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Implicit Differentiation (with STACK)This unit explains how to differentiate a function defined implicitly. Additionally, it has links to STACK for on-line exercises.
Note that there is a mathtutor video to accompany this text.
Integrating Algebraic Fractions (with STACK)Sometimes the integral of an algebraic fraction can be found by first expressing the algebraic fraction as the sum of its partial fractions. In this unit we will illustrate this idea. We will see that it is also necessary to draw upon a wide variety of other techniques such as completing the square, integration by substitution, using standard forms, and so on.
Additionally, this file has links to STACK on-line exercises
Note there is a mathtutor video to accompany this text.
Integration by parts (with STACK)A special rule, integration by parts, is available for integrating
products of two functions. This unit derives and illustrates this rule with a
number of examples.
This file has links to STACK on-line exercises.
Note there is an accompanying mathtutor video.
Integration by substitution (with STACK)There are occasions when it is possible to perform an apparently difficult piece of integration by first making a
substitution. This has the effect of changing the variable and the integrand. When dealing with definite integrals,
the limits of integration can also change.
In this unit we will meet several examples of integrals where it is appropriate to make a substitution.
This is text to accompany a mathtutor video, and there are links to on-line exercises provided through the STACK system
Integration that leads to logarithms (with STACK)The derivative of ln x is 1/x. As a consequence, if we reverse
the process, the integral of 1/x is ln x+c. In this unit we
generalise this result and see how a wide variety of integrals result in
logarithm functions.
This file has links to STACK on-line exercises.
Note there is a mathtutor video to accompany this text.
Integration using a table of anti-derivatives (with STACK)We may regard integration as the reverse of differentiation. So if we have
a table of derivatives, we can read it backwards as a table of
anti-derivatives. When we do this, we often need to deal with constants
which arise in the process of differentiation.
This file has links to STACK on-line exercises.
Note there is a mathtutor video tutorial to accompany this text.
Integration using trig identities and trig substitutions (with STACK)This unit explains how trig identities and trig substitutions can help when finding integrals.
This file has links to STACK on-line exercises.
Note there is an accompanying mathtutor video.
Parametric Differentiation (with STACK)This unit explains how to differentiate a function defined parametrically.
This file has links to STACK on-line exercises.
Note there is an accompanying video tutorial.
The Chain Rule (with STACK)This teach-yourself workbook explains the chain rule which is used to differentiate a function of a function.
Additionally, it has links to STACK on line exercises.
Note that there is a mathtutor video to accompany this text.
The product rule (with STACK)This workbook explains the product rule for differentiation.
This file has links to STACK on-line exercises.
Note there is an accompanying video tutorial.
The quotient rule (with STACK)This teach-yourself workbook explains the quotient rule for differentiation.
This file has links to STACK on-line exercises.
Note there is an accompanying video tutorial.
Using a table of derivatives (with STACK)This unit provides a basic table of some standard derivatives.
Many of the results are derived.
This file has links to STACK on-line exercises.
Note there is an accompanying mathtutor video.
