# Courses Taught

Mathematics instruction is more than grilling students to know facts and procedures. It is a means through which we enhance student thinking by using mathematical concepts to create new neural pathways of understanding. For it is through human critical thinking and understanding, coupled with the speed of computing, that solutions will be created for the problems facing our human existence.

MA 550

## Nonlinear Partial Differential Equations

In this course we discuss analysis of linear and nonlinear PDE's. Necessary functional analysis such as Lp spaces, Hilbert spaces, linear operator theory, dual spaces and weak convergence, Sobolev spaces are included. Methods studied include classical maximum principles, Galerkin truncation methods for global existence of weak solutions, and finite time blow up.

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Semesters Taught: Spring 2024.

MA 522

## Classical Real Analysis

This course is an introduction to Lebesgue’s theory of measures and its application to defining a general theory of integration with respect to measures. Topics covered include: Outer Measure, Measurable Spaces and Functions, Measures and their Properties, Lebesgue Measure, Egorov's Theorem, Luzin's Theorem, Monotone Convergence Theorem, Dominated Convergence Theorem, Vitali Covering Lemma, Lebesgue Differentiation Theorem, Tonelli's Theorem, Fubini's Theorem.

Semesters Taught: Fall 2023.

MA 521

## Classical Complex Analysis

In this course we study the beautiful theory of complex analysis. Topics covered include: Topology of the complex plane, Analytic functions, Mobius transformations, Power series representation of analytic functions, Cauchy's Theorem and integral formula, Homotopic version of Cauchy's Theorem and Integral formula, Open Mapping Theorem, Goursat's Theorem, Singularities, Residues, Argument Principle, Maximum principle, Harmonic Functions.

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Semesters Taught: Spring 2022

MA 571

## Numerical Solution of Differential Equations

In this course we study numerical methods for solving ordinary and partial differential equations. We discuss the theory motivating the development and analysis of these methods as well as implement them in MATLAB to solve simple differential equations. Topics covered include: Euler's method and variants, Multistep methods, Runge-Kutta methods, Stiffness, Stability and Functional Iteration, Finite Difference Methods for Elliptic, Parabolic and Hyperbolic PDEs,.

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Semesters Taught: Spring 2021

## MA 362/562

### Complex Analysis with Applications

This course covers the algebra of complex numbers, continuity and differentiability of complex functions, inifinite series representation of analytic functions and complex integration. Applications to fluid flow are discussed. The materials is designed as an introduction to complex analysis for first year graduate students or upper level undergraduate students.

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Semester Taught: Spring 2023

## MA 377

### Numerical Methods

This course is an introduction to Numerical Methods. Topics to be studied include Error analysis, Approximating roots of nonlinear function, Solving linear and nonlinear systems of equations, Interpolation and polynomial approximation of functions, Numerical differentiation and integration, Numerical solutions to differential equations.

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Semseters Taught: Fall 2020, 2021, 2023

## MA 363

### Mathematical modeling

This course introduces techniques to model various physical and biological processes. Techniques to be discussed include Difference and Differential Equations, Linear and nonlinear Optimization, Markov Chains, Birth and Death Processes.

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Semseters Taught: Spring 2021, 2022, 2023

## MA 330

### Advanced Engineering Mathematics

In this course we study mathematical methods that are crucial for solving engineering problems. Theoretical discussions are motivated by relevant engineering challenges. We begin with a discussion on quality control and the statistical methods that are pertinent to ensuring that a production meets quality standards. We then move on to discuss mathematical models of forced oscillations and resonance which will motivate the study of techniques to solve ordinary differential equations and linear algebra. We cap the course with models of vibrating systems and temperature diffusion using partial differential equations and some solution techniques using Fourier series and Fourier analysis.

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Semester Taught: Fall 2022

## MA 232

### Ordinary Differential Equations

In this course students are introduced to methods for solving and describing ODEs. Applications considered include chemical reactions, growth of biological populations, the motion of a spring-mass systems and the flow of current in an electrical circuit. We explore techniques to solve ODEs exactly, qualitatively, and numerically (using MATLAB or an equivalent high level programming language). We focus on techniques for solving first order equations, linear equations of higher order as well as linear and nonlinear systems. .

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Semester Taught: Fall 2021