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Application of Derivatives
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CC BY-SA
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We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.).Differentiation is also used in analysis of finance and economics.

Subject:
Business and Communication
Finance
Geometry
Mathematics
Material Type:
Simulation
Provider:
GeoGebra
Provider Set:
GeoGebraTube
Date Added:
03/12/2012
BlendEd Best Practices - Applications of Differentiation
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CC BY-NC-SA
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In this unit students will analyze and manipulate functions in order to apply them to real-life optimization (minimum/maximum) situations.

Subject:
Education
Mathematics
Material Type:
Activity/Lab
Assessment
Homework/Assignment
Lesson
Lesson Plan
Teaching/Learning Strategy
Unit of Study
Date Added:
07/01/2019
Calculus I
Unrestricted Use
CC BY
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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
Mathematics
Material Type:
Assessment
Full Course
Reading
Syllabus
Textbook
Provider:
The Saylor Foundation
Date Added:
04/16/2012
Calculus I:  Implicit Differentiation MGK
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CC BY-NC-ND
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This is a lesson on finding the difference between an implicit and explicit function and finding the derivative of functions implicitly. It also covers finding the equation of a tangent line from a function in implicit form . There are self check throughout the lesson. The text that I use in my calculus class is Larson Calculus 11th edition. This corresponds to chapter 2 section 5 in that text but Implicit Differentiation is a common topic in any Calculus I or AP Calculus course.

Subject:
Mathematics
Material Type:
Lecture
Lesson
Author:
Cara Kern
Date Added:
07/09/2020
Calculus - TI Activities (Student's Edition)
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CC BY-NC-SA
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CK-12's Texas Instrument Calculus Student 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
Mathematics
Material Type:
Textbook
Provider:
CK-12 Foundation
Provider Set:
CK-12 FlexBook
Author:
Jordan, Lori
Date Added:
12/15/2010
Calculus - TI Activities (Teacher's Edition)
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CC BY-NC-SA
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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
Mathematics
Material Type:
Textbook
Provider:
CK-12 Foundation
Provider Set:
CK-12 FlexBook
Author:
Jordan, Lori
Date Added:
12/17/2010
Calculus: Taking Derivatives
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CC BY-NC-SA
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This series of videos focusing on calculus covers calculating derivatives, power rule, product and quotient rules, chain rule, implicit differentiation, derivatives of common functions.

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
05/28/2013
Calculus - Taking Derivatives: Chain Rule
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CC BY-NC-SA
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You can take the derivatives of f(x) and g(x), but what about f(g(x)) or g(f(x))? The chain rule gives us this ability. Because most complex and hairy functions can be thought of the composition of several simpler ones (ones that you can find derivatives of), you'll be able to take the derivative of almost any function after this tutorial. Just imagine.

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
05/30/2013
Calculus - Taking Derivatives: Introduction To Differential Calculus
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CC BY-NC-SA
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The topic that is now known as "calculus" was really called "the calculus of differentials" when first devised by Newton (and Leibniz) roughly four hundred years ago. To Newton, differentials were infinitely small "changes" in numbers that previous mathematics didn't know what to do with. Think this has no relevence to you? Well how would you figure out how fast something is going *right* at this moment (you'd have to figure out the very, very small change in distance over an infinitely small change in time)? This tutorial gives a gentle introduction to the world of Newton and Leibniz.

Subject:
Calculus
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
05/30/2013
Calculus - Taking Derivatives: Proofs of Derivatives of Common Functions
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CC BY-NC-SA
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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
Mathematics
Material Type:
Lecture
Provider:
Khan Academy
Provider Set:
Khan Academy
Date Added:
05/30/2013
Calculus Volume 1
Unrestricted Use
CC BY
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Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 1 covers functions, limits, derivatives, and integration

Subject:
Calculus
Mathematics
Material Type:
Textbook
Provider:
Rice University
Provider Set:
OpenStax College
Author:
Alfred K. Mulzet
Catherine Abbott
David McCune
David Smith
David Torain
Edwin “Jed” Herman
Elaine A. Terry
Erica M. Rutter
Gilbert Strang
Joseph Lakey
Joyati Debnath
Julie Levandosky
Kirsten R. Messer
Michelle Merriweather
Nicoleta Virginia Bila
Sheri J. Boyd
Valeree Falduto
William Radulovich
Date Added:
02/01/2016
Calculus for the Life Sciences: A Modeling Approach Volume 1
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CC BY-NC-SA
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Our writing is based on three premises. First, life sciences students are motivated by and respond well to actual data related to real life sciences problems. Second, the ultimate goal of calculus in the life sciences primarily involves modeling living systems with difference and differential equations. Understanding the concepts of derivative and integral are crucial, but the ability to compute a large array of derivatives and integrals is of secondary importance. Third, the depth of calculus for life sciences students should be comparable to that of the traditional physics and engineering calculus course; else life sciences students will be short changed and their faculty will advise them to take the 'best' (engineering) course.

Subject:
Calculus
Mathematics
Material Type:
Textbook
Provider:
University of Minnesota
Provider Set:
University of Minnesota Libraries Publishing
Author:
James L. Cornette
Ralph A. Ackerman
Date Added:
01/01/2012
Financial Management
Unrestricted Use
CC BY
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Thompson Rivers University (TRU) has developed an OER in financial management consisting of 21 learning modules that can be used to teach courses in introductory and advanced financial management at the undergraduate and graduate levels as well as a course in business valuations. Each module consists of a detailed reading, presentation slides, learning problems, and answer keys. A number of case studies in areas such as financial statement analysis, financing planning, capital budgeting, and cost of capital are also included along with sample course outlines.

Faculty can select whatever modules they feel are needed to achieve the specific learning outcomes for a course. As OERs, faculty are also free to modify the readings, problems, or case studies so they better meet their needs and those of their students. These modules can be quickly imported into a learning management system such as Moodle or Blackboard to produce a challenging face-to-face or online learning experience.

With the rising cost of education, particularly textbooks, faculty are obligated to “adopt and adapt” OERs whenever possible to help their students.

Subject:
Business and Communication
Finance
Material Type:
Module
Author:
Dan Thompson CMA CPA CFA
Date Added:
07/30/2020
Notes and Practice Problems for OpenStax Calculus I
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The following notes and practice problems are ancillary materials for OpenStax Calculus Volume 1. Topics include:

Limit of a Function
Continuity
Derivatives
Differentiation

Subject:
Calculus
Mathematics
Material Type:
Homework/Assignment
Provider:
Fort Valley State University
Author:
Ishwari Kunwar
Patachin Marion
Date Added:
10/03/2022
Practice of Finance: Advanced Corporate Risk Management
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CC BY-NC-SA
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This is a course in how corporations make use of the insights and tools of risk management. Most courses on derivatives, futures and options, and financial engineering are taught from the viewpoint of investment bankers and traders in the securities. This course is taught from the point of view of the manufacturing corporation, the utility, the software firm—any potential end-user of derivatives, but not the dealer. Most related courses focus on the extensive taxonomy of instruments and the complex models developed to price them, and on ways to exploit mispricing. While this course will make use of some of these pricing models, the focus is on how corporations use the insights and models to improve their operations, to increase the value of their real assets, or to create the financial flexibility necessary to implement their core strategy.

Subject:
Business and Communication
Economics
Finance
Management
Social Science
Material Type:
Full Course
Provider:
MIT
Provider Set:
MIT OpenCourseWare
Author:
Parsons, John
Date Added:
02/01/2009