# Michaela Kubacki

## Assistant Professor of Mathematics

mkubacki@middlebury.edu

work(802) 443-5293

WF 10am-11am, MF 2:45pm-4pm

on leave academic year

**Degrees, Specializations & Interests:**

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

(Numerical Analysis, Computational Fluid Dynamics)

## Publications

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## Courses

Courses offered in the past four years.

▲ *indicates offered in the current term*

▹ *indicates offered in the upcoming term[s]*

##### MATH 0121 - Calculus I

**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. 4 hrs. lect./disc. **DED**

Spring 2018

##### MATH 0122 - Calculus II

**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 by waiver) 4 hrs. lect./disc. **DED**

Fall 2015, Fall 2017, Fall 2018

##### MATH 0223 - Multivariable Calculus

**Multivariable Calculus**

The calculus of functions of more than one variable. Introductory vector analysis, analytic geometry of three dimensions, partial differentiation, multiple integration, line integrals, elementary vector field theory, and applications. (MATH 0122 and MATH 0200 or by waiver) 3 hrs. lect./disc. **DED**

Spring 2016

##### MATH 0225 - Topics in Linear Alg & Diff Eq

**Topics in Linear Algebra and Differential Equations**

Topics may include diagonalization of matrices, quadratic forms, inner product spaces, canonical forms, the spectral theorem, positive matrices, the Cayley-Hamilton theorem, ordinary differential equations of arbitrary order, systems of first-order differential equations, power series, and eigenvalue methods of solution, applications. (MATH 0200 or by waiver) 3 hrs. lect./disc. **DED**

Fall 2015, Spring 2019

##### MATH 0228 - Intro to Numerical Analysis

**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 0200) **DED**

Spring 2016, Fall 2017

##### MATH 0328 - Numerical Linear Algebra

**Numerical Linear Algebra**

Numerical linear algebra is the study of algorithms for solving problems such as finding solutions of linear systems and eigenvalues of matrices. Many real-life applications simplify to these scenarios and often involve millions of variables. We will analyze shortcomings of direct methods such as Gaussian Elimination, which theoretically produces the true solution but fails in practical applications. In contrast, iterative methods are often more practical and precise, and continually evolve with changing technology and our understanding of mathematics. Our study will include the First Order Richardson, Steepest Descent, and Conjugate Gradient algorithms for linear systems, and the power method for eigenvalue problems. (MATH 0200) 3 hrs. lect. **CW DED**

Spring 2017, Spring 2019

##### MATH 0500 - Advanced Study ▲

**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.

Fall 2015, Winter 2016, Spring 2016, Fall 2016, Winter 2017, Spring 2017, Fall 2017, Winter 2018, Spring 2018, Fall 2018, Winter 2019, Spring 2019, Fall 2019

##### MATH 0728 - Math Fluid Dynamics Seminar

**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) **DED**

Spring 2018