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Book of Proof
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
Date Added:
01/01/2009
Calculus I
Unrestricted Use
CC BY
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0.0 stars

This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and LĺÎĺ_ĺĚĺ_hopitalĺÎĺ_ĺĚĺ_s Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using NewtonĺÎĺ_ĺĚĺ_s Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005)

Subject:
Calculus
Functions
Material Type:
Assessment
Full Course
Reading
Syllabus
Textbook
Provider:
The Saylor Foundation
Date Added:
10/24/2019
Calculus I (MATH 151)
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
Reading
Syllabus
Provider:
Washington State Board for Community & Technical Colleges
Provider Set:
Open Course Library
Date Added:
10/31/2011
Category Theory for Scientists, Spring 2013
Conditional Remix & Share Permitted
CC BY-NC-SA
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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:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
David I. Spivak
Date Added:
01/01/2013
College Algebra Course Content, Functions, Functions
Conditional Remix & Share Permitted
CC BY-NC
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0.0 stars

This material covers Chapter 3: Functions chapter of the OpenStax College Algebra Text. This module contains an overview of learning objectives mapped to the OTM state standards, worksheets that correspond to chapter sections, interactive Desmos Activities that pair with the chapter, and a list of supplemental videos that correspond to the chapter content.

Subject:
Mathematics
Algebra
Functions
Material Type:
Module
Author:
OER Librarian
Date Added:
05/07/2021
Combinatorics Through Guided Discovery
Read the Fine Print
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0.0 stars

his book is an introduction to combinatorial mathematics, also known as combinatorics. The book focuses especially but not exclusively on the part of combinatorics that mathematicians refer to as “counting.” The book consists almost entirely of problems. Some of the problems are designed to lead you to think about a concept, others are designed to help you figure out a concept and state a theorem about it, while still others ask you to prove the theorem. Other problems give you a chance to use a theorem you have proved. From time to time there is a discussion that pulls together some of the things you have learned or introduces a new idea for you to work with. Many of the problems are designed to build up your intuition for how combinatorial mathematics works. There are problems that some people will solve quickly, and there are problems that will take days of thought for everyone. Probably the best way to use this book is to work on a problem until you feel you are not making progress and then go on to the next one. Think about the problem you couldn’t get as you do other things. The next chance you get, discuss the problem you are stymied on with other members of the class. Often you will all feel you’ve hit dead ends, but when you begin comparing notes and listening carefully to each other, you will see more than one approach to the problem and be able to make some progress. In fact, after comparing notes you may realize that there is more than one way to interpret the problem. In this case your first step should be to think together about what the problem is actually asking you to do. You may have learned in school that for every problem you are given, there is a method that has already been taught to you, and you are supposed to figure out which method applies and apply it. That is not the case here. Based on some simplified examples, you will discover the method for yourself. Later on, you may recognize a pattern that suggests you should try to use this method again.

Subject:
Mathematics
Functions
Material Type:
Textbook
Provider:
Dartmouth College
Author:
Kenneth Bogart
Date Added:
01/01/2004
Intermediate Algebra 2e
Unrestricted Use
CC BY
Rating
0.0 stars

The 2nd Edition of Intermediate Algebra, Intermediate Algebra 2e, is designed to meet the scope and sequence requirements of a one-semester intermediate algebra course. The book’s organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. The material is presented as a sequence of clear steps, building on concepts presented in prealgebra and elementary algebra courses.

The second edition contains detailed updates and accuracy revisions to address comments and suggestions from users. Dozens of faculty experts worked through the text, exercises and problems, graphics, and solutions to identify areas needing improvement. Though the authors made significant changes and enhancements, exercise and problem numbers remain nearly the same in order to ensure a smooth transition for faculty.

Subject:
Mathematics
Algebra
Functions
Material Type:
Answer Key
Full Course
Lecture Notes
Textbook
Provider:
Rice University
Provider Set:
OpenStax College
Author:
Andrea Honeycutt Mathis
Lynn Marecek
Date Added:
09/22/2020
Introduction To MATLAB Programming, Fall 2011
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

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:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Yossi Farjoun
Date Added:
01/01/2011
Introduction to C++, January IAP 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:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Dunietz, Jesse
Kovacs, Geza
Marrero, John
Date Added:
01/01/2010
Introduction to Functional Analysis, Spring 2009
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:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Melrose, Richard
Date Added:
01/01/2009
Modeling Dynamics and Control I, Spring 2005
Conditional Remix & Share Permitted
CC BY-NC-SA
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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:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Dubowsky, Steven
Trumper, David L.
Date Added:
01/01/2005
Precalculus I (MATH 141)
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
Reading
Syllabus
Provider:
Washington State Board for Community & Technical Colleges
Provider Set:
Open Course Library
Date Added:
10/31/2011
Solutions to Applications of College Algebra
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating
0.0 stars

Students often express trouble with application, or "word", problems in typical College Algebra classes. This accessible document contains the solutions, both handwritten and typed, for 135 application problems from various open source mathematics textbooks. Topics include linear, polynomial, rational, exponential, and logarithmic functions. This guide can be used to supplement your College Algebra (or similar) course. 

Subject:
Algebra
Functions
Material Type:
Answer Key
Author:
Jesse Kiefner
Radhakrishnan Palaniswamy
DANIELLE TRUSZKOWSKI
Date Added:
06/10/2020