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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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Math C185: Calculus II
Michael Everett · Coastline College
Second course in the calculus sequence. It satisfies the requirement for majors in mathematics, science, or engineering. Topics include techniques and applications of integration, calculus applied to parametric curves and polar curves, analytic geometry, sequences, series, and an introduction to differential equations.
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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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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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College Technical Math 1B (NWTC)
LibreTexts
This text covers advanced mathematical concepts essential for technical fields, including polynomials, factoring, quadratic equations, rational expressions, and systems of equations. It equips students with the skills needed for technical problem-solving and further studies in mathematics.
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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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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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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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Math 223 Calculus 3
LibreTexts
This book considers what happens when we broaden our view of what a function is to include functions that have more than one input, or that produce more than one result, or both. In particular, we consider what it means for such a function to have a limit, and how to differentiate or integrate such functions. In the course of learning these things, we will also encounter many applications of so-called multivariable and vector-valued functions in the natural and social sciences.
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Mathematical Computing with Python
Dennis Hall · Angelo State University
In-progress textbook based on course notes from Angelo State University's Numerical Analysis (Math 4311) course.
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HiSetMatematicas
Saul Lopez · Santiago Canyon College
LibreTexts
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Numerical Methods
Jeffrey R. Chasnov · Hong Kong University of Science and Technology
These notes, taught at the Hong Kong University of Science and Technology with two lecture hours per week, are primarily for non-mathematics majors and were required by several engineering departments.
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Math 222: Calculus II
LibreTexts
Math 222, Calculus II, is the second semester course of the calculus series and is intended as a continuation of the development of single-variable calculus. We will cover the differential calculus of transcendental functions (exponentials, logarithms, inverse trig functions, etc.) as well as continue the integral calculus we began in Math 221, Calculus I. We will introduce techniques of integration such as integration by parts, trigonometric substitution, and partial fraction decompositions.
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An IBL Introduction to Geometries
Mark A. Fitch · University of Alaska Anchorage
This text was designed for an IBL approach to Introduction to Geometries and covers geometry topics required for secondary teacher certification. As a result it covers synthetic, transformational, and a tiny bit of analytic approaches to geometry and covers both Euclidean (parabolic), hyperbolic, and some projective geometry. Students are expected to have completed a proofs course covering proof techniques, basic set operations, and cardinality as a prerequisite.
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Analytic Geometry and Calculus I (IVC Math 3A OER)
Leonard Lamp, Kenn Huber & Mohamad Youssef · Irvine Valley College
This course covers basic concepts of analytic geometry, limits and continuity; and differentiation and integration of algebraic, trigonometric, exponential, logarithmic and hyperbolic functions. Applications include related rates and optimization problems. L'hospital's rule is studied. Credit may be earned in MATH 3A or 3AH, but not both. C-ID: MATH 210
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Visual Statistics Use R!
Alexey Shipunov · Minot State University
The ignorance of the statistical methods can lead to mistakes and misinterpretations. Unfortunately, understanding of these methods is far from common. Many college majors require a course in probability theory and mathematical statistics, but all many of us remember from these courses is horror and/or frustration at complex mathematical formulas filled with Greek letters, some of them wearing hats.
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Elementary Trigonometry
Michael Corral · Schoolcraft College
This is a text on elementary trigonometry, designed for students who have completed courses in high-school algebra and geometry. Though designed for college students, it could also be used in high schools. The traditional topics are covered, but a more geometrical approach is taken than usual. Also, some numerical methods (e.g. the secant method for solving trigonometric equations) are discussed. A brief tutorial on using Gnuplot to graph trigonometric functions is included.