This tutorial classifies regions in three dimensions. Comes in useful for some types of double integrals and we use these ideas to prove the divergence theorem.
This video looks at the definition and intuition for Type 2 Regions.
This video looks at the definition and intuition for type 3 regions.
U-substitution is a must-have tool for any integrating arsenal (tools aren't normally put in arsenals, but that sounds better than toolkit). It is essentially the reverise chain rule. U-substitution is very useful for any integral where an expression is of the form g(f(x))f'(x)(and a few other cases). Over time, you'll be able to do these in your head without necessarily even explicitly substituting. Why the letter "u"? Well, it could have been anything, but this is the convention. I guess why not the letter "u" :)
This video looks at another example of using u-subsitution.
This video looks at manipulating the expression to make u-substitution a little more obvious.
This video looks at using u-substitution and "back substituting" for x to simplify an expression.
This video covers example of using u-substitution to evaluate a definite integral.
This video covers doing u-substitution with ln(x).
This 12-minute video gives an example of using a line integral to find the work done by a vector field.
This video looks at using the product rule and the chain rule.
This 16-minute video lesson shows that unlike line integrals of scalar fields, line integrals over vector fields are path direction dependent.
This video looks at different ways of representing a flux integral.
This 13-minute video lesson provides a concrete example of the derivative of a vector valued function to better understand what it means.
This video provides a Visualizing derivatives exercise.
This 7-minute video lecture looks at using the Wolfram Alpha to approximate sin(x).
This 7-minute video lesson looks at visualizing the Taylor Series for e^x.
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.