Digital library
Textbooks, references and open learning resources.
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Relativity Lite - A Pictorial Translation of Einstein’s Theories of Motion and Gravity
Jack C. Straton · Portland State University
Relativity Lite is designed for courses like my 100-student General Astronomy sequence. Relativity Lite translates the mathematical equations conventional relativity texts rely upon into pictures that are readily understood and contain within them the mathematical essentials. This new book would provide the comprehensive coverage needed to understand, in sufficient depth, these three linked areas of our reality.
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Applied Calculus
Shana Calaway, Dale Hoffman, & David Lippman · LibreTexts
An openly licensed applied calculus textbook, covering derivatives, integrals, and an intro to multivariable calculus.
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Intermediate Algebra and Precalculus
Margaret H. Dean · Borough of Manhattan Community College
This course integrates Intermediate Algebra and Trigonometry with Precalculus. Topics include properties of real numbers, polynomials and factoring, equations and inequalities in one and two variables, systems of linear equations, rational expressions and functions, rational exponents and roots, quadratic functions, exponential and logarithmic functions, and trigonometric functions.
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Partial Differential Equations
Erich Miersemann · Universität Leipzig
Partial differential equations are differential equations that contains unknown multivariable functions and their partial derivatives
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Matrix Algebra with Computational Applications
Dirk Colbry · Michigan State University
In the contents: 42.2: Review of Python Math Package · 42.5: LaTeX Math · 44.2: Review of Python Math Package
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Differential Equations for Engineers
Jiří Lebl · Oklahoma State University
A one semester first course on differential equations, aimed at engineering students. This course covers techniques of solving ordinary differential equations including exact, separable, and linear equations; integrating factors; the method of undetermined coefficients; variation of parameters; Laplace transforms; series solutions; systems of differential equations; and applications.
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Introduction to the Modeling and Analysis of Complex Systems
Hiroki Sayama · Binghamton University, State University of New York
Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways.
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Abstract Algebra: Theory and Applications
Thomas W. Judson · Stephen F. Austing State University
In the contents: 2.01: Mathematical Induction
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Linear Algebra
Isaiah Lankham, Bruno Nachtergaele, & Anne Schilling · University of California, Davis
In the contents: 13.03: Some Common Mathematical Symbols and Abbreviations
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Biological Statistics
John H. McDonald · University of Delaware
The goal in that class is to teach biology students how to choose the appropriate statistical test for a particular experiment, then apply that test and interpret the results. In my class and in this textbook, I spend relatively little time on the mathematical basis of the tests; for most biologists, statistics is just a useful tool, like a microscope, and knowing the detailed mathematical basis of a statistical test is as unimportant to most biologists as knowing which kinds of glass were used
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Agent-Based Evolutionary Game Dynamics
Luis R. Izquierdo, Segismundo S. Izquierdo, & William H. Sandholm · University of Wisconsin - Madison
A guide to implement and analyze Agent-Based Models within the framework of Evolutionary Game Theory, using NetLogo
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Physics Formulas
Johan Wevers · Eindhoven University of Technology
This formulary is written at advanced undergraduate/postgraduate level. It is intended to be a short reference for anyone who works with physics and often needs to look up equations.
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Elementary College Geometry
Henry Africk · CUNY New York City College of Technology
This text is intended for a brief introductory course in plane geometry. It covers the topics from elementary geometry that are most likely to be required for more advanced mathematics courses. The only prerequisite is a semester of algebra. The emphasis is on applying basic geometric principles to the numerical solution of problems.
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Prealgebra
OpenStax · LibreTexts
In the contents: 09: Math Models and Geometry · 9.0E: 9.E: Math Models and Geometry (Exercises) · 9.0S: 9.S: Math Models and Geometry (Summary)
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Differential Equations for Engineers
Jiří Lebl · Oklahoma State University
A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence.
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Complex Analysis - A Visual and Interactive Introduction
Juan Carlos Ponce Campuzano · University of Queensland
The study of complex analysis is important for students in engineering and the physical sciences and is a central subject in mathematics. In addition to being mathematically elegant, complex analysis provides powerful tools for solving problems that are either very difcult or virtually impossible to solve in any other way. In this book you will find examples, problems and applets that allow you to explore complex analysis by using the visual interactive power of the computer (or tablet).
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Interactive Linear Algebra
Dan Margalit & Joseph Rabinoff · Georgia Institute of Technology
The name of the textbook highlights an important theme: the synthesis between algebra and geometry. It will be very important to us to understand systems of linear equations both algebraically (writing equations for their solutions) and geometrically (drawing pictures and visualizing).
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Introduction to Partial Differential Equations
Russell Herman · University of North Carolina Wilmington
This is a self-published text book with excellent coverage and solid mathematics and theory to support applications. Each chapter is rich in applications, described in good detail and fine exercises which involve solution techniques, but many applications and variations. There are many applications of second order differential equations with complete and thorough discussion of damping, eigenvalues, and characteristic equation.
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Algebra and Trigonometry
Jay Abramson · Arizona State University
Algebra is the study of mathematical symbols and the rules for manipulating these symbols. It is a unifying thread of almost all of mathematics. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Elementary algebra differs from arithmetic in the use of abstractions, such as using letters to stand for numbers that are either unknown or allowed to take on many values.
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Prealgebra
OpenStax · LibreTexts
In the contents: 09: Math Models and Geometry · 9.12: Math Models and Geometry (Exercises) · 9.13: Math Models and Geometry (Summary)