Digital library
Textbooks, references and open learning resources.
External
Multivariable Calculus Text (Supplement to Open Stax Text)
Karla Westphal · Saddleback College
This is a supplement to OpenStax Calculus V3. It is meant to substitute for section 4.2, limits of functions of more than 1 variable, placing less emphasis on using the definition directly and more on techniques like substitution, changing coordinate systems, and paths.
External
Calculus for Business and Social Sciences Corequisite Workbook
Victoria Dominguez, Cristian Martinez, & Sanaa Saykali · Citrus College
This text serves as a Corequisite Workbook for an Applied Calculus course. It is vitally important for students who take this course (and its corequisite) to have a thorough and complete refresher of Algebra skills needed for Calculus. These problems may be assigned as in-class practice problems, and can be also assigned as homework, to be graded and counted toward the Applied Calculus corequisite final grade.
External
Partial Differential Equations
Erich Miersemann · Universität Leipzig
Partial differential equations are differential equations that contains unknown multivariable functions and their partial derivatives
External
Math 175: Plane Trigonometry
LibreTexts
This course is designed for students who are majoring in math, science, and engineering. This course equips students with the skills necessary for success in pre-calculus. It presents the concepts of plane trigonometry using a functions approach. Included is a study of basic relations, functions, and transformations, as well as circular functions, trigonometric functions of angles, identities, inverse functions and their equations and solutions of triangles.
External
Matrix Algebra with Computational Applications
Dirk Colbry · Michigan State University
Matrix Algebra with Computational Applications is a collection of Open Educational Resource (OER) materials designed to introduce students to the use of Linear Algebra to solve real world problems. These materials were developed specifically for students and instructors working in a “flipped classroom” model that emphasizes hands-on problem solving activities during class meetings, with students watching lectures and completing readings and assignments outside of the classroom.
External
Math 098: Intermediate Algebra for Calculus
Highline College
This text introduces a variety of algebraic techniques and functions that will prepare you for calculus. Focus will be placed on quadratic, rational, and radical functions with emphasis on algebraic techniques used to combine and simplify them. Techniques will include factoring, simplifying (adding/subtracting/multiplying/dividing) polynomials, rational and radical expressions, and relationships between equations and their respective functions and graphs.
External
Math C097: Support for Precalculus Corequisite: MATH C170
Chau D. Tran · Coastline College
This course includes, but not limited to piece-wise, composite, inverse, polynomial, rational, exponential, and logarithmic functions. Also discussed are properties of functions, their relationship to equations and inequalities, as well as applications, and circles.
External
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.
External
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.
External
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.
External
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
External
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.
External
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
External
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.
External
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
External
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.
External
First Semester Calculus (Westphal, adapted from Open Stax)
Karla Westphal · Saddleback College
This text is a first semester calculus text adapted from the OpenStax Calculus 1 text. Some of the material has been re-ordered; the primary change is that derivatives of exponential and log functions are covered earlier in chapter 3 than they were in the OpenStax text.
External
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.
External
Math 372: College Algebra for Calculus
Roy Simpson · Cosumnes River College
In the contents: 10: Appendix - The Language of Mathematics
External
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.