Physical Sciences and Mathematics Commons^™

Elementary Differential Equations, William F. Trench

Textbooks Collection

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra.

In writing this book I have been guided by the these principles:

An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough.

An …

Student Solutions Manual For Elementary Differential Equations And Elementary Differential Equations With Boundary Value Problems, William F. Trench

Textbooks Collection

No abstract provided.

Introduction To Real Analysis, William F. Trench

Textbooks Collection

This is a text for a two-term course in introductory real analysis for junior or senior math- ematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathe- matical maturity that can be gained from an introductory real analysis course.

The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calcu- lus sequence …

Elementary Differential Equations With Boundary Value Problems, William F. Trench

Textbooks Collection

Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some prepa- ration in linear algebra.

In writing this book I have been guided by the these principles:

An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. …

Measuring Habits Of Mind: Toward A Prompt-Less Instrument For Assessing Quantitative Literacy, Stuart Boersma, Dominic Klyve

Numeracy

In this study, we offer a new “prompt-less” instrument for measuring students’ habits of mind in the field of quantitative literacy. The instrument consists of a series of questions about a newspaper article the students read. The questions do not explicitly solicit quantitative information; students’ habit of mind is assessed by their use of quantitative reasoning even when it is not asked for. Students’ answers were graded according to a modified version of the Quantitative Literacy Assessment Rubric (QLAR) published in this journal (vol. 4, issue 2). We applied the instrument and rubric to assess pre- and post-intervention habits of …

Using A Media-Article Approach To Quantitative Reasoning As An Honors Course: An Exploratory Study, Stuart Boersma, Dominic Klyve

Numeracy

In this study, we investigate student performance on a basic skills assessment of percentages and ratios in two cohorts of students: the general (non-STEM) student body (cohort G) and (non-STEM) honors students (cohort H). Both cohorts used a media-article approach to the study of quantitative reasoning. A pre- and a post-intervention assessment were administered with a two-week intervention period consisting of critical analyses of the use of percentages and ratios in media articles. Using non-parametric techniques, no statistically significant improvement was measured in cohort G while cohort H students showed statistically significant improvement on several items.

The Scope Of Numeracy After Five Years, H. L. Vacher, Dorothy Wallace

Numeracy

The purpose of this editorial is to provide an efficient way for readers and potential authors to see (a) what type of papers are published in this journal and (b) what subjects are appropriate. The editorial consists mainly of about a dozen pages of tables including live links to the papers’ access/abstract pages to facilitate easy browsing. In the first table, the 85 papers that have been published in the journal’s first five years are classified into: review papers; research papers; case studies; essays; book reviews; columns; and editorials about the journal. In the second table, the papers are inventoried …

Analytic Functions With Real Boundary Values In Smirnov Classes EP, Lisa De Castro

USF Tampa Graduate Theses and Dissertations

This thesis concerns the classes of analytic functions on bounded, n-connected domains known as the Smirnov classes E^p, where p > 0. Functions in these classes satisfy a certain growth condition and have a relationship to the more well known classes of functions known as the Hardy classes H^p. In this thesis I will show how the geometry of a given domain will determine the existence of non-constant analytic functions in Smirnov classes that possess real boundary values. This is a phenomenon that does not occur among functions in the Hardy classes.

The preliminary and background information …

High Jump Analysis, Paige Cooke

Undergraduate Journal of Mathematical Modeling: One + Two

This project presents a mathematical analysis of the high jump, a popular track and field event. The first and second stages of the high jump correspond to the athlete’s run along two distinct trajectories. The third stage is the actual jump. We propose an individual model for each of these stages and show how to combine these models to study the dynamics of the entire high jump.

Nonlinear Techniques For Stochastic Systems Of Differential Equations, Tadesse G. Zerihun

USF Tampa Graduate Theses and Dissertations

Two of the most well-known nonlinear methods for investigating nonlinear dynamic processes in sciences and engineering are nonlinear variation of constants parameters and comparison method. Knowing the existence of solution process, these methods provide a very powerful tools for investigating variety of problems, for example, qualitative and quantitative properties of solutions, finding error estimates between solution processes of stochastic system and the corresponding nominal system, and inputs for the designing engineering and industrial problems. The aim of this work is to systematically develop mathematical tools to undertake the mathematical frame-work to investigate a complex nonlinear nonstationary stochastic systems of differential …

A Study Of Permutation Polynomials Over Finite Fields, Neranga Fernando

USF Tampa Graduate Theses and Dissertations

Let p be a prime and q = p^k. The polynomial g_n,q isin F_p[x] defined by the functional equation Sigma_{a isin Fq} (x+a)ⁿ = g_n,q(x^q- x) gives rise to many permutation polynomials over finite fields. We are interested in triples (n,e;q) for which g_n,q is a permutation polynomial of F_q^e. In Chapters 2, 3, and 4 of this dissertation, we present many new families of permutation polynomials in the form of g_n,q. The permutation behavior of g_n,q is becoming increasingly more …

Towards Interference-Immune And Channel-Aware Multicarrier Schemes: Filters, Lattices, And Interference Issues, Alphan Sahin

USF Tampa Graduate Theses and Dissertations

In this dissertation, multicarrier schemes are reviewed within the framework of Gabor Systems. Their fundamental elements; what to transmit, i.e., symbols, how to transmit, i.e., filters or pulse shape, and where/when to transmit, i.e., lattices are investigated extensively. The relations between different types of multicarrier schemes are discussed.

Within the framework of Gabor systems, a new windowing approach, edge windowing, is developed to address the out-of-band (OOB) radiation problem of orthogonal frequency division multiplexing (OFDM) based multicarrier schemes. To the best of our knowledge, for the first time, the diversity on the range of the users is exploited to suppress …

Topological Degree And Variational Inequality Theories For Pseudomonotone Perturbations Of Maximal Monotone Operators, Teffera Mekonnen Asfaw

USF Tampa Graduate Theses and Dissertations

Let X be a real reflexive locally uniformly convex

Banach space with locally uniformly convex dual space X^*

. Let G be a

bounded open subset of X. Let T:X⊃ D(T)⇒ 2X^*

be maximal

monotone and S: X ⇒ 2X^*

be bounded

pseudomonotone and such that 0 notin cl((T+S)(D(T)∩partG)). Chapter 1 gives general introduction and mathematical prerequisites. In

Chapter 2 we develop a homotopy invariance and uniqueness results for the degree theory constructed by Zhang and Chen for multivalued (S₊) perturbations of

maximal monotone operators. Chapter 3 is devoted to the construction of a new …

Modeling State Transitions With Automata, Egor Dolzhenko

USF Tampa Graduate Theses and Dissertations

Models based on various types of automata are ubiquitous in modern science. These models allow reasoning about deep theoretical questions and provide a basis for the development of efficient algorithms to solve related computational problems. This work discusses several types of automata used in such models, including cellular automata and mandatory results automata.

The first part of this work is dedicated to cellular automata. These automata form an important class of discrete dynamical systems widely used to model physical, biological, and chemical processes. Here we discuss a way to study the dynamics of one-dimensional cellular automata through the theory of …

Boolean Partition Algebras, Joseph Anthony Van Name

USF Tampa Graduate Theses and Dissertations

A Boolean partition algebra is a pair $(B,F)$ where $B$ is a Boolean

algebra and $F$ is a filter on the semilattice of partitions of $B$ where $\bigcup F=B\setminus\{0\}$. In this dissertation, we shall investigate the algebraic theory of Boolean partition algebras and their connection with uniform spaces. In particular, we shall show that the category of complete non-Archimedean uniform spaces

is equivalent to a subcategory of the category of Boolean partition algebras, and notions such as supercompleteness

of non-Archimedean uniform spaces can be formulated in terms of Boolean partition algebras.

Optimization In Non-Parametric Survival Analysis And Climate Change Modeling, Iuliana Teodorescu

USF Tampa Graduate Theses and Dissertations

Many of the open problems of current interest in probability and statistics involve complicated data

sets that do not satisfy the strong assumptions of being independent and identically distributed. Often,

the samples are known only empirically, and making assumptions about underlying parametric

distributions is not warranted by the insufficient information available. Under such circumstances,

the usual Fisher or parametric Bayes approaches cannot be used to model the data or make predictions.

However, this situation is quite often encountered in some of the main challenges facing statistical,

data-driven studies of climate change, clinical studies, or financial markets, to name a few. …

Adiabatic Flame Temperature For Combustion Of Methane Ii, Rebeca Pupo

Undergraduate Journal of Mathematical Modeling: One + Two

We calculate the adiabatic flame temperature of a mixture of methane and oxygen in the presence of a diluent gas then determine the mole fractions of methane without respect to nitrogen and solve for the moles of oxygen present. Knowing the moles of methane and oxygen, allows us to calculate the moles of nitrogen present at four constant mole fractions of nitrogen, and the adiabatic flame temperature is determined from the energy released by the reaction. Lastly, we produce several graphs to compare the adiabatic flame temperatures at different mole fractions of nitrogen.

Volatilization Of Benzene In A River, Eric Dunlop

Undergraduate Journal of Mathematical Modeling: One + Two

Benzene is a volatile organic compound: when it contaminates a river, some of the substance will evaporate as it flows through. We examine the volumetric flow rate to find how volatilization affects the concentration levels of benzene as the substance flows through several consecutive sections of a river, using a specific example to illustrate the general method.

Diffusion Of Vitamin B12 Across A Mesoporous Metal Organic Framework, Veronica Valencia

Undergraduate Journal of Mathematical Modeling: One + Two

We measure the rate of uptake and the rate of release of a Vitamin B12 solution (dissolved in water) at 2 different temperatures (room temperature and 37°C) by the mesoporous metal organic framework TbMOF-100 at 1-hour intervals using a spectrophotometer. Using the Beer-Lambert law, we calculate the concentration of the stock solution based on the absorbance values obtained with the spectrophotometer. These values allow for the quantification of the initial rate of uptake and the rate of uptake at a random incubation time of the Vitamin B12 by the TbMOF-100. We also calculate the value of the coefficient of diffusion …

A Simplified Model Of The Internal Combustion Engine, Christofer Neff

Undergraduate Journal of Mathematical Modeling: One + Two

This project further investigates a model of a simplified internal combustion engine considered by Kranc in 1977. Using Euler’s method for ordinary differential equations, we modeled the interaction between the engine’s flywheel and thermodynamic power cycle. Approximating with sufficiently small time intervals (0.001 seconds over a period of 12 seconds) reproduced Kranc’s results with the engine having an average angular velocity of 72/sec.

Study Of Dieldrin In Coralville Reservoir, Jeremy Smith

Undergraduate Journal of Mathematical Modeling: One + Two

Using existing experimental data taken over a period of roughly 12 years that documents the concentrations of dieldrin levels in the environment and fatty tissue of the fish, we construct a model of the total dieldrin concentration decline. Comparisons between the experimental data and speculative data can be made using calculus and elements of statistics in order to better understand the movement of dieldrin in the reservoir. Because of the potentially harmful exposure effects of dieldrin to humans as well as the environment, it is important to be able to predict when stability has been restored to the ecosystem.

Finding The Area Of A Major League Baseball Field, Jacob Courchaine

Undergraduate Journal of Mathematical Modeling: One + Two

Using a Major League Baseball (MLB) baseball field template for guidelines, we estimate the cost of building the largest possible field accepted under MLB standards. This includes finding the areas of both the clay and grassy regions and determining how many bags of clay and fertilizer are required to cover the field.