Digital library
Textbooks, references and open learning resources.
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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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Math 370: Precalculus
Carl Stitz & Jeff Zeager · Lakeland Community College & Lorain County Community College
This course improves upon the foundational mathematics and critical thinking skills required in the calculus sequence for STEM majors. Course content includes a rigorous treatment of the properties of polynomial, rational, exponential, logarithmic, and trigonometric functions. Additional topics include systems of linear and non-linear equations and inequalities, conic sections, sequences and series, analytic geometry, vectors, parametric equations, and polar equations.
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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
This is an open source textbook designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many nontrivial applications. The first half of the book presents group theory, through the Sylow theorems. The second-half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galo
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Math 126: Calculus with Review II
Katharine Vance · Hope College
This course is a continuation of Math 125. The topics covered are the topics typically taught in the second half of a Calculus I course. The calculus material in the course is supplemented by reviewing topics of high school mathematics as needed. The calculus topics are also taught at a slower pace. Topics include implicit differentiation, applications of differentiation, L'Hospital's rule, Newton's method, the integral, and applications of integration.
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Math 130: Math for Elementary School Teachers
Amy Lagusker · College of the Canyons
In the contents: 01: Overview of Elementary Common Core Mathematics · 1.02: The Importance of Mathematics for Elementary School Students · 02: Empathy and Primary Mathematics
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Math 401: Calculus II - Integral Calculus
Roy Simpson · Cosumnes River College
Topics covered will include techniques of integration, numerical integration, improper integrals, infinite series, parametric equations, polar equations, and possibly conic sections. Many applications will be covered including those involving areas between planar curves, volumes of revolution, work, moments, center of mass, average value, arc length, and surface area.
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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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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
Prealgebra is designed to meet scope and sequence requirements for a one-semester prealgebra course. The text introduces the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. Each topic builds upon previously developed material to demonstrate the cohesiveness and structure of mathematics.
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Math 372: College Algebra for Calculus
Roy Simpson · Cosumnes River College
In the contents: 10: Appendix - The Language of Mathematics
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Friendly Introduction to Mathematical Logic
Christopher Leary & Lars Kristiansen · SUNY Geneseo & University of Oslo
At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary’s user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study.
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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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Math 373: Trigonometry for Calculus
Roy Simpson · Cosumnes River College
In the contents: 10: The Language of Mathematics
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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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Math 15E - Concurrent Support for Quantitative Reasoning
LibreTexts
Topics from intermediate algebra and geometry are covered to build a foundation for college-level quantitative reasoning. Strategic reading, critical thinking and problem solving are incorporated to build the strategies needed to solve contextualized problems. Topics in the area of study skills and metacognition are also included to support students in a college level math course.
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Math 111: College Algebra
Highline College
This texts address applications of functions (linear, quadratic, exponential and logarithmic) in business and social sciences, including total cost revenue and profit; break-even analysis; supply/demand and market equilibrium; exponential growth and decay; fitting curves to data with graphing utilities; theory of matrices; graphical methods for optimization (linear programming problems); and mathematics of finance (arithmetic and geometric sequences and sums).
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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.