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Advanced Calculus
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Advanced Calculus

Some of the topics that this book addresses are: Vector spaces; finite-dimensional ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Textbooks
Provider:
Harvard University
Provider Set:
Individual Authors
Author:
Sternberg Shlomo and Lynn Loomis
Calculus
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Calculus

ublished in 1991 by Wellesley-Cambridge Press, the book is a useful resource ... (more)

ublished 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. (less)

Subject:
Mathematics
Material Type:
Lesson Plans
Student Guide
Textbooks
Provider:
University of Minnesota
Provider Set:
University of Minnesota - Open Academics Textbooks
Author:
Gilbert Strang
Calculus I
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Calculus I

Designed for students intending to earn an Associate of Science degree and ... (more)

Designed for students intending to earn an Associate of Science degree and then transfer to a mathematics, engineering program, or other calculus-based major at a four-year institution. Students will gain a basic understanding of calculus, the mathematics of motion and change. Topics include limits and continuity, differentiation, applications of differentiation, integration, applications of integration, derivatives of exponential functions, logarithmic functions, inverse trigonometric functions, hyperbolic functions and related integrals. Students must have a working knowledge of college algebra and trigonometry. (less)

Subject:
Mathematics and Statistics
Material Type:
Full Course
Lecture Notes
Syllabi
Provider:
Dixie State College of Utah
Provider Set:
Dixie State College Opencourseware
Author:
Costel Ionita
Ph.D.
Whitman Calculus
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Whitman Calculus

An introductory level single variable calculus book, covering standard topics in differential ... (more)

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. (less)

Subject:
Mathematics
Material Type:
Textbooks
Provider:
University of Minnesota
Provider Set:
University of Minnesota - Open Academics Textbooks
Author:
David Guichard
Active Calculus
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Active Calculus

In Active Calculus, we endeavor to actively engage students in learning the ... (more)

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. (less)

Subject:
Mathematics
Material Type:
Textbooks
Provider:
University of Minnesota
Provider Set:
University of Minnesota - Open Academics Textbooks
Author:
Matt Boelkins, David Austin, Steve Schlicker
Calculus I
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Calculus I

In this course, we will study the foundations of calculus, the study ... (more)

In this course, we will study the foundations of calculus, the study of functions and their rates of change. We want you to learn how to model situations in order to solve problems. If you have already taken calculus before, we want you to gain an even deeper understanding of this fascinating subject. The derivative measures the instantaneous rate of change of a function. The definite integral measures the total accumulation of a function over an interval. These two ideas form the basis for nearly all mathematical formulas in science. The rules by which we can compute the derivative (respectively, the integral) of any function are called a calculus. The Fundamental Theorem of Calculus links the two processes of differentiation and integration in a beautiful way. (less)

Subject:
Mathematics and Statistics
Material Type:
Video Lectures
Provider:
New York University
Provider Set:
New York University
Author:
Matthew Leinngang
APEX Calculus
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APEX Calculus

This text comprises a three–text series on Calculus. The first part covers ... (more)

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. (less)

Subject:
Mathematics
Material Type:
Textbooks
Provider:
University of Minnesota
Provider Set:
University of Minnesota - Open Academics Textbooks
Author:
regory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar
Vector calculus
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Vector calculus

This is a two-semester course in n-dimensional calculus with a review of ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Homework and Assignments
Lecture Notes
Readings
Syllabi
Textbooks
Provider:
Intelligent Perception
Provider Set:
Individual Authors
Author:
Peter Saveliev
Vector Calculus
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Vector Calculus

This is a text on elementary multivariable calculus, designed for students who ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Activities and Labs
Homework and Assignments
Textbooks
Provider:
Schoolcraft College
Provider Set:
Schoolcraft College
Author:
Michael Corral
Calculus I
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Calculus I

This course begins with a review of algebra specifically designed to help ... (more)

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) (less)

Subject:
Mathematics and Statistics
Material Type:
Assessments
Full Course
Readings
Syllabi
Textbooks
Provider:
The Saylor Foundation
Provider Set:
Saylor Foundation
Calculus: Fundamental Theorem of Calculus
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Calculus: Fundamental Theorem of Calculus

You get the general idea that taking a definite integral of a ... (more)

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. (less)

Subject:
Mathematics and Statistics
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: Multivariable Calculus, Fall 2011

Calculus Revisited is a series of videos and related resources that covers ... (more)

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. (less)

Subject:
Mathematics and Statistics
Material Type:
Full Course
Homework and Assignments
Readings
Syllabi
Provider:
M.I.T.
Provider Set:
MIT OpenCourseWare
Author:
Herbert Gross
Calculus I, Summer 2009
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Calculus I, Summer 2009

This course is an introduction to differential and integral calculus. It begins ... (more)

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. (less)

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