Office
Warner 206
Tel
(802) 443-5293
Email
mkubacki@middlebury.edu
Office Hours
Mondays and Wednesdays 3:00pm-4:30pm, Thursdays 9am-10:30am. Alternate appointments available by request.

## Courses Taught

Course Description

Calculus I
Introductory analytic geometry and calculus. Topics include limits, continuity, differential calculus of algebraic and trigonometric functions with applications to curve sketching, optimization problems and related rates, the indefinite and definite integral, area under a curve, and the fundamental theorem of calculus. Inverse functions and the logarithmic and exponential functions are also introduced along with applications to exponential growth and decay. (by waiver) 4 hrs. lect./disc.

Terms Taught

Fall 2021

Requirements

DED

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Course Description

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. 4 hrs. lect/disc.

Terms Taught

Fall 2020, Spring 2021

Requirements

DED

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Course Description

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) 3 hrs. lect./disc.

Terms Taught

Fall 2022, Spring 2023, Spring 2024, Fall 2024

Requirements

DED

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Course Description

MATH 0226, 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 and MATH 0200 or by waiver) (formerly MATH 0225) 3 hrs. lect./disc.

Terms Taught

Spring 2023, Fall 2023, Fall 2024

Requirements

DED

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Course Description

Introduction to Numerical Analysis
We will study the development, analysis, and implementation of numerical methods for approximating solutions to mathematical problems. We will begin with applications of Taylor polynomials, computer representation of numbers, and types of errors. Other topics will include polynomial and spline interpolation, numerical integration and differentiation, rootfinding, and numerical solutions of differential equations. Accuracy will be quantified by the concept of numerical error. Additionally, we will study the stability, efficiency, and implementation of algorithms. We will utilize the software MATLAB throughout to demonstrate concepts, as well as to complete assignments and projects. (MATH 0122)

Terms Taught

Fall 2021

Requirements

DED

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Course Description

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 and either of MATH 0225 or MATH 0226) 3 hr lect.

Terms Taught

Fall 2023

Requirements

DED

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Course Description

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)

Terms Taught

Fall 2020, Fall 2022

Requirements

CW, DED

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Course Description

Advanced Study
Individual study for qualified students in more advanced topics in algebra, number theory, real or complex analysis, topology. Particularly suited for those who enter with advanced standing. (Approval required) 3 hrs. lect./disc.

Terms Taught

Fall 2020, Spring 2021, Fall 2021, Spring 2022, Fall 2022, Spring 2023, Fall 2023, Spring 2024, Fall 2024, Spring 2025

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Course Description

Mathematical Methods in Fluid Dynamics
This course is an introduction to the mathematical models and methods used in modern fluid dynamics. Students will derive and analyze fundamental equations of fluid flow, explore their applications, as well as examine theoretical and practical solution techniques. Equations of study will include the Poisson, diffusion, and Navier-Stokes equations. We will also introduce basic methods of computational fluid dynamics. Working independently and in small groups, students will gain experience reading advanced sources and communicating their insights in expository writing and oral presentations. Fulfills the capstone senior work requirement for the mathematics major. 3 hrs. Lect./Lab (Approval Only)

Terms Taught

Spring 2021, Spring 2024

Requirements

DED

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## Areas of Interest

Numerical Analysis, Computational Fluid Dynamics

## Academic Degrees

B.A., Washington & Jefferson College; M.A., University of Pittsburgh; Ph.D., University of Pittsburgh

## Publications

Coffer, B.; Kubacki, M.; Wen, Y.; Zhang, T.; Barajas, C.; Gobbert, M. Brice Machine Learning with Feature Importance Analysis for Tornado Prediction from Environmental Sounding Data. PAMM, 20, 1, (2021).

Coffer, B.; Kubacki, M.; Wen, Y., Zhang, T.;  Barajas, C.; and Gobbert, M. Using machine learning techniques for supercell tornado prediction with environmental sounding data, Tech. Rep. HPCF–2020–18, UMBC High Performance Computing Facility, University of Maryland, Baltimore County, 2020. http://hpcf.umbc.edu/publications/.

Ervin, V.; Kubacki, M.; Layton, W.; Moraiti, M.; Si, Z.; Trenchea, C. Partitioned penalty methods for the transport equation in the evolutionary Stokes-Darcy-transport problem. Numer. Methods Partial Differential Eq. 2018; 35: 349-374. https://doi.org/10.1002/num.22303.

Kubacki, M.; Tran, H. Non-Iterative Partitioned Methods for Uncoupling Evolutionary Groundwater-Surface Water Flows. Fluids 2017, 2(3). http://www.mdpi.com/journal/fluids/special_issues/turbulence.

Ervin, V.J.; Kubacki, M.; Layton, W.; Moraiti, M.; Si, Z.; Trenchea, C. On Limiting Behavior of Contaminant Transport Models in Coupled Surface and Groundwater Flows. Axioms 2015, 4, 518-529.

Kubacki, M. and Moraiti, M. Analysis of a Second-Order, Unconditionally Stable, Partitioned Method for the Evolutionary Stokes-Darcy Model. Int. J. Numer. Anal. Mod., 12 (2015), pp. 704-730.

Jiang, N.; Kubacki, M.; Layton, W.; Moraiti, M.; Tran, H. A Crank-Nicolson Leapfrog stabilization: Unconditional stability and two applications, Journal of Computational and Applied Mathematics, Volume 281, June 2015, Pages 263-276, ISSN 0377-0427.

Kubacki, M. Higher-Order, Strongly Stable Methods for Uncoupling Groundwater-Surface Water Flow (Doctoral dissertation). University of Pittsburgh D-Scholarship Database, http://d-scholarship.pitt.edu/21894/ (2014).

Kubacki, M. Uncoupling evolutionary groundwater-surface water flows using the Crank-Nicolson Leapfrog method. Numer. Methods Partial Differential Eq., 29:1192-1216, 2013.