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Advanced Calculus

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
Collection:
Individual Authors
Provider:
Harvard University
Author:
Sternberg Shlomo and Lynn Loomis
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Calculus I

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
Collection:
Dixie State College Opencourseware
Provider:
Dixie State College of Utah
Author:
Costel Ionita
Ph.D.
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Calculus: Fundamental Theorem of Calculus

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
Collection:
Khan Academy
Provider:
Khan Academy
Author:
Khan, Salman
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Calculus I

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
Collection:
New York University
Provider:
New York University
Author:
Matthew Leinngang
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Topics in Calculus

Topics in Calculus

This page emphasizes the practical concepts of calculus, and is intended to ... (more)

This page emphasizes the practical concepts of calculus, and is intended to provide a new context for the student already familiar with much of the material. The emphasis is on how calculus can actually be used outside of the classroom, and how the language of calculus is important in many other disciplines. It features articles for download, on topics from exponential growth and decay to discontinuities, vector fields and differential equations. All of the articles include extensive notes, examples, and figures. This resource is part of the Teaching Quantitative Skills in the Geosciences collection. http://serc.carleton.edu/quantskills/ (less)

Subject:
Mathematics and Statistics
Material Type:
Readings
Collection:
University of Hawaii
Provider:
University of Hawaii
Author:
E. Lady
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Vector calculus

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
Collection:
Individual Authors
Provider:
Intelligent Perception
Author:
Peter Saveliev
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Vector Calculus

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
Collection:
Schoolcraft College
Provider:
Schoolcraft College
Author:
Michael Corral
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Calculus on the Web

Calculus on the Web

COW is an internet utility for learning and practicing calculus. The principal ... (more)

COW is an internet utility for learning and practicing calculus. The principal purpose of COW is to provide you, the student or interested user, with the opportunity to learn and practice problems in calculus (and in the future other topics in mathematics) in a friendly environment via the internet. The most important feature of the COW is that you get to know whether your answer is correct almost immediately. It is as if you had a tutor looking over your shoulder and helping you along as you work. This will be true no matter where you are or what computer you use, as long as it is connected to the internet and has a web browser. The student component of COW (called the Manager) generates calculus examples and exercises in "modules" for studying, tutoring and practice. A number of the modules allow you to experiment by letting you change values or parameters in a function or graph and then see the effect. These modules are called "hands on" modules, and are marked with an asterisk. The component of the COW accessible by instructors (called the Reporter) handles assignment and automatic grading of homework, reporting on student work and class management. (less)

Subject:
Mathematics and Statistics
Material Type:
Activities and Labs
Collection:
Temple University
Provider:
Temple University
Author:
Dan Reich
Gerardo Mendoza
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Calculus I

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
Collection:
Saylor Foundation
Provider:
The Saylor Foundation
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Subject:
Science and Technology
Material Type:
Assessments
Full Course
Homework and Assignments
Lecture Notes
Syllabi
Collection:
MIT OpenCourseWare
Provider:
M.I.T.
Author:
George Kocur
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