Vernerey, Divya E.

Research

research overview

Dr. Vernerey's research interests are mathematical modeling and solving systems of nonlinear reaction-diffusion equations. This work in applied mathematics utilizes her training in mathematical physics, differential equations, asymptotical and perturbation methods, and numerical solutions of partial differential equations. These areas have been the building blocks for her research in the mathematical modeling of frontal polymerization. This area of research opens the door to fascinating studies at the interface between mathematics, physics, chemistry, and biology. One such multi-disciplinary topic is combustion theory (exothermic polymerization waves are in many respects similar to combustion waves) and another involves the emerging field of tissue engineering and tissue growth. This later application typically deals with diffusion-reaction equations, which can, in some cases lead to the propagation of degradation fronts.

keywords

partial differential equations, traveling waves in nonlinear reaction-diffusion systems, frontal polymerization

Publications

selected publications

journal article
- Mathematical modeling of thiol-ene frontal polymerization. Chemical Engineering Science. 1261-1275. 2006
- Mathematical modeling of radially propagating polymerization waves with the gel effect. Applied Mathematics and Computation. 1036-1053. 2006
- Modeling isothermal free-radical frontal polymerization with gel effect using free volume theory, with and without inhibition. Journal of Mathematical Chemistry. 73-105. 2006

Teaching

courses taught

APPM 4120 - Introduction to Operations Research
Primary Instructor - Spring 2018 / Spring 2020 / Spring 2022
Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Same as APPM 5120 and MATH 4120 and MATH 5120.
APPM 4650 - Intermediate Numerical Analysis 1
Primary Instructor - Spring 2019 / Spring 2021 / Spring 2022
Focuses on numerical solution of nonlinear equations, interpolation, methods in numerical integration, numerical solution of linear systems, and matrix eigenvalue problems. Stresses significant computer applications and software. Department enforced prerequisite: knowledge of a programming language. Same as MATH 4650.
APPM 5120 - Introduction to Operations Research
Primary Instructor - Spring 2018 / Spring 2020 / Spring 2022
Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Recommended prerequisites: APPM 3310 OR MATH 2130 OR MATH 2135 or equivalent. Same as APPM 4120 and MATH 4120 and MATH 5120.
CSCI 2820 - Linear Algebra with Computer Science Applications
Primary Instructor - Fall 2023 / Fall 2024
Introduces the fundamentals of linear algebra in the context of computer science applications. Includes vector spaces, matrices, linear systems, and eigenvalues. Includes the basics of floating point computation and numerical linear algebra. Same as CSPB 2820.
CSCI 3104 - Algorithms
Primary Instructor - Spring 2024
Covers the fundamentals of algorithms and various algorithmic strategies, including time and space complexity, sorting algorithms, recurrence relations, divide and conquer algorithms, greedy algorithms, dynamic programming, linear programming, graph algorithms, problems in P and NP, and approximation algorithms. Same as CSPB 3104.

CSCI 3656 - Numerical Computation
Primary Instructor - Fall 2023 / Fall 2024
Covers development, computer implementation, and analysis of numerical methods for applied mathematical problems. Explores topics such as floating point arithmetic, numerical solution of linear systems of equations, root finding, numerical interpolation, differentiation, and integration.

MATH 1150 - Precalculus Mathematics
Primary Instructor - Spring 2018 / Summer 2018 / Fall 2018
Develops techniques and concepts prerequisite to calculus through the study of trigonometric, exponential, logarithmic, polynomial and other functions. For more information about the math placement referred to in the "Enrollment Requirements", please contact your academic advisor. Degree credit not granted for this course and APPM 1235 or MATH 1021.

MATH 1151 - Precalculus Supplemental Lab
Secondary Instructor - Spring 2018
Provides students concurrently enrolled in MATH 1150 with supplemental instruction.

MATH 1212 - Data and Models
Primary Instructor - Spring 2019 / Fall 2019 / Fall 2020 / Fall 2021
Engages students in statistical and algebraic problem solving through modeling data and real world questions taken from the social and life sciences. The course will emphasize these skills and the mathematical background needed for a university level statistics course. Credit not granted for this course and MATH 1011.

MATH 3430 - Ordinary Differential Equations
Primary Instructor - Summer 2018 / Fall 2018 / Summer 2019 / Fall 2019 / Spring 2020 / Summer 2020 / Fall 2020 / Summer 2021
Involves an elementary systematic introduction to first-order scalar differential equations, nth order linear differential equations, and n-dimensional linear systems of first-order differential equations. Additional topics are chosen from equations with regular singular points, Laplace transforms, phase plane techniques, basic existence and uniqueness and numerical solutions. Formerly MATH 4430.

MATH 3850 - Seminar in Guided Mathematics Instruction
Primary Instructor - Spring 2018 / Spring 2019
Provides learning assistants with an opportunity to analyze assessment data for formative purposes and develop instructional plans as a result of these analyses. These formative assessment analyses will build on the literature in the learning sciences. Students gain direct experiences interacting with the tools of the trade, especially with actual assessment data and models of instruction. May be repeated up to 3 total credit hours. Restricted to learning assistants in Math.

MATH 4120 - Introduction to Operations Research
Primary Instructor - Spring 2018 / Spring 2020 / Spring 2022
Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Same as APPM 5120 and APPM 4120 and MATH 5120.

MATH 4470 - Partial Differential Equations
Primary Instructor - Fall 2021
Studies initial, boundary, and eigenvalue problems for the wave, heat, and potential equations. Solution by separation of variables, Green's function, and variational methods. Same as MATH 5470.

MATH 4650 - Intermediate Numerical Analysis 1
Primary Instructor - Spring 2019 / Spring 2021 / Spring 2022
Focuses on numerical solution of nonlinear equations, interpolation, methods in numerical integration, numerical solution of linear systems, and matrix eigenvalue problems. Stresses significant computer applications and software. Department enforced prerequisite: knowledge of a programming language. Same as APPM 4650.

MATH 4820 - History of Mathematical Ideas
Primary Instructor - Spring 2021
Examines the evolution of a few mathematical concepts (e.g., number, geometric continuum, or proof), with an emphasis on the controversies surrounding these concepts. Begins with Ancient Greek mathematics and traces the development of mathematical concepts through the middle ages into the present. Recommended restriction: completion of upper division Written Communication requirement. Same as MATH 5820.

MATH 5120 - Introduction to Operations Research
Primary Instructor - Spring 2018 / Spring 2020 / Spring 2022
Studies linear and nonlinear programming, the simplex method, duality, sensitivity, transportation and network flow problems, some constrained and unconstrained optimization theory, and the Kuhn-Tucker conditions, as time permits. Recommended prerequisites: APPM 3310 OR MATH 2130 OR MATH 2135 or equivalent. Same as APPM 4120 and MATH 4120 and APPM 5120.

MATH 5470 - Partial Differential Equations
Primary Instructor - Fall 2021
Studies initial boundary and eigenvalue problems for the wave, heat and potential equations. Solution by separation of variables, Green's function, and variational methods. Department enforced prerequisite: MATH 3430 or MATH 5430. Instructor consent required for undergraduates. Same as MATH 4470.

MATH 5820 - History of Mathematical Ideas
Primary Instructor - Spring 2021
Examines the evolution of a few mathematical concepts (e.g., number, geometric continuum, or proof), with an emphasis on the controversies surrounding these concepts. Begins with Ancient Greek mathematics and traces the development of mathematical concepts through the middle ages into the present. Recommended requisite: completion of upper division Written Communication requirement. Same as MATH 4820.

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Research

research overview

keywords

Publications

selected publications

journal article

Teaching

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