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Calculus I
Unrestricted Use
CC BY
Rating

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:
03/04/2019
Category Theory for Scientists, Spring 2013
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

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
Introduction To MATLAB Programming, Fall 2011
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

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

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

" 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
Rating

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 (was College Algebra)
Unrestricted Use
CC BY
Rating

Precalculus (was College Algebra) is an introductory text. The material is presented at a level intended to prepare students for Calculus while also giving them relevant mathematical skills that can be used in other classes. The authors describe their approach as "Functions First," believing introducing functions first will help students understand new concepts more completely. Each section includes homework exercises, and the answers to most computational questions are included in the text (discussion questions are open-ended). Graphing calculators are used sparingly and only as a tool to enhance the Mathematics, not to replace it. Note: this book was updated on the BC Open textbook Project site on February, 17, 2015 to include the version of the textbook with chapters on Trigonometry.

Subject:
Mathematics
Algebra
Functions
Trigonometry
Material Type:
Textbook
Provider:
BCcampus
Provider Set:
BCcampus Faculty Reviewed Open Textbooks
Author:
Carl Stitz
Jeff Zeager
Date Added:
02/17/2015
A Spiral Workbook for Discrete Mathematics
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

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:
OpenSUNY Textbooks
Author:
Harris Kwong, SUNY Fredonia
Date Added:
11/06/2015