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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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A First Course in Electrical and Computer Engineering
Louis Scharf · OpenStax CNX · 2009
This book was written for an experimental freshman course at the University of Colorado. The course is now an elective that the majority of our electrical and computer engineering students take in the second semester of their freshman year, just before their first circuits course. Our department decided to offer this course for several reasons: we wanted to pique student' interest in engineering by acquainting them with engineering teachers early in their university careers and by providing with exposure to the types of problems that electrical and computer engineers are asked to solve; we wanted students entering the electrical and computer engineering programs to be prepared in complex analysis, phasors, and linear algebra, topics that are of fundamental importance in our discipline; we wanted students to have an introduction to a software application tool, such as MATLAB, to complete their preparation for practical and efficient computing in their subsequent courses and in their professional careers; we wanted students to make early contact with advanced topics like vector graphics, filtering, and binary coding so that they would gain a more rounded picture of modern electrical and computer engineering. In order to introduce this course, we had to sacrifice a second semester of Pascal programming. We concluded that the sacrifice was worth making because we found that most of our students were prepared for high-level language computing after just one semester of programming. We believe engineering educators elsewhere are reaching similar conclusions about their own students and curriculums. We hope this book helps create a much needed dialogue about curriculum revision and that it leads to the development of similar introductory courses that encourage students to enter and practice our craft.Students electing to take this course have completed one semester of calculus, computer programming, chemistry, and humanities. Concurrently with this course, students take ph
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An Introduction to Matlab and Mathcad
Troy Siemers · APEX Calculus · 2011
This textbook, or really a “coursebook” for a college freshman-level class, has been updated for Spring 2014 and provides an introduction to programming and problem solving using both Matlab and Mathcad. We provide a balanced selection of introductory exercises and real-world problems (i.e. no “contrived” problems). We include many examples and screenshots to guide the reader. We assume no prior knowledge of Matlab or Mathcad.
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Think Bayes: Bayesian Statistics Made Simple
Allen Downey · Green Tea Press · 2012
Think Bayes is an introduction to Bayesian statistics using computational methods. The premise of this book, and the other books in the Think X series, is that if you know how to program, you can use that skill to learn other topics. Most books on Bayesian statistics use mathematical notation and present ideas in terms of mathematical concepts like calculus. This book uses Python code instead of math, and discrete approximations instead of continuous mathematics. As a result, what would be an integral in a math book becomes a summation, and most operations on probability distributions are simple loops. I think this presentation is easier to understand, at least for people with programming skills. It is also more general, because when we make modeling decisions, we can choose the most appropriate model without worrying too much about whether the model lends itself to conventional analysis. Also, it provides a smooth development path from simple examples to real-world problems.
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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
Có trong mục lục: 10.03: Calculus in More than One Variable
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Analysis
CK-Foundation · LibreTexts
Có trong mục lục: 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
Có trong mục lục: 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
Có trong mục lục: 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
Có trong mục lục: 02: Calculus in the 17th and 18th Centuries · 2.E: Calculus in the 17th and 18th Centuries (Exercises)
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Sets, Logic, Computation
Richard Zach et al. · Open Logic Project
Có trong mục lục: 2.3.02: The Sequent Calculus · 2.04: The Sequent Calculus
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CHEM 2141: Survey of Physical Chemistry
LibreTexts
Có trong mục lục: 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
Có trong mục lục: 16.01: Vector Calculus