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Advanced Calculus
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Some of the topics that this book addresses are: Vector spaces; finite-dimensional ...

Some of the topics that this book addresses are: Vector spaces; finite-dimensional vector spaces; differential calculus; compactness and completeness; scalar product space; differential equations; multilenear functionals; integration; differentiable manifolds; integral calculus on manifolds; exterior calculus.

Note: this is a 57 MB PDF Document.

Subject:
Calculus
Material Type:
Textbooks
Provider:
Harvard University
Provider Set:
Individual Authors
Author:
Sternberg Shlomo and Lynn Loomis
Calculus
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Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource ...

Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications.

In addition to the Textbook, there is also an online Instructor's Manual and a student Study Guide. Prof. Strang has also developed a related series of videos, Highlights of Calculus, on the basic ideas of calculus.

Subject:
Mathematics
Calculus
Material Type:
Lesson Plans
Student Guide
Textbooks
Provider:
University of Minnesota
Provider Set:
Open Textbook Library
Author:
Gilbert Strang
Applied Calculus
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No Strings Attached
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Applied Calculus instructs students in the differential and integral calculus of elementary ...

Applied Calculus instructs students in the differential and integral calculus of elementary functions with an emphasis on applications to business, social and life science. Different from a traditional calculus course for engineering, science and math majors, this course does not use trigonometry, nor does it focus on mathematical proofs as an instructional method.

Subject:
Calculus
Material Type:
Full Course
Textbooks
Provider:
Lumen Learning
Provider Set:
Candela Courseware
Author:
Dale Hoffman
David Lippman
Shana Calaway
Whitman Calculus
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An introductory level single variable calculus book, covering standard topics in differential ...

An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Late transcendentals and multivariable versions are also available.

Subject:
Mathematics
Calculus
Material Type:
Textbooks
Provider:
University of Minnesota
Provider Set:
Open Textbook Library
Author:
David Guichard
Active Calculus
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In Active Calculus, we endeavor to actively engage students in learning the ...

In Active Calculus, we endeavor to actively engage students in learning the subject through an activity-driven approach in which the vast majority of the examples are completed by students. Where many texts present a general theory of calculus followed by substantial collections of worked examples, we instead pose problems or situations, consider possibilities, and then ask students to investigate and explore.

Subject:
Mathematics
Calculus
Material Type:
Textbooks
Provider:
University of Minnesota
Provider Set:
Open Textbook Library
Author:
Matt Boelkins, David Austin, Steve Schlicker
Brief Calculus
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No Strings Attached
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This short text is designed more for self-study or review than for ...

This short text is designed more for self-study or review than for classroom use; full solutions are given for nearly all the end-of-chapter problems. For a more traditional text designed for classroom use, see Fundamentals of Calculus (http://www.lightandmatter.com/fund/). The focus is mainly on integration and differentiation of functions of a single variable, although iterated integrals are discussed. Infinitesimals are used when appropriate, and are treated more rigorously than in old books like Thompson's Calculus Made Easy, but in less detail than in Keisler's Elementary Calculus: An Approach Using Infinitesimals. Numerical examples are given using the open-source computer algebra system Yacas, and Yacas is also used sometimes to cut down on the drudgery of symbolic techniques such as partial fractions. Proofs are given for all important results, but are often relegated to the back of the book, and the emphasis is on teaching the techniques of calculus rather than on abstract results.

Subject:
Mathematics
Calculus
Material Type:
Textbooks
Provider:
BCcampus
Provider Set:
BCcampus Open Textbooks
Author:
Benjamin Crowell
Calculus
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This is a four unit module. The first two units cover the ...

This is a four unit module. The first two units cover the basic concepts of the differential and integral calcualus of functions of a single variable. The third unit is devoted to sequences of real numbers and infinite series of both real numbers and of some special functions. The fourth unit is on the differential and integral calculus of functions of several variables. Starting with the definitions of the basic concepts of limit and continuity of functions of a single variable the module proceeds to introduce the notions of differentiation and integration, covering both methods and applications. Definitions of convergence for sequences and infinite series are given. Tests for convergence of infinite series are presented, including the concepts of interval and radius of convergence of a power series. Partial derivatives of functions of several variables are introduced and used in formulating Taylor’s theorem and finding relative extreme values.

Subject:
Calculus
Material Type:
Module
Video Lectures
Provider:
African Virtual university
Provider Set:
OER@AVU
Author:
Masenge, Ralph W. P.
Business Calculus
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No Strings Attached
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This course provides an introduction to applied concepts in Calculus that are ...

This course provides an introduction to applied concepts in Calculus that are relevant to the managerial, life, and social sciences. Students should have a firm grasp of the concept of functions to succeed in this course. Topics covered include derivatives of basic functions and how they can be used to optimize quantities such as profit and revenues, as well as integrals of basic functions and how they can be used to describe the total change in a quantity over time.

Subject:
Calculus
Material Type:
Full Course
Textbooks
Provider:
Lumen Learning
Provider Set:
Candela Courseware
Vector calculus
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This is a two-semester course in n-dimensional calculus with a review of ...

This is a two-semester course in n-dimensional calculus with a review of the necessary linear algebra. It covers the derivative, the integral, and a variety of applications. An emphasis is made on the coordinate free, vector analysis.

Subject:
Calculus
Material Type:
Homework and Assignments
Lecture Notes
Readings
Syllabi
Textbooks
Provider:
Intelligent Perception
Provider Set:
Individual Authors
Author:
Peter Saveliev
APEX Calculus
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This text comprises a three–text series on Calculus. The first part covers ...

This text comprises a three–text series on Calculus. The first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6.1. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to sequences, series and Taylor Polynomials, found in Chapters 5 through 8. The third text covers topics common in “Calc 3” or “multivariable calc:” parametric equations, polar coordinates, vector–valued functions, and functions of more than one variable, found in Chapters 9 through 13. All three are available separately for free at www.vmi.edu/APEX.

Subject:
Mathematics
Calculus
Functions
Material Type:
Textbooks
Provider:
University of Minnesota
Provider Set:
Open Textbook Library
Author:
regory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar
Vector Calculus
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This is a text on elementary multivariable calculus, designed for students who ...

This is a text on elementary multivariable calculus, designed for students who have completed courses in single-variable calculus. The traditional topics are covered: basic vector algebra; lines, planes and surfaces; vector-valued functions; functions of 2 or 3 variables; partial derivatives; optimization; multiple integrals; line and surface integrals.

Subject:
Calculus
Material Type:
Activities and Labs
Homework and Assignments
Textbooks
Provider:
Schoolcraft College
Author:
Michael Corral
Calculus I
Conditions of Use:
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This course begins with a review of algebra specifically designed to help ...

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:
Assessments
Full Course
Readings
Syllabi
Textbooks
Provider:
The Saylor Foundation
Calculus: Fundamental Theorem of Calculus
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You get the general idea that taking a definite integral of a ...

You get the general idea that taking a definite integral of a function is related to evaluating the antiderivative, but where did this connection come from. This tutorial focuses on the fundamental theorem of calculus which ties the ideas of integration and differentiation together. We'll explain what it is, give a proof and then show examples of taking derivatives of integrals where the Fundamental Theorem is directly applicable.

Subject:
Calculus
Material Type:
Video Lectures
Provider:
Khan Academy
Provider Set:
Khan Academy
Author:
Khan, Salman
Calculus Revisited: Multivariable Calculus, Fall 2011
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Calculus Revisited is a series of videos and related resources that covers ...

Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Multivariable Calculus is the second course in the series, consisting of 26 videos, 4 Study Guides, and a set of Supplementary Notes. The series was first released in 1971 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time.

Subject:
Calculus
Material Type:
Full Course
Textbooks
Provider:
M.I.T.
Provider Set:
M.I.T. OpenCourseWare
Author:
Herbert Gross
Calculus I, Summer 2009
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This course is an introduction to differential and integral calculus. It begins ...

This course is an introduction to differential and integral calculus. It begins with a short review of basic concepts surrounding the notion of a function. Then it introduces the important concept of the limit of a function, and use it to study continuity and the tangent problem. The solution to the tangent problem leads to the study of derivatives and their applications. Then it considers the area problem and its solution, the definite integral. The course concludes with the calculus of elementary transcendental functions.

Subject:
Calculus
Material Type:
Full Course
Homework and Assignments
Syllabi
Provider:
UMass Boston
Provider Set:
UMass Boston OpenCourseWare
Author:
Catalin Zara