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Giáo trình, tài liệu tham khảo và tài nguyên học tập mở.
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Mathematical Methods
Pamini Thangarajah · Mount Royal University
Mathematical Methods provides an introduction to vector calculus, ordinary differential equations, and partial differential equations including a variety of applications. Topics include: optimization, line and surface integrals, Green’s theorem, Stokes’ theorem, the Divergence theorem, and the theory of systems of linear differential equations.
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Open Algebra and Knots
Matthew Salomone · Bridgewater State University
The theory of knots has been well studied since the early 20th century, and has many connections to geometry and topology, and applications to physics, biology, and beyond. We’ll investigate perhaps its most fundamental connection: to algebra. In what ways are knots algebraic objects? How can we use algebraic structures and reasoning to classify knots? And how can this help us to think algebraically beyond the classroom?
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CLP-4 Vector Calculus (Feldman, Rechnitzer, and Yeager)
Joel Feldman, Andrew Rechnitzer and Elyse Yeager · University of British Columbia
This textbook covers Vector Calculus. There are chapters on curves, vector fields, surface integrals and integral theorems (such as the divergence theorem).
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Scientific Computing
Peter Staab · Fitchburg State University
Solving problems is the essence of scientific computing. Many problems arise naturally from the sciences or mathematics and often to solve difficult problem relies on some computing resources. In a nutshell, this text is the blend of science, mathematics and computer science needed to solve problems. The intended audience for this text one who is interested in writing computer code that will solve a problem that you have.
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MTH 65: Algebra 2
Math Department · Clackamas Community College
TThis book builds a strong algebra foundation. You’ll review core skills like order of operations, fractions, and linear equations, then expand into polynomials, exponents, roots, and radicals. Finally, you’ll explore absolute value to model distance, tolerance, and precision. These connected skills form a toolkit to solve problems confidently and prepare you for advanced math and real-world applications.
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Matrix Analysis
Steve Cox · Rice University
Equilibria and the solution of linear and linear least squares problems. Dynamical systems and the eigenvalue problem with the Jordan form and Laplace transform via complex integration.
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MATH 1200: Calculus for Scientists I
Pamini Thangarajah · Mount Royal University
This course provides an introduction to calculus with exposure to applications in sciences. The main concepts covered are limits, derivatives, and integrals. Derivatives of transcendental functions are used to solve optimization, linear approximation, and related rates problems. Studying calculus will expose students to a variety of important mathematical ideas and help students develop their critical thinking and problem solving skills.
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NWFSC MGF 1130 Text
Allison Godwin · Northwest Florida State University
MGF 1130: Mathematical Thinking is a general education mathematics course designed to improve practical problem-solving skills and logical reasoning
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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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TMCC: Precalculus I and II
OpenStax · LibreTexts
This precalculus textmap is intended for college-level Precalculus students and is a comprehensive book that covers more ground than an instructor could likely cover in a typical one- or two-semester course; but instructors should find, almost without fail, that the topics they wish to include in their syllabus are covered in the text.
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Arithmetic and Algebra
Samar ElHitti, Marianna Bonanome, Holly Carley, Thomas Tradler, & Lin Zhou · CUNY New York City College of Technology & NYC College of Technology
Arithmetic | Algebra provides a customized open-source textbook for the math developmental students at New York City College of Technology. The book consists of short chapters, addressing essential concepts necessary to successfully proceed to credit-level math courses. Each chapter provides several solved examples and one unsolved “Exit Problem”. Each chapter is also supplemented by its own WeBWork online homework assignment.
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Active Prelude to Calculus
Matthew Boelkins, David Austin & Steven Schlicker · Grand Valley State University
This text is designed for college students who aspire to take calculus and who either need to take a course to prepare them for calculus or want to do some additional self-study. Many of the core topics of the course will be familiar to students who have completed high school. At the same time, we take a perspective on every topic that emphasizes how it is important in calculus. The reader will find that the text requires them to engage actively with the material.
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Math C185: Calculus II (Tran)
Chau D. Tran · Coastline College
LibreTexts
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Applied Calculus
Shana Calaway, Dale Hoffman, & David Lippman · LibreTexts
An openly licensed applied calculus textbook, covering derivatives, integrals, and an intro to multivariable calculus.
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Intermediate Algebra and Precalculus
Margaret H. Dean · Borough of Manhattan Community College
This course integrates Intermediate Algebra and Trigonometry with Precalculus. Topics include properties of real numbers, polynomials and factoring, equations and inequalities in one and two variables, systems of linear equations, rational expressions and functions, rational exponents and roots, quadratic functions, exponential and logarithmic functions, and trigonometric functions.
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Partial Differential Equations
Erich Miersemann · Universität Leipzig
Partial differential equations are differential equations that contains unknown multivariable functions and their partial derivatives
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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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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.
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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.
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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.