Digital library
Textbooks, references and open learning resources.
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CLP-3 Multivariable Calculus
Joel Feldman, Andrew Rechnitzer, & Elyse Yeager · University of British Columbia
This textbook covers multivariable Calculus. There are chapters on vectors and geometry in 2 and 3 dimensions, partial derivatives, and multivariable integrals.
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Math 141: Precalculus I (old edition)
LibreTexts
This text prepares students for the calculus sequence. Real-valued functions, including techniques for graphing polynomial, rational, piecewise, exponential, and logarithmic functions. The text also includes circles, basic function properties, nonlinear inequalities, and complex numbers.
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MAT 2410: Calculus 1
Peggy Beck · Prince George's Community College
This texts address a three-semester sequence of university-level calculus for a variety of majors including, but not exclusive to, science, engineering, and mathematics. It provides an introduction to single variable calculus; study of limits, continuity, differentiation and its applications, definite and indefinite integrals and the Fundamental Theorem of Calculus.
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Real Analysis
Eugene Boman & Robert Rogers · Pennsylvania State University & SUNY Fredonia
The typical introductory real analysis text starts with an analysis of the real number system and uses this to develop the definition of a limit, which is then used as a foundation for the definitions encountered thereafter. While this is certainly a reasonable approach from a logical point of view, it is not how the subject evolved, nor is it necessarily the best way to introduce students to the rigorous but highly non-intuitive definitions and proofs found in analysis.
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APEX PreCalculus
Amy Givler Chapman, Meagan Herald, Jessica Libertini · Virginia Military Institute
This text is not intended to fully prepare students with all of the mathematical knowledge they need to tackle Calculus, rather it is designed to review mathematical concepts that are often stumbling blocks in the Calculus sequence. It starts basic and builds to more complex topics. This text is written so that each section and topic largely stands on its own, making it a good resource for students in Calculus who are struggling with the supporting mathemathics found in Calculus courses.
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Math 10: Elementary Statistics
Zoya Kravets · Mission College
Students study and demonstrate knowledge and understanding of descriptive and inferential statistics including data analysis, correlation and linear regression, probability, probability distributions and assorted hypothesis testing. Particular emphasis is placed on applications.
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An Introduction to Proof via Inquiry-Based Learning
Dana Ernst · Northern Arizona University
This book is intended to be used for a one-semester/quarter introduction to proof course (sometimes referred to as a transition to proof course). The purpose of this book is to introduce the reader to the process of constructing and writing formal and rigorous mathematical proofs. The intended audience is mathematics majors and minors. However, this book is also appropriate for anyone curious about mathematics and writing proofs.
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Math 142: Precalculus II
LibreTexts
This text prepares students for calculus sequence. Concepts, properties and algebra of trigonometric functions, including their graphs, inverses, laws of sines and cosines, identities and equations. The text also covers vectors, polar coordinates and conic sections.
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MATH 011: Math Concepts for Elementary School Teachers – Number Systems
Melissa Flora · College of the Desert
In the contents: 11.01: Careful Use of Language in Mathematics
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MAT 1350: Precalculus Part I
Jay Abramson · Prince George's Community College
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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MAT 206Precalculus
Borough of Manhattan Community College · LibreTexts
OpenStax Precalculus text, modified for MAT 206-1202, Professor Margaret Dean, Mathematics Department, BMCC/CUNY
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Vector Calculus
Michael Corral · Schoolcraft College
The term "vector calculus" is sometimes used as a synonym for the broader subject of multivariable calculus. Vector calculus is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space. The content in this Textmap is complemented by Vector Calculus Modules in the Core and the Vector Calculus (UCD Mat 21D) Libretext.
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Understanding Linear Algebra
David Austin · Grand Valley State University
This book arises from my belief that linear algebra, as presented in a traditional undergraduate curriculum, has for too long lived in the shadow of calculus. Many mathematics programs currently require their students to complete at least three semesters of calculus, but only one semester of linear algebra, which often has two semesters of calculus as a prerequisite.
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Elementary Number Theory
Mike Barrus & W. Edwin Clark · University of Rhode Island
The great Carl Friedrich Gauss once wrote, "Mathematics is the queen of sciences and arithmetic the queen of mathematics." What Gauss called arithmetic, we now call number theory. This text is an extensive update of an original manuscript by Professor W. Edwin Clark (now Emeritus) of the University of South Florida, written in 2002 and made freely available on his website. It is designed for a one-semester undergraduate course and for self study.
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Math 400: Calculus I - Differential Calculus
Roy Simpson · Cosumnes River College
This text explores the basic concepts of analytic geometry, limits (including indeterminate forms), derivatives, and integrals. The topics covered will include graphs, derivatives, and integrals of algebraic, trigonometric, exponential, logarithmic, and hyperbolic functions. Standard proofs will be covered, such as delta-epsilon proofs and proofs of some theorems. Applications will be covered, including those involving rectilinear motion, differentials, related rates, graphing, and optimization.
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Math C180: Calculus I
Chau D Tran · Coastline College
This is the first course in the calculus sequence. It satisfies the requirement for majors in mathematics, science, or engineering. Topics include limits, derivatives of algebraic and transcendental functions, applications of derivatives, indefinite integrals, definite integrals, the Fundamental Theorem of Calculus, and applications of integration.
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Linear Algebra
David Cherney, Tom Denton, & Andrew Waldron · University of California, Davis
Linear algebra is the study of vectors and linear transformations. This text is suitable for a sophomore level linear algebra course taught in about twenty-five lectures. It is designed both for engineering and science majors, but has enough abstraction to be useful for potential math majors. Our goal in writing it was to produce students who can perform computations with linear systems and also understand the concepts behind these computations.
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Introduction to Mathematical Analysis I
Lafferriere, Lafferriere, and Nguyen · LibreTexts
Our goal with this textbook is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. Students should be familiar with most of the concepts presented here after completing the calculus sequence. However, these concepts will be reinforced through rigorous proofs.
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A Primer of Real Analysis
Dan Sloughter · Furman University
This is a short introduction to the fundamentals of real analysis. Although the prerequisites are few, I have written the text assuming the reader has the level of mathematical maturity of one who has completed the standard sequence of calculus courses, has had some exposure to the ideas of mathematical proof (including induction), and has an acquaintance with such basic ideas as equivalence relations and the elementary algebraic properties of the integers.
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Applied Geometric Algebra (Tisza)
László Tisza · Massachusetts Institute of Technology
Over the last 100 years, 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.