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Numerical Methods in Scientific Computing
Jos van Kan; Guus Segal; Fred Vermolen · TU Delft Open · 2023
This is a book about numerically solving partial differential equations occurring in technical and physical contexts and the authors have set themselves a more ambitious target than to just talk about the numerics. Their aim is to show the place of numerical solutions in the general modeling process and this must inevitably lead to considerations about modeling itself. Partial differential equations usually are a consequence of applying first principles to a technical or physical problem at hand. That means, that most of the time the physics also have to be taken into account especially for validation of the numerical solution obtained. This book aims especially at engineers and scientists who have ’real world’ problems. It will concern itself less with pesky mathematical detail. For the interested reader though, we have included sections on mathematical theory to provide the necessary mathematical background. Since this treatment had to be on the superficial side we have provided further reference to the literature where necessary.
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Introducing Mathematical Biology
Alex Best · The University of Sheffield · 2023
Mathematical modelling plays an increasingly important role in almost any area of life sciences, and this interactive textbook focuses on the areas of population ecology, infectious diseases, immunology and cell dynamics, gene networks and pharmacokinetics. It is aimed at anyone who is interested in learning about how to model biological systems, including undergraduate and postgraduate mathematics students who have not studied mathematical biology before, life-sciences students with an interest in modelling, and post-16 mathematics students interested in university-level material. Some mathematical knowledge is assumed, and the mathematical models used are all in the form of ordinary differential equations.
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Calculus in Context
James Callahan; David Cox; Kenneth Hoffman · Smith College Open Educational Resources: Textbooks · 1994
Designing the curriculum We believe that calculus can be for students what it was for Euler and the Bernoullis: a language and a tool for exploring the whole fabric of science. We also believe that much of the mathematical depth and vitality of calculus lies in connections to other sciences. The mathematical questions that arise are compelling in part because the answers matter to other disciplines. We began our work with a "clean slate," not by asking what parts of the traditional course to include or discard. Our starting points are thus our summary of what calculus is really about. Our curricular goals are what we aim to convey about the subject in the course. Our functional goals describe the attitudes and behaviors we hope our students will adopt in using calculus to approach scientific and mathematical questions. Starting Points Calculus is fundamentally a way of dealing with functional relationships that occur in scientific and mathematical contexts. The techniques of calculus must be subordinate to an overall view of the questions that give rise to these relationships. Technology radically enlarges the range of questions we can explore and the ways we can answer them. Computers and graphing calculators are much more than tools for teaching the traditional calculus. The concept of a dynamical system is central to science. Therefore, differential equations belong at the center of calculus, and technology makes this possible at the introductory level. The process of successive approximation is a key tool of calculus, even when the outcome of the process--the limit--cannot be explicitly given in closed form. Curricular Goals Develop calculus in the context of scientific and mathematical questions. Treat systems of differential equations as fundamental objects of study. Construct and analyze mathematical models. Use the method of successive approximations to define and solve problems. Develop geometric visualization with hand-drawn and computer graphics. Give num
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Informal Calculus with Applications to Biological and Environmental Sciences
Tyler Seacrest; Debbie Seacrest; Rebekah Levine; Michele Anderson · TRAILS · 2021
This book is an approachable introduction to calculus with applications to biology and environmental science. For example, one application in the book is determining the volume of earth moved in the 1959 earthquake that created Quake Lake. Another application uses differential equations to model various biological examples, including moose and wolf populations at Isle Royale National Park, ranavirus in amphibians, and competing species of protozoa. The text focuses on intuitive understanding of concepts, but still covers most of the algebra and calculations common in a survey of calculus course.
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Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students
Jason Lachniet · Jason Lachniet · 2017
This brief book provides a noncomprehensive introduction to GNU Octave, a free open source alternative to MatLab. The basic syntax and usage is explained through concrete examples from the mathematics courses a math, computer science, or engineering major encounters in the first two years of college: linear algebra, calculus, and differential equations.
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Calculus
Gilbert Strang · OpenStax · 2016
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.
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A Gentle Introduction to the Art of Mathematics
Joseph Fields · Southern Connecticut State University · 2015
This book is designed for the transition course between calculus and differential equations and the upper division mathematics courses with an emphasis on proof and abstraction. The book has been used by the author and several other faculty at Southern Connecticut State University. There are nine chapters and more than enough material for a semester course. Student reviews are favorable. It is written in an informal, conversational style with a large number of interesting examples and exercises, so that a student learns to write proofs while working on engaging problems.
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Calculus for the Life Sciences: A Modeling Approach
James Cornette; Ralph Ackerman · A.T. Still University · 2013
Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course. In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.
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Calculus for the Life Sciences: A Modeling Approach
James Cornette; Ralph Ackerman · A.T. Still University · 2011
Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course. In our text, mathematical modeling and difference and differential equations lead, closely follow, and extend the elements of calculus. Chapter one introduces mathematical modeling in which students write descriptions of some observed processes and from these descriptions derive first order linear difference equations whose solutions can be compared with the observed data. In chapters in which the derivatives of algebraic, exponential, or trigonometric functions are defined, biologically motivated differential equations and their solutions are included. The chapter on partial derivatives includes a section on the diffusion partial differential equation. There are two chapters on non-linear difference equations and on systems of two difference equations and two chapters on differential equations and on systems of differential equation.
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Aerospace Structures
Eric Johnson · Virginia Tech Publishing · 2022
Aerospace Structures by Eric Raymond Johnson is a 600+ page text and reference book for junior, senior, and graduate-level aerospace engineering students. The text begins with a discussion of the aerodynamic and inertia loads acting on aircraft in symmetric flight and presents a linear theory for the status and dynamic response of thin-walled straight bars with closed and open cross-sections. Isotropic and fiber-reinforced polymer (FRP) composite materials including temperature effects are modeled with Hooke’s law. Methods of analyses are by differential equations, Castigliano’s theorems, the direct stiffness method, the finite element method, and Lagrange’s equations. There are numerous examples for the response axial bars, beams, coplanar trusses, coplanar frames, and coplanar curved bars. Failure initiation by the von Mises yield criterion, buckling, wing divergence, fracture, and by Puck’s criterion for FRP composites are presented in the examples. Professors, if you are considering or reviewing this book for adoption in your course, please let us know here. Problem sets: http://hdl.handle.net/10919/104169 ePub and LaTeX source files: Expected late spring 2022
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Electromagnetics
Steven Ellingson · Virginia Tech Libraries · 2018
Electromagnetics Volume 1 by Steven W. Ellingson is a 238-page, peer-reviewed open educational resource intended for electrical engineering students in the third year of a bachelor of science degree program. It is intended as a primary textbook for a one-semester first course in undergraduate engineering electromagnetics. The book employs the “transmission lines first” approach in which transmission lines are introduced using a lumped-element equivalent circuit model for a differential length of transmission line, leading to one-dimensional wage equations for voltage and current. Additional ResourcesProblem sets and the corresponding solution manual are also available.
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Introduction to Linear, Time-Invariant, Dynamic Systems for Students of Engineering
William Hallauer · A.T. Still University · 2016
This is a complete college textbook, including a detailed Table of Contents, seventeen Chapters (each with a set of relevant homework problems), a list of References, two Appendices, and a detailed Index. The book is intended to enable students to: Solve first-, second-, and higher-order, linear, time-invariant (LTI) ordinary differential equations (ODEs) with initial conditions and excitation, using both time-domain and Laplace-transform methods; Solve for the frequency response of an LTI system to periodic sinusoidal excitation and plot this response in standard form; Explain the role of the time constant in the response of a first-order LTI system, and the roles of natural frequency, damping ratio, and resonance in the response of a second-order LTI system; Derive and analyze mathematical models (ODEs) of low-order mechanical systems, both translational and rotational, that are composed of inertial elements, spring elements, and damping devices; Derive and analyze mathematical models (ODEs) of low-order electrical circuits composed of resistors, capacitors, inductors, and operational amplifiers; Derive (from ODEs) and manipulate Laplace transfer functions and block diagrams representing output-to-input relationships of discrete elements and of systems; Define and evaluate stability for an LTI system; Explain proportional, integral, and derivative types of feedback control for single-input, single-output (SISO), LTI systems; Sketch the locus of characteristic values, as a control parameter varies, for a feedback-controlled SISO, LTI system; Use MATLAB as a tool to study the time and frequency responses of LTI systems. The book's general organization is: Chapters 1-10 deal primarily with the ODEs and behaviors of first-order and second-order dynamic systems; Chapters 11 and 12 discuss the ODEs and behaviors of mechanical systems having two degrees of freedom, i.e., fourth-order systems; Chapters 13 and 14 introduce classical feedback control; Chapter 15 pre
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Calculus Volume 3
Gilbert Strang; Nicoleta Virginia Bila; Sheri J. Boyd; David Smith · OpenStax, Rice University
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations. Please note that this title is published under a CC BY-NC-SA 4.0 license, which means that you are free to use and adapt, but not for commercial purposes. Changes you make need to be shared using this license.
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Calculus Volume 2
William Radulovich; Erica M. Rutter; David Smith; Gilbert Strang · OpenStax, Rice University
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates. Please note that this title is published under a CC BY-NC-SA 4.0 license, which means that you are free to use and adapt, but not for commercial purposes. Changes you make need to be shared using this license.
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Free Energy 1e (Snee)
Preston Snee · University of Illinois Chicago
Có trong mục lục: 01: Gas Equations of State · 2.01: Work and the inexact differential
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Thermodynamics and Introduction to Quantum Mechanics
Cathrine Southern · DePaul University
Có trong mục lục: 1.03: Equations of State for Real Gases · 2.05: Exact and Inexact Differentials · 2.5.01: Total and Exact Differentials
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Heat and Thermodynamics
Jeremy Tatum · University of Victoria
Có trong mục lục: 1.06: Applicability of Equations · 2.05: Second Derivatives and Exact Differentials · 13: Expansion Compression and the TdS Equations
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Scientific Computing
Jeffrey R. Chasnov · Hong Kong University of Science and Technology
Có trong mục lục: 4: Differential Equations · 14: The Governing Equations · 16: Stream Function Vorticity Equations
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Dynamic Systems and Control
Mohammed Dahleh, Munther A. Dahleh, and George Verghese · Massachusetts Institute of Technology
Có trong mục lục: 1.05: Linear Systems of Equations · 8.03: Realization from an LTI Differential Difference equation
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https://math.libretexts.org/Workbench/Calculus_2_OER
Leonard Lamp · Irvine Valley College
Có trong mục lục: 04: Introduction to Differential Equations · 4.01: Basics of Differential Equations · 4.03: Separable Equations