William F. Trenchhttps://works.bepress.com/william_trench/Recent works by William F. Trenchen-usCopyright (c) 2019 All rights reserved.Mon, 01 Dec 2014 00:00:00 +00003600An unnoticed consequence of Szego's distribution theoremhttps://works.bepress.com/william_trench/148/William F. TrenchMon, 01 Dec 2014 00:00:00 +0000https://works.bepress.com/william_trench/148/ArticlesCharacterization and properties of $(P_\sigma,Q)$ symmetric and co-symmetric matriceshttps://works.bepress.com/william_trench/115/William F. TrenchWed, 01 Jan 2014 00:00:00 +0000https://works.bepress.com/william_trench/115/ArticlesElementary Differential Equationshttps://works.bepress.com/william_trench/128/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 elementary text can’t be better than its exercises. This text includes 1695 numbered exercises, many with several parts. They range in difficulty from routine to very challenging.
An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and def- initions, preferring to deal with concepts in a more conversational way, copiously illustrated by 250 completely worked out examples. Where appropriate, concepts and results are depicted in 144 figures.William F. TrenchSun, 01 Dec 2013 08:00:00 +0000https://works.bepress.com/william_trench/128/Free Textbooks and SupplementsStudent Solutions Manual for Elementary Differential Equations and Elementary Differential Equations with Boundary Value Problemshttps://works.bepress.com/william_trench/127/Sun, 01 Dec 2013 08:00:00 +0000https://works.bepress.com/william_trench/127/Free Textbooks and SupplementsIntroduction to Real Analysishttps://works.bepress.com/william_trench/126/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 is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equa- tion, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.Sun, 01 Dec 2013 08:00:00 +0000https://works.bepress.com/william_trench/126/Free Textbooks and SupplementsElementary Differential Equations with Boundary Value Problemshttps://works.bepress.com/william_trench/129/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.
An elementary text can’t be better than its exercises. This text includes 2041 numbered exercises, many with several parts. They range in difficulty from routine to very challenging.
An elementary text should be written in an informal but mathematically accurate way, illustrated by appropriate graphics. I have tried to formulate mathematical concepts succinctly in language that students can understand. I have minimized the number of explicitly stated theorems and def- initions, preferring to deal with concepts in a more conversational way, copiously illustrated by 299 completely worked out examples. Where appropriate, concepts and results are depicted in 188 figures.Sun, 01 Dec 2013 08:00:00 +0000https://works.bepress.com/william_trench/129/Free Textbooks and SupplementsInverse problems for unilevel block $\alpha$-circulantshttps://works.bepress.com/william_trench/122/William F. TrenchFri, 01 Mar 2013 00:00:00 +0000https://works.bepress.com/william_trench/122/ArticlesFunctions Defined by Improper Integralshttps://works.bepress.com/william_trench/131/<p>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</p>
<p>Attribution-NonCommercial-ShareAlike 3.0 Unported License.</p>
<p>A complete instructor's solution manual is available by email to wtrench@trinity.edu subject to verification of the requestor's faculty status.</p>
William F. TrenchTue, 01 Jan 2013 00:00:00 +0000https://works.bepress.com/william_trench/131/Free Textbooks and SupplementsThe Method of Lagrange Multipliershttps://works.bepress.com/william_trench/130/<p>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 Open Textbook Initiative.</p>
<p>It may be copied, modified, redistributed, translated, and built upon subject to the Creative Commons</p>
<p>Attribution-NonCommercial-ShareAlike 3.0 Unported License.</p>
<p>A complete instructor's solution manual is available by email to wtrench@trinity.edu, subject to verification of the requestor's faculty status.</p>
William F. TrenchTue, 01 Jan 2013 00:00:00 +0000https://works.bepress.com/william_trench/130/Free Textbooks and SupplementsCharacterization and properties of $(R,S_\sigma)$-commutative matriceshttps://works.bepress.com/william_trench/114/William F. TrenchSun, 01 Jan 2012 00:00:00 +0000https://works.bepress.com/william_trench/114/Articles