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This week we will examine the concept of a function, a fundamental concept underlying all of modern mathematics. You’re undoubtedly already familiar with functions in an intuitive sense: a function is something which, given
an input, produces an output. But you’ve probably never seen the formal definition of a function as it relates to set theory, which is what we’ll look at this week.

Subject:
Functions
Material Type:
Author:
Brent Yorgey
06/03/2021
Only Sharing Permitted
CC BY-ND
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This book will initiate you into an esoteric world. You will learn and apply the methods of thought that mathematicians use to verify theorems, explore mathematical truth and create new mathematical theories. This will prepare you for advanced mathematics courses, for you will be better able to understand proofs, write your own proofs and think critically and inquisitively about mathematics.

Subject:
Functions
Material Type:
Textbook
Provider:
Virginia Commonwealth University
Author:
Richard Hammack
01/01/2009
Unrestricted Use
CC BY
Rating
0.0 stars

This course is an introduction to contemporary calculus and is the first of a three-part sequence. In this course students explore the concepts, applications, and techniques of Calculus - the mathematics of change. Calculus has wide-spread application in science, economics and engineering, and is a foundation college course for further work in these areas. This is a required class for most science and mathematics majors.Login: guest_oclPassword: ocl

Subject:
Calculus
Functions
Material Type:
Full Course
Homework/Assignment
Lecture Notes
Lesson Plan
Syllabus
Provider:
Washington State Board for Community & Technical Colleges
Provider Set:
Open Course Library
10/31/2011
Conditional Remix & Share Permitted
CC BY-NC-SA
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0.0 stars

CK-12's Texas Instruments Calculus Teacher's Edition is a useful companion to a Calculus course, offering extra assignments and opportunities for students to understand course material through their graphing calculator.

Subject:
Calculus
Functions
Material Type:
Textbook
Provider:
CK-12 Foundation
Provider Set:
CK-12 FlexBook
Author:
Jordan, Lori
12/17/2010
Conditional Remix & Share Permitted
CC BY-NC-SA
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0.0 stars

We told you about the derivatives of many functions, but you might want proof that what we told you is actually true. That's what this tutorial tries to do!

Subject:
Calculus
Functions
Material Type:
Lecture
Provider:
Provider Set:
08/13/2020
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.

Subject:
Functions
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
David I. Spivak
01/01/2013
Some Rights Reserved
Rating
0.0 stars

Subject:
Mathematics
Functions
Material Type:
Textbook
Provider:
Dartmouth College
Author:
Kenneth Bogart
01/01/2004
Conditional Remix & Share Permitted
CC BY-NC-SA
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0.0 stars

This site teaches Building Functions to High Schoolers through a series of 1355 questions and interactive activities aligned to 13 Common Core mathematics skills.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Interactive
Provider:
Provider Set:
08/13/2020
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
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This site teaches Interpreting Functions to High Schoolers through a series of 3578 questions and interactive activities aligned to 38 Common Core mathematics skills.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Interactive
Provider:
Provider Set:
08/13/2020
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
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This site teaches Linear, Quadratic, and Exponential Models to High Schoolers through a series of 137 questions and interactive activities aligned to 6 Common Core mathematics skills.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Interactive
Provider:
Provider Set:
08/13/2020
Conditional Remix & Share Permitted
CC BY-NC-SA
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This site teaches Trigonometric Functions to High Schoolers through a series of 915 questions and interactive activities aligned to 15 Common Core mathematics skills.

Subject:
Mathematics
Functions
Material Type:
Activity/Lab
Interactive
Provider:
Provider Set:
08/13/2020
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
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This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB in particular.

Subject:
Computer Science
Information Science
Functions
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Yossi Farjoun
01/01/2011
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This is a fast-paced introductory course to the C++ programming language. It is intended for those with little programming background, though prior programming experience will make it easier, and those with previous experience will still learn C++-specific constructs and concepts. This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

Subject:
Computer Science
Information Science
Functions
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Dunietz, Jesse
Kovacs, Geza
Marrero, John
01/01/2010
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

" This is a undergraduate course. It will cover normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of L-p spaces; Hilbert space; compact, Hilbert-Schmidt and trace class operators; as well as spectral theorem."

Subject:
Functions
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Melrose, Richard
01/01/2009
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course.

The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.

Subject:
Mathematics
Calculus
Functions
Material Type:
Textbook
Provider:
Trinity University
Provider Set:
Digital Commons @Trinity University
Author:
William Trench
12/01/2013
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
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First of two-term sequence on modeling, analysis and control of dynamic systems. Mechanical translation, uniaxial rotation, electrical circuits and their coupling via levers, gears and electro-mechanical devices. Analytical and computational solution of linear differential equations and state-determined systems. Laplace transforms, transfer functions. Frequency response, Bode plots. Vibrations, modal analysis. Open- and closed-loop control, instability. Time-domain controller design, introduction to frequency-domain control design techniques. Case studies of engineering applications.

Subject:
Functions
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Dubowsky, Steven
Trumper, David L.
01/01/2005
Unrestricted Use
CC BY
Rating
5.0 stars

The attached file is a .bok TestGen file which contains the first two chapters of the OpenStax College Algebra Textbook. Using the TestGen software, one can create quizzes, tests and homework assignments compatible with Canvas, Blackboard, Moodle and D2L.

Subject:
Algebra
Functions
Numbers and Operations
Ratios and Proportions
Material Type:
Activity/Lab
Assessment
Homework/Assignment
Textbook
Unit of Study
Author:
Larry Whittington
12/20/2021
Unrestricted Use
CC BY
Rating
0.0 stars

This course will cover families of functions, their properties, graphs and applications. These functions include: polynomial, rational, exponential, logarithmic functions and combinations of these. We will solve related equations and inequalities and conduct data analysis, introductory mathematical modeling and develop competency with a graphing calculator.Login: guest_oclPassword: ocl

Subject:
Functions
Material Type:
Full Course
Homework/Assignment
Lecture Notes
Lesson Plan
Syllabus
Provider:
Washington State Board for Community & Technical Colleges
Provider Set:
Open Course Library
10/31/2011
Unrestricted Use
CC BY
Rating
5.0 stars

This is an example of a redesigned course that uses the OpenStax PreCaculus Textbook. Emphasis is placed on the structure of course (which is not conics centric) and how homework is implemented. To avoid the financial responsiblity of the student or higher education institution purchasing publisher online homework services like Pearson's MyMathLab, ConnectMath or Aleks; students are assigned exercises from the textbook that have answers available. The strategy is to give access to the answers of the problems so that the students have to prove how the answer was obtained. This allows the students some immediate feedback if their written process does not obtain the solution given in the back of the textbook.This allows the student to recognize that a process, operation or strategy was carried out incorrectly which can be used to draw attention that a question needs to be raised during the next lecture or additional assistance may be required on their journey to mastery of the content.

Subject:
Mathematics
Algebra
Calculus
Functions
Ratios and Proportions
Material Type:
Full Course
Homework/Assignment
Syllabus
Author:
Larry Whittington
12/23/2021
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

This is a text that covers the standard topics in a sophomore-level course in discrete mathematics: logic, sets, proof techniques, basic number theory, functions, relations, and elementary combinatorics, with an emphasis on motivation. It explains and clarifies the unwritten conventions in mathematics, and guides the students through a detailed discussion on how a proof is revised from its draft to a final polished form. Hands-on exercises help students understand a concept soon after learning it. The text adopts a spiral approach: many topics are revisited multiple times, sometimes from a different perspective or at a higher level of complexity. The goal is to slowly develop students’ problem-solving and writing skills.

Subject:
Mathematics
Functions
Numbers and Operations
Material Type:
Textbook
Provider:
State University of New York
Provider Set:
Milne Open Textbooks
Author:
Harris Kwong, SUNY Fredonia