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Textbooks, references and open learning resources.
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Calculus II: Integral Calculus
Doli Bambhania, Neelam R. Shukla & Danny Tran · De Anza College
This second book in a four-part calculus series is designed for both beginners and advanced students, emphasizing a strong conceptual foundation. It explores essential topics such as rates of change and calculating areas and volumes of irregular shapes, with numerous examples and applications across physics, economics, and engineering.
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Elementary Abstract Algebra
W Edwin Clark · University of South Florida
This book is intended for a one semester introduction to abstract algebra. We assume that students have some familiarity with basic set theory linear algebra and calculus. But very little of this nature will be needed To a great extent the course is self contained except for the requirement of a certain amount of mathematical maturity. And hopefully the student's level of mathematical maturity will increase as the course progresses.
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Numerically Solving Ordinary Differential Equations
Stuart Brorson · Northeastern University
The booklet covers basic Euler solvers, Runge-Kutta, and linear multistep methods and discusses explicit vs. implicit methods. It discusses stability and the stability domains of some of the methods and talks about adaptive methods and the concept of stiffness and concluding with a chapter on symplectic methods and why they are important. Beyond the solver algorithms, the book includes many example ODEs and shows their solutions using the methods discussed. Matlab programs accompany the text.
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Complex Variables with Applications
Jeremy Orloff · Massachusetts Institute of Technology
Complex analysis is a basic tool in many mathematical theories. By itself and through some of these theories it also has a great many practical applications. There are a small number of far-reaching theorems that we’ll explore in the first part of the class. Along the way, we’ll touch on some mathematical and engineering applications of these theorems. The last third of the class will be devoted to a deeper look at applications.
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Combinatorics
Joy Morris · University of Lethbridge
Combinatorics is an upper-level introductory course in enumeration, graph theory, and design theory. The text focuses on combinations and arrangements of discrete structures. There are five major branches of combinatorics that we will touch on in this course: enumeration, graph theory, Ramsey Theory, design theory, and coding theory. We will focus on enumeration, graph theory, and design theory, but will briefly introduce the other two topics.
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Math C280: Calculus III
Michael Everett · Coastline College
LibreTexts
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Differential Calculus for the Life Sciences
Leah Edelstein-Keshet · University of British Columbia
Calculus arose as a tool for solving practical scientific problems through the centuries. However, it is often taught as a technical subject with rules and formulas (and occasionally theorems), devoid of its connection to applications. In this course, the applications form an important focal point, with emphasis on life sciences. This places the techniques and concepts into practical context, as well as motivating quantitative approaches to biology taught to undergraduates.
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Math 4A: Multivariable Calculus
Kenn Huber · Irvine Valley College
This textbook covers a standard course in multivariable calculus. Studies include the three dimensional space, vectors, space curves, surfaces, multivariable functions, limits, partial derivatives, tangent planes, extrema, double and triple integration, changes of variables, line integrals, surface integrals, and the four major Theorems to connect these topics.
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Math C180: Calculus I (Nguyen)
Math C180: Calculus I · Son Nguyen
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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MATH 241: Calculus 3
Justin Wyss-Gallifent · University of Maryland
An introduction to multivariable calculus, including vectors and vector-valued functions, partial derivatives and applications of partial derivatives (such as tangent planes and Lagrange multipliers), multiple integrals, volume, surface area, and the classical theorems of Green, Stokes and Gauss.
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MATH 2150: Higher Arithmetic
Pamini Thangarajah · Mount Royal University
This course explores elementary number theory, numeration systems, operations on integers and rational numbers, and elementary combinatorics, using both inductive and deductive methods. Emphasis will be placed on the development of clarity and understanding of mathematical processes and ideas, the application of these ideas to problem-solving and the communication of these ideas to other people.
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An Introduction to the Theory of Numbers
Leo Moser · University of Alberta
This book, which presupposes familiarity only with the most elementary concepts of arithmetic (divisibility properties, greatest common divisor, etc.), is an expanded version of a series of lectures for graduate students on elementary number theory. Topics include: Compositions and Partitions; Arithmetic Functions; Distribution of Primes; Irrational Numbers; Congruences; Diophantine Equations; Combinatorial Number Theory; and Geometry of Numbers.
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MATH 110: Techniques of Calculus I
Debbie Gaydos · Penn State University, Greater Allegeheny
Page notifications On picture_as_pdf Readability Cite this page An openly licensed applied calculus textbook, covering derivatives, integrals, and an intro to multivariable calculus.
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College Algebra (NWTC)
Northeast Wisconsin Technical College · College Algebra (NWTC)
This text covers a comprehensive range of algebraic principles, including equations and inequalities, functions, polynomial and rational functions, exponential and logarithmic functions, and systems of equations and inequalities. It provides a solid foundation in algebra.
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Mathematical Reasoning
Pamini Thangarajah · Mount Royal University
In the contents: 1: Basic Language of Mathematics · 1.0 : Introduction to the Basic Language of Mathematics · 1.E: Basic Language of Mathematics (Exercises)
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Linear Algebra with Applications
W. Keith Nicholson · University of Calgary
The aim of the textbook is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work. The contents have enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course.
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Business Calculus with Excel
Mike May, S.J. & Anneke Bart · Saint Louis University
This text is intended for a one semester calculus course for business students with the equivalent of a college algebra prerequisite. Rather than being a three-semester engineering calculus course that has been watered down to fit into one semester it is designed for the business students.
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Combinatorics and Graph Theory
David Guichard · Whitman College
Combinatorics is often described briefly as being about counting, and indeed counting is a large part of combinatorics.Graph theory is concerned with various types of networks, or really models of networks called graphs. These are not the graphs of analytic geometry, but what are often described as "points connected by lines''.
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Differential Equations and Linear Algebra
Anup Lamichhane · Oho Northern University
In this book, you will learn key techniques for solving differential equations that arise in science and engineering applications. You will also build a strong foundation in linear algebra concepts that support these methods.
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An Inquiry-Based Approach to Abstract Algebra
Dana Ernst · Northern Arizona University
In the contents: 9.03: A.3- Definitions in Mathematics