General Results for First-Order Linear Differential Systems
7.4 Vector Differential Equations: Non-defective Coefficient Matrix
7.6 Variation of Parameters for Linear Systems

The Laplace Transform and Some Elementary Applications
8.1 Definition of Laplace Transform
8.2 Existence of the Laplace Transform and Inverse Transform
8.4 The Transform of Derivatives and Solution of Initial-Value Problems
8.5 The First Shifting Theorem
8.6 The Unit Step Function
8.7 The Second Shifting Theorem

Optional topics that could be taught at the discretion of the instructor:
1.8 Change of Variables, Homogeneous Equations, Bernoulli's Equation
1.11 Some Higher-Order Differential Equations
5.8 Diagonalization
5.9 An introduction to the Matrix Exponential Function
6.9 Reduction of Order

Courses, Curricula, Colleges, Offices, Concentrations, and Minors that mention Math 2090

A. College of Engineering
A.1. Curriculum in Chemical Engineering (Department of Chemical Engineering).
A.2. Curriculum in Computer Science (Division of Computer Science & Engineering).
A.3. Curriculum in Computer Engineering (Division of Electrical & Computer Engineering).
A.4. Curriculum in Electrical Engineering (Division of Electrical & Computer Engineering).
A.5. Curriculum in Industrial Engineering (Dept. of Mechanical & Industrial Engineering).
A.6. Curriculum in Mechanical Engineering (Dept. of Mechanical & Industrial Engineering).
A.7. CHE 2176, 3101, 3102.
A.8. CE 4450.
A.9. CSC 4512.
A.10. EE 2120, 2130, 3140, 4730, 4745.
A.11. IE 3520.
A.12. ME 3143, 3834, 4143, 4163, 4183, 4433, 4843.

B. College of Science
B.1. Concentration in Chemical Physics, Curriculum in Chemistry (Department of Chemistry).
B.2. Concentration in Geophysics, Curriculum in Geology (Department of Geology & Geophysics).
B.3. Concentration in Computational Mathematics, Curriculum in Math (Department of Math).
B.4. Minor in Mathematics (Department of Mathematics).
B.5. Curriculum in Physics (Department of Physics & Astronomy).
B.6. CHEM 3491.
B.7. GEOL 7065.
B.8. MATH 2065, 2070, 2085, 2086, 3903, 4038, 4064, 4066, 4325, 4340, 4345, 4470.
B.9. NS 4411.
B.10. PHYS 2231, 2411, 4112, 4125, 4135, 4141.

Approvals of affected units

Date: Sun, 7 Oct 2012 21:25 -0500
From: "Jack E. Helms, Jr." <helms@me.lsu.edu>
To:   Charles N. Delzell <delzell@math.lsu.edu>
Subj: Re: Requesting approval 2 drop mention of Math 2070 & Fourier series from Math 2090.

Dr. Delzell,

ME is aware of the proposed changes to MATH 2090 and has no objections.  We support the changes.

Jack Helms

Jack E. Helms, Ph.D., P.E.
Professional-in-Residence & Undergraduate Coordinator & ABET Coordinator
Mechanical Engineering Department
2210 Patrick F. Taylor Hall
Louisiana State University
Baton Rouge, LA 70803
Phone: 225-578-6299
Fax: 225-578-5924

Date: Mon, 8 Oct 2012 11:59 +0000
From: Carol Wicks <cwicks@lsu.edu>
To:   Charles N. Delzell <delzell@math.lsu.edu>
Subj: RE: Requesting approval 2 drop mention of Math 2070 & Fourier series from Math 2090.

Charles,

The Department of Geology and Geophysics confirms that the change is acceptable.

Carol Wicks

225-578-2692 (office)
225-223-2846 (cell)
Chair and Frank W. and Patricia Harrison Family Professor
Department of Geology and Geophysics
E235 Howe-Russell-Kniffen Geoscience Complex
College of Science
Louisiana State University
Baton Rouge LA 70803

Date: Mon, 8 Oct 2012 13:31 +0000
From: Linda Allen <lallen3@lsu.edu>
To:   Charles N. Delzell <delzell@math.lsu.edu>
Subj: RE: Requesting approval 2 drop mention of Math 2070 & Fourier series from Math 2090.

The Chemistry Department approves the changes you have outlined in the course description/course coverage of MATH 2090.

Sincerely,
Linda R. Allen, PhD
Department of Chemistry
College of Science
LSU

Date: Mon, 8 Oct 2012 10:49 -0500
From: Coretta Douglas <douglas@csc.lsu.edu>
To:   Charles N. Delzell <delzell@math.lsu.edu>
Cc:   "Shah, Rahul" <rahul@csc.lsu.edu>
Subj: Re: Requesting approval 2 drop mention of Math 2070 & Fourier series from Math 2090.

Dr. Delzell,

The Division of Computer Science and Engineering has no objections to the 2 changes proposed for MATH 2090.

Regards,
Coretta

Coretta Douglas, Ph.D. Computer Science