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Full-Text Articles in Physical Sciences and Mathematics

Elementary Differential Equations With Boundary Value Problems, William F. Trench Dec 2014

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

William F. Trench

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. …


Elementary Differential Equations, William F. Trench Dec 2014

Elementary Differential Equations, William F. Trench

William F. Trench

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 Dec 2014

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

William F. Trench

No abstract provided.


Introduction To Real Analysis, William F. Trench Dec 2014

Introduction To Real Analysis, William F. Trench

William F. Trench

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 …


An Unnoticed Consequence Of Szego's Distribution Theorem, William F. Trench Nov 2014

An Unnoticed Consequence Of Szego's Distribution Theorem, William F. Trench

William F. Trench

No abstract provided.


Inverse Problems For Unilevel Block $\Alpha$-Circulants, William F. Trench Feb 2013

Inverse Problems For Unilevel Block $\Alpha$-Circulants, William F. Trench

William F. Trench

No abstract provided.


Functions Defined By Improper Integrals, William F. Trench Dec 2012

Functions Defined By Improper Integrals, William F. Trench

William F. Trench

This is a supplement to the author's Introduction to Real Analysis. It has been judged to meet the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Textbook Initiative. It may be copied, modified, redistributed, translated, and built upon subject to the Creative Commons license

Attribution-NonCommercial-ShareAlike 3.0 Unported License.

A complete instructor's solution manual is available by email to wtrench@trinity.edu subject to verification of the requestor's faculty status.


Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench Dec 2011

Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench

William F. Trench

No abstract provided.


Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench Dec 2010

Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench

William F. Trench

No abstract provided.


The Relationship Between Trench's Toeplitz Inversion Algorithm And The Gohberg-Semencul Formula, William F. Trench Dec 2010

The Relationship Between Trench's Toeplitz Inversion Algorithm And The Gohberg-Semencul Formula, William F. Trench

William F. Trench

No abstract provided.


Spectral Decomposition Of Kac-Murdock-Szego Matrices, William F. Trench Dec 2009

Spectral Decomposition Of Kac-Murdock-Szego Matrices, William F. Trench

William F. Trench

No abstract provided.


Inverses Of Lower Triangular Toeplitz Matrices, William F. Trench Dec 2008

Inverses Of Lower Triangular Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.


Functional Perturbations Of Nonoscillatory Second Order Difference Equations, William F. Trench Dec 2005

Functional Perturbations Of Nonoscillatory Second Order Difference Equations, William F. Trench

William F. Trench

No abstract provided.


Characterization And Properties Of $(R,S)$-Symmetric, $(R,S)$-Skew Symmetric, And $(R,S)$-Conjugate Matrices, William F. Trench Dec 2004

Characterization And Properties Of $(R,S)$-Symmetric, $(R,S)$-Skew Symmetric, And $(R,S)$-Conjugate Matrices, William F. Trench

William F. Trench

No abstract provided.


On Matrices With Rotative Symmetries, William F. Trench Dec 2004

On Matrices With Rotative Symmetries, William F. Trench

William F. Trench

No abstract provided.


Asymptotic Relationships Between Singular Values Of Structured Matrices Similarly Generated By Different Formal Expansions Of A Rational Function, William F. Trench Dec 2004

Asymptotic Relationships Between Singular Values Of Structured Matrices Similarly Generated By Different Formal Expansions Of A Rational Function, William F. Trench

William F. Trench

No abstract provided.


Simplification And Strengthening Of Weyl's Definition Of Asymptotic Equal Distribution Of Two Families Of Finite Sets, William F. Trench Dec 2003

Simplification And Strengthening Of Weyl's Definition Of Asymptotic Equal Distribution Of Two Families Of Finite Sets, William F. Trench

William F. Trench

No abstract provided.


Spectral Distribution Of Hermitian Toeplitz Matrices Formally Generated By Rational Functions, William F. Trench Dec 2002

Spectral Distribution Of Hermitian Toeplitz Matrices Formally Generated By Rational Functions, William F. Trench

William F. Trench

No abstract provided.


Asymptotically Constant Solutions Of Functional Difference Systems, William F. Trench Dec 2001

Asymptotically Constant Solutions Of Functional Difference Systems, William F. Trench

William F. Trench

No abstract provided.


Systems Of Difference Equations With Asymptotically Constant Solutions, William F. Trench Dec 1999

Systems Of Difference Equations With Asymptotically Constant Solutions, William F. Trench

William F. Trench

No abstract provided.


Conditional Convergence Of Infinite Products, William F. Trench Dec 1998

Conditional Convergence Of Infinite Products, William F. Trench

William F. Trench

No abstract provided.


Linear Asymptotic Equilibrium For Nilpotent Systems Of Difference Equations, William F. Trench Dec 1998

Linear Asymptotic Equilibrium For Nilpotent Systems Of Difference Equations, William F. Trench

William F. Trench

No abstract provided.


Trench's Canonical Form For A Disconjugate $N$Th-Order Linear Difference Equation, William F. Trench, Bennette Harris, Robert Krueger Dec 1997

Trench's Canonical Form For A Disconjugate $N$Th-Order Linear Difference Equation, William F. Trench, Bennette Harris, Robert Krueger

William F. Trench

No abstract provided.


Numerical Solution Of The Inverse Eigenvalue Problem For Real Symmetric Toeplitz Matrices, William F. Trench Dec 1996

Numerical Solution Of The Inverse Eigenvalue Problem For Real Symmetric Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.


A Note On The Real Symmetric Eigenvalue, William F. Trench Dec 1993

A Note On The Real Symmetric Eigenvalue, William F. Trench

William F. Trench

No abstract provided.


A Note On Computing Eigenvalues Of Banded Hermitian Toeplitz Matrices, William F. Trench Dec 1992

A Note On Computing Eigenvalues Of Banded Hermitian Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.


Global Solutions Of Nonlinear Differential Equations, William F. Trench Dec 1991

Global Solutions Of Nonlinear Differential Equations, William F. Trench

William F. Trench

No abstract provided.


Asymptotic Behavior Of Solutions Of Functionally Perturbed Nonoscillatory Second Order Differential Equations, William F. Trench Dec 1990

Asymptotic Behavior Of Solutions Of Functionally Perturbed Nonoscillatory Second Order Differential Equations, William F. Trench

William F. Trench

No abstract provided.


Spectral Evolution Of A One-Parameter Extension Of A Real Symmetric Toeplitz Matrix, William F. Trench Dec 1989

Spectral Evolution Of A One-Parameter Extension Of A Real Symmetric Toeplitz Matrix, William F. Trench

William F. Trench

No abstract provided.


General Functional Differential Systems With Asymptotically Constant Solutions, William F. Trench Dec 1988

General Functional Differential Systems With Asymptotically Constant Solutions, William F. Trench

William F. Trench

No abstract provided.