Digital library
Textbooks, references and open learning resources.
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Geometry with an Introduction to Cosmic Topology
Michael P. Hitchman · Linfield College
Motivated by questions in cosmology, the open-content text Geometry with an Introduction to Cosmic Topology uses Mobius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe. The text, written for students who have taken vector calculus, also explores the interplay between the shape of a space and the type of geometry it admits.
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Linear Algebra: A First Course
Doli Bambhania, Fatemeh Yarahmadi and Bill Wilson · De Anza College
This book offers a comprehensive and accessible introduction to linear algebra. It begins with methods for solving linear systems, followed by an exploration of matrices and their properties, including a dedicated chapter on determinants. The text then introduces vectors, covering essential concepts such as span, linear independence, subspaces, and linear transformations. From there, it develops spectral theory, including diagonalization and orthogonal diagonalization with their applications.
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Elementary First Order Dynamic Equations on Time Scales
Svetlin G. Georgiev · Sorbonne University
In the contents: 1.07: Mathematical Modelling with First Order Dynamic Equations
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Partial Differential Equations
Niels Walet · University of Manchester
A partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model. PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics.
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International Finance - Theory and Policy
Anonymous · LibreTexts
Intermediate-level international economics texts seem to fall into one of two class. Some are written for students who may one day continue in advanced training and develop advanced general equilibrium models and use sophisticated mathematics. Other intermediate texts are written for noneconomics majors and present descriptive information about the world and the bare basics about how economic models are used to describe that world. This text strives to reach a median between both approaches.
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Elementary Algebra
Lynn Marecek (OpenStax) · Sante Ana College
In the contents: 03: Math Models
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Introductory Probability
Charles Grinstead & J. Laurie Snell · Dartmouth & Swarthmore Universities
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 and techniques necessary for a firm understanding of the subject. The text can be used in a variety of course lengths, levels, and areas of emphasis.
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Active Calculus
Matthew Boelkins, David Austin & Steven Schlicker · Grand Valley State University
The style of the Active Calculus text requires students to be active learners — there are very few worked examples in the text, with there instead being 3-4 activities per section that engage students in connecting ideas, solving problems, and developing understanding of key calculus concepts; each section begins with motivating questions, a brief introduction, and a preview activity, all of which are designed to be read and completed prior to class; the exercises are few in number.
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Physical Modeling in MATLAB
Allen B. Downey · Olin College
Modeling and simulation are powerful tools for explaining the world, making predictions, designing things that work, and making them work better. Learning to use these tools can be difficult; this book is my attempt to make the experience as enjoyable and productive as possible. By reading this book—and working on the exercises—you will learn some programming, some modeling, and some simulation. With basic programming skills, you can create models for a wide range of physical systems.
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Yet Another Calculus Text - A Short Introduction with Infinitesimals
Dan Sloughter · Furman University
This text is an introduction to calculus based on the hyperreal number system and uses infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, none are provided for the hyperreals. The text is aimed primarily at readers who already have some familiarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, in practice the pace is too fast for most o
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MTH 36: Trigonometry
Antonio Gonzalez · Chabot College
This text covers plane trigonometry. Includes circular and right triangle trigonometric functions; trigonometric equations, graphs and identities; triangle solutions. Polar coordinates.
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Introductory Quantum Mechanics
Richard Fitzpatrick · University of Texas at Austin
This book is intendedas an introductory course on non-relativistic quantum mechanics. Readers need to be reasonably familiar with Newtonian dynamics, elementary classical electromagnetism and special relativity, the physics and mathematics of waves (including the representation of waves via complex functions), basic probability theory, ordinary and partial differential equations, linear algebra, vector algebra, and Fourier series and transforms.
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Chabot College College Algebra for BSTEM
Najla AbraoChabot College · Chabot College College Algebra for BSTEM
College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that the book meets the needs of a variety of courses. College Algebraoffers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.
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Ordinary Differential Equations
Stephen Wiggins · University of Bristol
This book consists of ten weeks of material given as a course on ordinary differential equations (ODEs) for second year mathematics majors at the University of Bristol. It is the first course devoted solely to differential equations that these students will take.
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Complex Methods for the Sciences
Y. D. Chong · Nanyang Technological University
In the contents: 01: Mathematical Functions
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Modern Geometry
Wayne Bishop · California State University, Los Angeles
The standard approach is to develop more results of advanced Euclidean geometry first and to eventually back up and go into hyperbolic geometry. In order to get where we need to get, we will not formally develop some of the advanced Euclidean results that are logically needed because we would never get to the "modern" part of the course’s name. We will come back and develop, or at least introduce conceptually, some of these when we need them late in the course.
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Applied Geometric Algebra
László Tisza · Massachusetts Institute of Technology
The mathematical tools employed by physicists have expanded considerably, from differential calculus, vector algebra and geometry, to advanced linear algebra, tensors, Hilbert space, spinors, Group theory and many others. These course notes attempt at bringing conceptual clarity and unity to the application and interpretation of these advanced mathematical tools. In particular, there is an emphasis on the unifying role that Group theory plays in classical, relativistic, and quantum physics.
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Seven Sketches in Compositionality: An Invitation to Applied Category Theory
Brendan Fong & David I. Spivak · Massachusetts Institute of Technology
Category theory is a relatively new branch of mathematics that has transformed much of pure math research. The technical advance is that category theory provides a framework in which to organize formal systems and by which to translate between them, allowing one to transfer knowledge from one field to another. But this same organizational framework also has many compelling examples outside of pure math. In this text, we will give seven sketches on real-world applications of category theory.
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A First Course in Differential Equations for Scientists and Engineers
Russell Herman · University of North Carolina Wilmington
This book is written for an undergraduate course on the introduction to differential equations typically taken by majors in mathematics, the physical sciences, and engineering. In this course we will investigate analytical, graphical, and approximate solutions of differential equations. We will study the theory, methods of solution and applications of ordinary differential equations. This will include common methods of finding solutions, such as using Laplace transform and power series methods.
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Chem 371: P-Chem 2 to Folow Combined Biophysical and P-Chem 1
Jonathan Gutow · University of Wisconsin - Oshkosh
This compilation is aimed at second semester physical chemistry students who's first semester was a combined biophysical and physical chemistry course. It does expect students have enough math background to use concepts from multivariable calculus and calculus based physics.