# Tony Harkin

## Associate Professor

School of Mathematical Sciences

College of Science

585-943-7889

Office Hours

Monday 12pm Wednesday 12pm Friday 12pm and by appointment

Office Location

Office Mailing Address

Gosnell 1344

# Tony Harkin

## Associate Professor

School of Mathematical Sciences

College of Science

## Education

BS, State University College at Brockport; MS, Massachusetts Institute of Technology; Ph.D., Boston University

585-943-7889

Areas of Expertise

Applied and Computational Mathematics

Fluid Mechanics

PDE

Dynamical Systems

Mathematical Modeling

## Select Scholarship

Journal Paper

Harkin, Anthony, T.J. Kaper, and A. Nadim. "Energy Transfer Between the Shape and Volume Modes of a Nonspherical Gas Bubble."

*Physics of Fluids*25. 62101 (2013): 1-11. Print.Journal Editor

Harkin, Anthony, ed.

*International Journal of Applied Nonlinear Science.*Genèva Switzerland: Inderscience Publishers, 2013. Print.Published Article

Hollenbeck, Dawn, Michael K Martini, Andreas Langner,Anthony Harkin, David Ross, and George Thurston. “Model for evaluating patternedcharge-regulation contributions toelectrostatic interactions betweenlow-dielectric spheres.”

*Physical Review E*,82.3 (2010): n.p. Web. " *## Currently Teaching

MATH-181

Project-Based Calculus I

4 Credits

This is the first in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers functions, limits, continuity, the derivative, rules of differentiation, applications of the derivative, Riemann sums, definite integrals, and indefinite integrals.

MATH-182

Project-Based Calculus II

4 Credits

This is the second in a two-course sequence intended for students majoring in mathematics, science, or engineering. It emphasizes the understanding of concepts, and using them to solve physical problems. The course covers techniques of integration including integration by parts, partial fractions, improper integrals, applications of integration, representing functions by infinite series, convergence and divergence of series, parametric curves, and polar coordinates.

MATH-231

Differential Equations

3 Credits

This course is an introduction to the study of ordinary differential equations and their applications. Topics include solutions to first order equations and linear second order equations, method of undetermined coefficients, variation of parameters, linear independence and the Wronskian, vibrating systems, and Laplace transforms.

MATH-241

Linear Algebra

3 Credits

This course is an introduction to the basic concepts of linear algebra, and techniques of matrix manipulation. Topics include linear transformations, Gaussian elimination, matrix arithmetic, determinants, vector spaces, linear independence, basis, null space, row space, and column space of a matrix, eigenvalues, eigenvectors, change of basis, similarity and diagonalization. Various applications are studied throughout the course.

MATH-251

Probability and Statistics

3 Credits

This course introduces sample spaces and events, axioms of probability, counting techniques, conditional probability and independence, distributions of discrete and continuous random variables, joint distributions (discrete and continuous), the central limit theorem, descriptive statistics, interval estimation, and applications of probability and statistics to real-world problems. A statistical package such as Minitab or R is used for data analysis and statistical applications.

MATH-341

Advanced Linear Algebra

3 Credits

This is a second course in linear algebra that provides an in-depth study of fundamental concepts of the subject. It focuses largely on the effect that a choice of basis has on our understanding of and ability to solve problems with linear operators. Topics include linear transformations, similarity, inner products and orthogonality, QR factorization, singular value decomposition, and the Spectral Theorem. The course includes both computational techniques and the further development of mathematical reasoning skills.

MATH-381

Complex Variables

3 Credits

This course covers the algebra of complex numbers, analytic functions, Cauchy-Riemann equations, complex integration, Cauchy's integral theorem and integral formulas, Taylor and Laurent series, residues, and the calculation of real-valued integrals by complex-variable methods.

MATH-495

Undergraduate Research in Mathematical Sciences

1 - 3 Credits

This course is a faculty-directed project that could be considered original in nature. The level of work is appropriate for students in their final two years of undergraduate study.

MATH-498

Independent Study in Mathematical Sciences

1 - 3 Credits

This course is a faculty-guided investigation into appropriate topics that are not part of the curriculum.

MATH-741

Partial Differential Equations I

3 Credits

This course uses methods of applied mathematics in the solution of problems in physics and engineering. Models such as heat flow and vibrating strings will be formulated from physical principles. Characteristics methods, maximum principles, Green's functions, D'Alembert formulas, weak solutions and distributions will be studied.

MATH-742

Partial Differential Equations II

3 Credits

This is a continuation of Partial Differential Equations I and deals with advanced methods for solving partial differential equations arising in physics and engineering problems. Topics to be covered include second order equations, Cauchy-Kovalevskaya theorem, the method of descent, spherical means, Duhamels principle, and Greens function in higher dimensions.

MATH-790

Research & Thesis

0 - 9 Credits

Masters-level research by the candidate on an appropriate topic as arranged between the candidate and the research advisor.