Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn how to solve differential equations or needing a refresher on differential equations.
I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from a Calculus or Algebra class or contained in other sections of the notes.
A couple of warnings to my students who may be here to get a copy of what happened on a day that you missed.
- Because I wanted to make this a fairly complete set of notes for anyone wanting to learn differential equations I have included some material that I do not usually have time to cover in class and because this changes from semester to semester it is not noted here.
- In general I try to work problems in class that are different from my notes. However, with…
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 …
Over the years, when reviewing books we found that many had been mainstreamed by the publishers in an effort to appeal to everyone, leaving them with very little character. There were only a handful of books that had the conceptual and application driven focus we liked, and most of those were lacking in other aspects we cared about, like providing students sufficient examples and practice of basic skills. The largest frustration, however, was the never ending escalation of cost and being forced into new editions every three years. We began researching open textbooks, however the ability for those books to be adapted, remixed, or printed were often limited by the types of licenses, or didn’t approach the material the way we wanted.
In writing this book, our focus was on the story of functions. We begin with function notation, a basic toolkit of functions, and the basic operation with functions: composition and transformation. Building from these basic functions, as each new …
Este es un libro de cálculo diferencial e integral escrito por la profesora Elsie Hernández Saborio, profesora pensionada del Instituto Tecnológico de Costa Rica.
La primera presentación de este texto se realizó en los años 80, siendo una versión en papel digitada en las antiguas máquinas de escribir. La digital actual fue impulsada por el deseo de rescatar la obra de una profesora muy calificada en la enseñanza de la matemática dentro de un campo de gran interés para el estudiante. Por completitud, se incluye un capítulo sobre "Relaciones Relacionadas" escrito por la profesora Sharay Meneses, también profesora pensionada del Instituto Tecnológico de Costa Rica.
Esta versión estará en revisión en todo este I semestre de 2013.
Los principales aspectos que aquí se tratan son:
- Límites y continuidad de funciones
- Derivada de una función
- Aplicaciones de la Derivada
- Razones de Cambio Relacionadas
- Integral …