The course will cover the following topics: Introduction to and classification of second-order partial differential equations, wave equation, heat equation and Laplace equation, D'Alembert solution to the wave equation, solution of the heat equation, maximum principle, energy methods, separation of variables, Fourier series, Fourier transform methods and operator eigenvalue problems. Time-permitting, we will briefly examine numerical methods for partial differential equations, as well as some select examples of nonlinear partial differential equations.

Topology of the euclidean space and functions of several variables (implicit function theorem), introduction to Fourier analysis, metric spaces and normed spaces. Applications to differential equations, calculus of variations, and others.

This course is an introduction to mathematical analysis. A rigorous treatment of the topics covered in calculus will be presented with a particular emphasis on proofs. Topics include: properties of real numbers, sequences and series, continuity, Riemann integral, differentiability, sequences of functions and uniform convergence.

The course introduces and uses Fourier series and Fourier transform as a tool to understand varies important problems in applied mathematics: linear ODE & PDE, time series, signal processing, etc. We'll treat convergence issues in a non-rigorous way, discussing the different types of convergence without technical proofs. Topics: complex numbers, sin & cosine series, orthogonality, Gibbs phenomenon, FFT, applications, including say linear PDE, signal processing, time series, etc; maybe ending with (continuous) Fourier transform.

The Commonwealth Honors College thesis or project is intended to provide students with the opportunity to work closely with faculty members to define and carry out in-depth research or creative endeavors. It provides excellent preparation for students who intend to continue their education through graduate study or begin their professional careers. The student works closely with their 499Y Honors Research sponsor to pursue research on a topic or question of special interest to them in preparation for writing a 499T Honors Thesis or completing a 499P Honors Project.

Honors Thesis expectations are high. The intended end-product is a traditional research manuscript with accompanying artifact(s), all theses: - are 6 credits or more of sustained research on a single topic, typically conducted over two semesters. - begin with creative inquiry and systematic research. - include documentation of substantive scholarly endeavor. - culminate in an oral defense or other form of public presentation.

Honors Thesis expectations are high. The intended end-product is a traditional research manuscript with accompanying artifact(s), all theses: - are 6 credits or more of sustained research on a single topic, typically conducted over two semesters. - begin with creative inquiry and systematic research. - include documentation of substantive scholarly endeavor. - culminate in an oral defense or other form of public presentation.

Honors Thesis expectations are high. The intended end-product is a traditional research manuscript with accompanying artifact(s), all theses: - are 6 credits or more of sustained research on a single topic, typically conducted over two semesters. - begin with creative inquiry and systematic research. - include documentation of substantive scholarly endeavor. - culminate in an oral defense or other form of public presentation.

Honors Thesis expectations are high. The intended end-product is a traditional research manuscript with accompanying artifact(s), all theses: - are 6 credits or more of sustained research on a single topic, typically conducted over two semesters. - begin with creative inquiry and systematic research. - include documentation of substantive scholarly endeavor. - culminate in an oral defense or other form of public presentation.

Honors Thesis expectations are high. The intended end-product is a traditional research manuscript with accompanying artifact(s), all theses: - are 6 credits or more of sustained research on a single topic, typically conducted over two semesters. - begin with creative inquiry and systematic research. - include documentation of substantive scholarly endeavor. - culminate in an oral defense or other form of public presentation.