MATH 436 Partial Differential Equations
Winter 2024
Course description: Well-posedness and representation formulae for solutions to the transport equation, Laplace equation, heat equation, and wave equation. Fundamental solutions. Properties of harmonic functions. Green's function. Mean value formulae. Energy methods. Maximum principles. Method of characteristics for quasilinear equations. Burgers’ equation. Shocks formation and entropy condition. Applications to fluid dynamics, elasticity problems and/or optimization problems.
MATH/MTHE 433 - MATH 833 Continuum Mechanics with Applications
Winter 2022, Fall 2022, Fall 2023
Course description: Continuum mechanics lays the foundations for the study of the mechanical behavior of solids and fluids. After a review of vector and tensor analysis, the kinematics of continua are introduced. Emphasis is given to the concepts of stress, strain and deformation. The fundamental laws of conservation of mass, balances of (linear and angular) momentum and energy are presented together with the constitutive models. Applications of these models are given in the theory of linearized elasticity and fluid dynamics.
onQ
MTHE 237 Differential Equations for Engineering Science
Fall 2019, Fall 2021, Fall 2022, Fall 2023
Course description: Topics include models for dynamical systems, classification of differential equations, methods for solving differential equations, systems of equations and connections with Linear Algebra, stability of dynamical systems and Lyapunov’s method, the Laplace Transform method, and numerical and computer methods.
onQ
MTHE 493 Engineering Mathematics Project
Academic Year 2021-22, 2022-23
Course description: This is the capstone design course for Mathematics and Engineering. Students must work in groups, with a typical group size being between two and four members. Projects are selected early in the year from a list put forward by Mathematics and Engineering faculty members who will also supervise the projects. There is a heavy emphasis on engineering design and professional practice. All projects must be open-ended and design oriented, and students are expected to undertake and demonstrate, in presentations and written work, a process by which the design facets of the project are approached. Projects must involve social, environmental, and economic factors, and students are expected to address these factors comprehensively in presentations and written work. Students are assessed individually and as a group on their professional conduct during the course of the project.
onQ
MATH/MTHE 439 - MATH 836 Lagrangian Mechanics, Dynamics, and Control
Winter 2021
Course description: Geometric modelling, including configuration space, tangent bundle, kinetic energy, inertia, and force. Euler-Lagrange equations using affine connections. Equilibria and stability.
MATH/MTHE 437 - MATH 837 Topics in Applied Mathematics: Continuum Mechanics and Applications
Winter 2020
Course description: Continuum mechanics lays the foundations for the study of the mechanical behavior of solids and fluids. After a review of vector and tensor analysis, the kinematics of continua are introduced. Emphasis is given to the concepts of stress, strain and deformation. The fundamental laws of conservation of mass, balances of (linear and angular) momentum and energy are presented together with the constitutive models. Applications of these models are given in the theory of linearized elasticity and fluid dynamics.
Vanderbilt University
MATH 2420 Methods of Ordinary Differential Equations
Spring 2017
Course description: Separable equations, first order linear differential equations, exact equations, applications. Higher order linear differential equations, method of undetermined coefficients, method of variation of parameters, applications. Laplace transform method and its applications. Power series and Frobenius method.
MATH 2610 - MATH 5610 Ordinary Differential Equations Fall 2017, Fall 2018
Course description: First- and second-order differential equations, applications. Matrix methods for linear systems. Stability theory of autonomous systems. Existence and uniqueness theory. Intended for mathematics and advanced science majors.
MATH 3120 - MATH 5120 Introduction to Partial Differential Equations Spring 2018
Course description: Initial- and boundary-value problems, separation of variables, Fourier series and integrals, representation of solutions, and explicit solutions of problems involving the heat equation, the wave equation, and Laplace's equation.
MATH 3100 - MATH 5100 Introduction to Analysis Spring 2019
Course description: Properties of real numbers, compactness and completeness. Limits, sequences and series, uniform convergence, and power series. Basic properties of functions on the real line, and the elementary theory of differentiation and integration. Emphasis on methods of proof used in advanced mathematics courses.
