Introduces the methods, theory, and applications of differential equations. Includes first-order, second and higher-order linear equations, series solutions, linear systems of first-order differential equations, and the associated matrix theory. May include numerical methods, non-linear systems, boundary value problems, and additional applications. Prerequisite: MATH 1320 or its equivalent.
Course Descriptions
Undergraduate Course Descriptions
Ordinary Differential Equations (4.00)
MATH 3255
Usually offered in the spring, this course covers the same material as MATH 3250 with some additional topics, including an introduction to Sturm-Liouville theory, Fourier series and boundary value problems, and their connection with partial differential equations. Physics majors should enroll in MATH 3255, although no knowledge of physics is assumed. Prerequisite: MATH 1320 or its equivalent.
Basic Real Analysis (3.00)
MATH 3310
A rigorous development of the properties of the real numbers and the ideas of calculus including theorems on limits/ continuity/differentiability/convergence of infinite series/the construction of the Riemann integral. The focus of students’ work will be on getting experience in constructing proofs and developing examples. Prerequisite: MATH 1320.
Advanced Calculus and Linear Algebra II (4.00)
MATH 3315
This course is a continuation of MATH 2315. Covers topics from linear algebra/differential equations/real analysis. Success in this course and MATH 2315 (grades of B- or higher) exempts the student from the math major requirement of taking MATH 3351 and MATH 3250. Students are encouraged to take more advanced courses in these areas. Prerequisite: MATH 2315.
Complex Variables with Applications (3.00)
MATH 3340
Covers functions of a complex variable that are complex differentiable and the unusual and useful properties of such functions. Some topics: Cauchy’s integral formula/power series/the residue theorem/Rouché’s theorem. Applications include doing real integrals using complex methods and applications to fluid flow in two dimensions. Prerequisite: MATH 2310.
Applied Linear Algebra (3.00)
MATH 3350
Topics include systems of linear equations, matrix operations, vector spaces, determinants, eigenvalues and eigenvectors, matrix factorizations, inner products and orthogonality, and linear transformations. Emphasis will be on applications, using computer software. The target audience is non-math majors from disciplines that apply tools from linear algebra. Credit is not given for both MATH 3350 and 3351.
Prerequisites: MATH 1310.
Elementary Linear Algebra (3.00)
MATH 3351
Includes matrices, elementary row operations, inverses, vector spaces and bases, inner products and Gram-Schmidt orthogonalization, orthogonal matrices, linear transformations and change of basis, eigenvalues, eigenvectors, and symmetric matrices. Prerequisite: MATH 1320.
Survey of Algebra (3.00)
MATH 3354
Surveys major topics of modern algebra: groups, rings, and fields. Presents applications to areas such as geometry and number theory; explores rational, real, and complex number systems, and the algebra of polynomials. Prerequisite: MATH 1320 or equivalent.
New Course in Mathematics (1.00 - 4.00)
MATH 3559
This course provides the opportunity to offer a new topic in the subject of mathematics.
Discrete Mathematics (3.00)
MATH 4040
Includes combinatorial principles, the binomial and multinomial theorems, partitions, discrete probability, algebraic structures, trees, graphs, symmetry groups, Polya's enumeration formula, linear recursions, generating functions and introduction to cryptography, time permitting. Prerequisite: MATH 3354 or instructor permission.
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