Using Green's Theorem to establish a two dimensional version of the Divergence Theorem
Intuition behind the Divergence Theorem in three dimensions
Using the first and second derivatives to identify critical points and inflection points and to graph the function.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Antiderivative of hairier expression.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Antiderivative of xcosx using integration by parts.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Antiderivatives and indefinite integrals.
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.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Applying the fundamental theorem of calculus.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Applying the product rule for derivatives.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Approximating equation of tangent line word problem.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Approximating instantaneous rate of change word problem.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Area between curves.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Area between curves with multiple boundaries.
The text is mostly an adaptation of two other excellent open- source calculus textbooks: Active Calculus by Dr. Matt Boelkins of Grand Valley State University and Drs. Gregory Hartman, Brian Heinold, Troy Siemers, Dimplekumar Chalishajar, and Jennifer Bowen of the Virginia Military Institute and Mount Saint Mary's University. Both of these texts can be found at http://aimath.org/textbooks/approved-textbooks/.
The authors of this text have combined sections, examples, and exercises from the above two texts along with some of their own content to generate this text. The impetus for the creation of this text was to adopt an open-source textbook for Calculus while maintaining the typical schedule and content of the calculus sequence at our home institution.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Basic trig and exponential antiderivatives.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Both bounds being a function of x.
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.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Building the idea of epsilon-delta definition.
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.
MATH&148 is a calculus course for business students. It is designed for students who want a brief course in calculus. Topics include differential and integral calculus of elementary functions. Problems emphasize business and social science applications. Translating words into mathematics and solving word problems are emphasized over algebra. Applications are mainly business oriented (e.g. cost, revenue, and profit). Mathematical theory and complex algebraic manipulations are not mainstays of this course, which is designed to be less rigorous than the calculus sequence for scientists and engineers. Topics are presented according to the rule of four: geometrically, numerically, analytically, and verbally. That is, symbolic manipulation must be balanced with graphical interpretation, numerical examples, and writing. Trigonometry is not part of the course.
Let's calculate the integral from the last video.
Evaluating integral set up with shell method for two functions.
Calculus is the mathematics of CHANGE and almost everything in our world is changing. In this course, you will investigate limits and how they are used to calculate rate of change at a point, define the continuity of a function and how they are used to define derivatives. Definite and indefinite integrals and their applications are covered, including improper integrals. Late in the course, you will find Calculus with parametric equations and polar coordinates, sequences and series, and vectors.
This contemporary calculus course is the third in a three-part sequence. In this course students continue to explore the concepts, applications, and techniques of Calculus - the mathematics of change. Calculus has wide-spread application in science, economics and engineering, and is a foundation college course for further work in these areas. This is a required class for most science and mathematics majors.Login: guest_oclPassword: ocl
This contemporary calculus course is the second in a three-part sequence. In this course students continue to explore the concepts, applications, and techniques of Calculus - the mathematics of change. Calculus has wide-spread application in science, economics and engineering, and is a foundation college course for further work in these areas. This is a required class for most science and mathematics majors.Login: guest_oclPassword: ocl
This course is an introduction to contemporary calculus and is the first of a three-part sequence. In this course students explore the concepts, applications, and techniques of Calculus - the mathematics of change. Calculus has wide-spread application in science, economics and engineering, and is a foundation college course for further work in these areas. This is a required class for most science and mathematics majors.Login: guest_oclPassword: ocl
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
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 2 covers integration, differential equations, sequences and series, and parametric equations and polar coordinates.
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 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.
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.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Chain rule definition and example.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Chain rule for derivative of 2^x.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Chain rule introduction.
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Chain rule with triple composition.
2010 IIT JEE Paper 1 Problem 52 Periodic Definite Integral. The second term at about minute 14 should have a positive sign. Luckily, it doesn't effect the final answer!
Showing that the line integral along closed curves of conservative vector fields is zero
Conceptual understanding of flux across a two-dimensional surface
Understanding the line integral as flux through a boundary
Understanding when you can use Stokes. Piecewise-smooth lines and surfaces
This video is from the Khan Academy subject of Math on the topic of Calculus and it covers Connecting the first and second fundamental theorems of calculus.