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)

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.

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.

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.

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

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.

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.

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.

Michaela Kubacki

Reviews and ratings for Michaela Kubacki at Middlebury College.Michaela Kubacki teaches Calculus II, Numerical Linear Algebra, Linear Algebra and more.  Explore top rated instructors and find the best for you.Is Michaela Kubacki good ? Find out on MiddCourses.

NLA was very hard because it was difficult to find matrix methods interesting. It was very theoretical, and most of the stuff went in one ear and straight out the other. This class was definitely worse in the past, but hopefully it continues to become more applications based in the future so the knowledge can at least seem relevant and important. The projects and matlab practice was fun.

It was a good class that was quick-paced and had decently fair grading. Homework tended to take a couple of hours a night and was fairly rigorous, but definitely prepared you for the exams. Exams made you think, but were fair.

This was a very interesting course. It covered a lot of topics but they were all useful. The biggest issue with this course is the same one a s with many numerical classes - the homework at times felt like tedious work with ugly numbers calculation. 