Digital library
Textbooks, references and open learning resources.
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Riemann-Stieltjes Integration on Time Scales
Svetlin G. Georgiev · Sorbonne University
S. Hilger introduced in 1990 the calculus on time scales or on measure chains.This kind of calculus showed the possibility to manage dynamic equations considering a very wide range of time scales transforming in this way the differential and difference calculus into special cases of a more general one. Examples of time scales are the real numbers, the integers, the sets having cluster points or even such as the Cantor set. In this cycle we study the process of Riemann-Stieltjes delta integrati
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PGCC: PHYS 2030 - General Physics
Neeharika Thakur · Prince George's Community College
This text addresses a calculus-based survey of kinetic theory, thermodynamics, electricity, and magnetism and electromagnetic phenomena. For science/engineering transfers.
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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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Transition to Higher Mathematics
Bob Dumas and John E. McCarthy · University of Washington and Washington University in St. Louis
This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics. This is the second edition of our text. It is intended for students who have taken a calculus course, and are interested in learning what higher mathematics is all about. It can be used as a textbook for an "Introduction to Proofs" course, or for self-study.
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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
In the contents: 7.05: The Fundamental Theorem of Calculus
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Applied Geometric Algebra (Tisza)
László Tisza · Massachusetts Institute of Technology
In the contents: 04: Spinor Calculus
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Elementary Trigonometry
Richard W. Beveridge · Clatsop Community College
Ancient trigonometry typically used angles and triangles that were embedded in circles so that many of the calculations used were based on the lengths of chords within a circle. The relationships between the lengths of the chords and other lines drawn within a circle and the measure of the corresponding central angle represent the foundation of trigonometry - the relationship between angles and distances.
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Trigonometry
Katherine Yoshiwara · Los Angeles Pierce College
This text covers the content of a standard trigonometry course, beginning with a review of facts from geometry.
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University Physics III: Optics & Modern Physics
OpenStax · LibreTexts
University Physics is designed for the two- or three-semester calculus-based physics course. This volume explores optics and modern physics, beginning with how light behaves through reflection, refraction, interference, and diffraction. It then moves into relativity and quantum mechanics, introducing photons, matter waves, and atomic structure. The text also covers condensed matter, nuclear physics, and cosmology, linking theory to technologies like lasers, semiconductors, and medical imaging.
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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.
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All Things Flow - Fluid Mechanics for the Natural Sciences
Bill Smyth · Oregon State University
In the contents: 04: Tensor Calculus · 4.01: Vector calculus operations
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Conceptual Mathematics in Society
Ricela Feliciano-Semidei · Northern Illinois University
This textbook supports a strong preparation for the precalculus and calculus sequence through college-level skills to complete mathematical work and to develop conceptual understanding, rather than focusing solely on memorization and repetition of processes.
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Mission College MAT 003B
Benjamin Fineman · Mission College
In the contents: 1.03: The Fundamental Theorem of Calculus · 1.08: Calculus of the Hyperbolic Functions
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Geometry with an Introduction to Cosmic Topology
Michael P. Hitchman · Linfield College
Motivated by questions in cosmology, the open-content text Geometry with an Introduction to Cosmic Topology uses Mobius transformations to develop hyperbolic, elliptic, and Euclidean geometry - three possibilities for the global geometry of the universe. The text, written for students who have taken vector calculus, also explores the interplay between the shape of a space and the type of geometry it admits.
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Elementary First Order Dynamic Equations on Time Scales
Svetlin G. Georgiev · Sorbonne University
This text introduces basic first-order differential-like equations within the framework of time scales calculus, a mathematical theory that unifies differential equations (continuous time) and difference equations (discrete time) into a single approach.
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Introductory Physics: Building Models to Describe Our World
Ryan D. Martin, Emma Neary, Joshua Rinaldo, and Olivia Woodman · Queen's University
In the contents: 3.03: Using Calculus to Describe Motion · 17.04: Interpretation of Gauss Law and vector calculus · 26: Calculus
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Applied Geometric Algebra
László Tisza · Massachusetts Institute of Technology
In the contents: 05: Spinor Calculus
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Chem 371: P-Chem 2 to Folow Combined Biophysical and P-Chem 1
Jonathan Gutow · University of Wisconsin - Oshkosh
This compilation is aimed at second semester physical chemistry students who's first semester was a combined biophysical and physical chemistry course. It does expect students have enough math background to use concepts from multivariable calculus and calculus based physics.
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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.