Digital library
Textbooks, references and open learning resources.
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Aerodynamics and Aircraft Performance
James Marchman III · Virginia Tech Libraries · 2004
Aerodynamics and Aircraft Performance, 3rd edition is a college undergraduate-level introduction to aircraft aerodynamics and performance. This text is designed for a course in Aircraft Performance that is taught before the students have had any course in fluid mechanics, fluid dynamics, or aerodynamics. The text is meant to provide the essential information from these types of courses that is needed for teaching basic subsonic aircraft performance, and it is assumed that the students will learn the full story of aerodynamics in other, later courses. The text assumes that the students will have had a university level Physics sequence in which they will have been introduced to the most fundamental concepts of statics, dynamics, fluid mechanics, and basic conservation laws that are needed to understand the coverage that follows. It is also assumed that students will have completed first year university level calculus sequence plus a course in multi-variable calculus. Separate courses in engineering statics and dynamics are helpful but not necessary. Any student who takes a course using this text after completing courses in aerodynamics or fluid dynamics should find the chapters of this book covering those subjects an interesting review of the material. The 236-page text was created specifically for use by undergraduate students in Aerospace Engineering and was based on Professor Marchman’s many years of experience teaching related subject matter as well as his numerous wind tunnel research projects related to aircraft aerodynamics and his personal experience as the owner and pilot of a general aviation airplane. It has been used at Virginia Tech and other universities. Instructors reviewing, adopting, or adapting parts or the whole of the text are requested to register their interest at: https://bit.ly/aerodynamics_interest.
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Notes on Diffy Qs: Differential Equations for Engineers
Jirí Lebl · Jirí Lebl · 2014
A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence. This free online book (e-book in webspeak) should be usable as a stand-alone textbook or as a companion to a course using another book such as Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modeling or Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems (section correspondence to these two is given). I developed and used these notes to teach Math 286/285 at the University of Illinois at Urbana-Champaign Sample Dirichlet problem solution (one is a 4-day-a-week, the other a 3-day-a-week semester-long course). I have also taught Math 20D at University of California, San Diego with these notes (a 3-day-a-week quarter-long course). There is enough material to run a 2-quarter course, and even perhaps a two semester course depending on lecturer speed.
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Elementary Differential Equations with Boundary Value Problems
William Trench · A.T. Still University · 2013
Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. 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 definitions, 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. Although I believe that the computer is an immensely valuable tool for learning, doing, and writing mathematics, the selection and treatment of topics in this text reflects my pedagogical orientation along traditional lines. However, I have incorporated what I believe to be the best use of modern technology, so you can select the level of technology that you want to include in your course. The text includes 336 exercises – identified by the symbols C and C/G – that call for graphics or computation and graphics. There are also 73 laboratory exercises – identified by L – that require extensive use of technology. In addition, several sections include informal advice on the use of technology. If you prefer not to emphasize technology, simply ignore these exercises and the advice.
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Introduction to Probability
Charles Grinstead; J. Laurie Snell · American Mathematical Society · 2006
Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continuedto influence such early researchers as Huygens, Bernoulli, and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a wellestablished branch of mathematics that finds applications in every area of scholarlyactivity from music to physics, and in daily experience from weather prediction topredicting the risks of new medical treatments. This text is designed for an introductory probability course taken by sophomores,juniors, and seniors in mathematics, the physical and social sciences, engineering,and computer science. It presents a thorough treatment of probability ideas andtechniques necessary for a form understanding of the subject. The text can be usedin a variety of course lengths, levels, and areas of emphasis. For use in a standard one-term course, in which both discrete and continuousprobability is covered, students should have taken as a prerequisite two terms ofcalculus, including an introduction to multiple integrals. In order to cover Chapter 11, which contains material on Markov chains, some knowledge of matrix theoryis necessary. The text can also be used in a discrete probability course. The material has beenorganized in such a way that the discrete and continuous probability discussions arepresented in a separate, but parallel, manner. This organization dispels an overlyrigorous or formal view of probability and o?ers some strong pedagogical valuein that the discrete discussions can sometimes serve to motivate the more abstractcontinuous probability discussions. For use in a discrete probability course, studentsshould have taken one term of calculus as a prerequisite. Very little computing background is assumed or necessary in order to obtain fullbenefits from the use of the comp
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University Physics Volume 3
Stephen D. Druger; Alice Kolakowska; Samuel J. Ling; David Anderson · OpenStax, Rice University
University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity, and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result.
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University Physics Volume 2
Gerald Friedman; Stephen D. Druger; Alice Kolakowska; Samuel J. Ling · OpenStax, Rice University
University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result.
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University Physics Volume 1
Stephen D. Druger; William Moebs; Samuel J. Ling; Jeff Sanny · OpenStax, Rice University
University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. Volume 1 covers mechanics, sound, oscillations, and waves. Volume 2 covers thermodynamics, electricity and magnetism, and Volume 3 covers optics and modern physics. This textbook emphasizes connections between theory and application, making physics concepts interesting and accessible to students while maintaining the mathematical rigor inherent in the subject. Frequent, strong examples focus on how to approach a problem, how to work with the equations, and how to check and generalize the result.
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Introducción al Cálculo Vectorial para Ingeniería
Omar Arturo Cevallos-Muñoz · Editorial Grupo AEA · 2024
El presente libro es una herramienta esencial para estudiantes de ingeniería que se inician en el estudio del Cálculo Vectorial, con el objetivo de proporcionar una comprensión sólida de los conceptos fundamentales del cálculo de varias variables y sus aplicaciones prácticas en ingeniería. Está estructurado en cinco unidades que comienzan con los fundamentos del cálculo vectorial, como la representación de puntos y vectores en el espacio, operaciones vectoriales, ecuaciones de rectas y planos, y geometría tridimensional. Estos fundamentos establecen una base para el estudio de temas más avanzados. La segunda unidad explora funciones vectoriales, abarcando el estudio de curvas en el espacio y campos vectoriales, con aplicaciones en física, lo que ayuda a los estudiantes a modelar y analizar fenómenos físicos con herramientas matemáticas. La tercera unidad se centra en el cálculo diferencial, cubriendo derivadas parciales, gradiente, divergencia y rotacional, además de la optimización de funciones de varias variables con multiplicadores de Lagrange. Esta parte es crucial para la resolución de problemas de optimización en ingeniería. La cuarta unidad aborda el cálculo integral, incluyendo integrales múltiples, cambio de variables y los teoremas de Green, Stokes y Gauss, esenciales para calcular volúmenes, áreas y flujos en problemas ingenieriles. La metodología del libro se basa en un aprendizaje simplificado, con explicaciones claras y concisas, y evita formalismos excesivos. Los numerosos ejemplos prácticos y ejercicios, tanto resueltos como propuestos, permiten a los estudiantes aplicar conceptos teóricos a problemas reales, reforzando su aprendizaje. Dirigido a estudiantes de ingeniería de la Universidad Técnica Estatal de Quevedo, especialmente a aquellos en el curso de Cálculo Vectorial, este libro es un recurso invaluable para profundizar en el campo del cálculo vectorial y sus aplicaciones en ingeniería.
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Free Energy 1e (Snee)
Preston Snee · University of Illinois Chicago
What is the role of mathematics in Chemistry? We use math to reveal relationships that exist in nature that cannot be determined by any other reasonable means. Often Physical Chemistry is the last stop on the way to your degree, and you probably put this class off till last due to an irrational fear of mathematics. And while it may be true that calculus derivations are not your “thing”, if you’re good at this, you might get a better, higher paying job. So, it’s worth the effort.
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Thermodynamics and Introduction to Quantum Mechanics
Cathrine Southern · DePaul University
In the contents: 10.03: Calculus in More than One Variable
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Analysis
CK-Foundation · LibreTexts
In the contents: 08: Introduction to Calculus · 8.01: Limits in Calculus · 8.5.01: Fundamental Theorem of Calculus
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Electromagnetics and Applications
David H. Staelin · Massachusetts Institute of Technology
In the contents: 14.05: Frequently Used Trigonometric and Calculus Expressions
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PGCC: PHYS 1030 - General Physics
Neeharika Thakur · Prince George's Community College
This text addresses a calculus-based study of classical mechanics, including laws of motion, force, energy, momentum, and gravitation.
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Spiral Physics: Algebra Based
Paul D'Alessandris · Monroe Community College
In the contents: 02. Using the Calculus · 03. Using the Calculus Another Example
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Real Analysis
Eugene Boman & Robert Rogers · Pennsylvania State University & SUNY Fredonia
In the contents: 02: Calculus in the 17th and 18th Centuries · 2.E: Calculus in the 17th and 18th Centuries (Exercises)
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CHEM 2141: Survey of Physical Chemistry
LibreTexts
In the contents: 1.02: Quantity Calculus
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University Physics I: Mechanics, Sound, Oscillations, and Waves
OpenStax · LibreTexts
University Physics is a three-volume collection that meets the scope and sequence requirements for two- and three-semester calculus-based physics courses. This text covers the fundamentals of mechanics, oscillations, waves, and sound. You’ll learn how to describe motion, apply Newton’s laws, and explore concepts of energy, momentum, rotation, and gravity. The text also introduces fluids, vibrations, and wave behavior, leading to the study of sound and resonance.
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Differential Equations and Linear Algebra
Steven Zook · Reedley College
This text is intended for engineering, science, and math majors who have completed a three semester calculus sequence.
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Gettysburg College Physics for Physics Majors
Kurt Andresen · Gettysburg College
In the contents: 16.01: Vector Calculus
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Time Scales Analysis
Svetlin G. Georgiev · Sorbonne University
In the contents: 23: A Supplementary Material- Diamond Alpha Calculus on Time Scales · 23.01: Diamond Alpha Differential Calculus · 23.02: Diamond Alpha Integral Calculus