Michaela Kubacki

Calculus II
A continuation of MATH 0121, may be elected by first-year students who have had an introduction to analytic geometry and calculus in secondary school. Topics include a brief review of natural logarithm and exponential functions, calculus of the elementary transcendental functions, techniques of integration, improper integrals, applications of integrals including problems of finding volumes, infinite series and Taylor's theorem, polar coordinates, ordinary differential equations. MATH 0121 or equivalent, or by placement) 4 hrs. lect/disc.

Linear Algebra
Matrices and systems of linear equations, the Euclidean space of three dimensions and other real vector spaces, independence and dimensions, scalar products and orthogonality, linear transformations and matrix representations, eigenvalues and similarity, determinants, the inverse of a matrix and Cramer's rule. (MATH 0121 or equivalent, or by placement) 3 hrs. lect./disc.

Differential Equations
This course provides an introduction into ordinary differential equations (ODEs) with an emphasis on linear and nonlinear systems using analytical, qualitative, and numerical techniques. Topics will include separation of variables, integrating factors, eigenvalue method, linearization, bifurcation theory, and numerous applications. In this course, we will introduce MATLAB programming skills and develop them through the semester. (MATH 0122 or equivalent, and MATH 0200.) 3 hrs. lect./disc.

Partial Differential Equations
An introduction to partial differential equations (PDEs) with an emphasis on first and second-order linear equations. Using analytical, qualitative, and numerical techniques, we will study the Laplace, heat, and wave equations, as well as their applications. MATLAB will be used where applicable. (MATH 0223 or MATH 0224, and MATH 0226) 3 hr lect.

Numerical Linear Algebra
Numerical Linear Algebra involves the development, analysis, and implementation of computational algorithms for solving linear algebra problems. These problems frequently arise in applications such as physical simulations, signal processing, neural network design, and many more. This course focuses on numerical methods for linear systems and eigenvalue problems. We will study both direct and iterative approaches, including Gaussian Elimination, LU Factorization, Jacobi and Gauss-Seidel Iterations, Steepest Descent, Conjugate Gradient, the Power Method, and more. Additional key topics include matrix decompositions, matrix/vector norms, computational efficiency, and stability. MATLAB programming skills will be introduced and developed throughout the semester. (MATH 0122 and MATH 0200)

Advanced Numerical Analysis
In this course, students will complete a senior project building on their prior knowledge and experience in numerical methods and analysis. Each iteration of the course may highlight different areas and applications of numerical analysis, shaped by the instructor’s expertise and areas of interest. Students will develop their ability to critically analyze, synthesize, and engage in meaningful discussions about relevant scientific literature. Emphasis is placed on clear written and oral communication of mathematical ideas, culminating in a formal scientific paper and a public presentation. This course fulfills the capstone senior work requirement for both the applied and general mathematics tracks. (Approval Only) 3 hrs. Sem.