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Inverse functionsAn inverse function is a second function which undoes the work of the first
one. In this unit we describe two methods for finding inverse functions, and we
also explain that the domain of a function may need to be restricted before an
inverse function can exist.
Inverse functionsAn inverse function is a second function which undoes the work of the first
one. In this unit we describe two methods for finding inverse functions, and we also explain that the domain of a function may need to be restricted before an inverse function can exist. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Inverse functionsAn inverse function is a second function which undoes the work of the first
one. In this unit we describe two methods for finding inverse functions, and we also explain that the domain of a function may need to be restricted before an inverse function can exist. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Hyperbolic functionsThe hyperbolic functions have similar names to the trigonmetric functions,
but they are defined in terms of the exponential function. In this unit we
define the three main hyperbolic functions, and sketch their graphs. We also
discuss some identities relating these functions, and mention their inverse
functions and reciprocal functions.
Hyperbolic functionsThe hyperbolic functions have similar names to the trigonmetric functions,
but they are defined in terms of the exponential function. In this unit we
define the three main hyperbolic functions, and sketch their graphs. We also
discuss some identities relating these functions, and mention their inverse
functions and reciprocal functions. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Hyperbolic functionsThe hyperbolic functions have similar names to the trigonmetric functions,
but they are defined in terms of the exponential function. In this unit we
define the three main hyperbolic functions, and sketch their graphs. We also
discuss some identities relating these functions, and mention their inverse
functions and reciprocal functions. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Diagnostic Test: Indefinite Integration - Numbas16 questions: Inverse of differentiation, substitution, inverse trig functions, partial fractions and by parts. For those that want a thorough testing of their basic techniques in integration.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Trigonometric functionsThe sine, cosine and tangent of an angle are all defined in terms of
trigonometry, but they can also be expressed as functions. In this unit we
examine these functions and their graphs. We also see how to restrict the
domain of each function in order to define an inverse function.
The inverse of a 2x2 matrixMatrices 7: This leaflet explains what is meant by the inverse of a 2x2 matrix and shows how to calculate this when it exists. There is an accompanying video tutorial.
The inverse of a 2x2 matrixMatrices 7: This video tutorial explains what is meant by the inverse of a 2x2 matrix and shows how to calculate this when it exists. There is an accompanying help leaflet.
The inverse of a 2x2 matrixMatrices 7: This video tutorial explains what is meant by the inverse of a 2x2 matrix and shows how to calculate this when it exists. There is an accompanying help leaflet.
The inverse of a 2x2 matrixThis leaflet explains what is meant by the inverse of a 2x2 matrix and how this can be found using a formula. (Engineering Maths First Aid Kit 5.4)
Using the inverse matrix to solve equationsThis leaflet explains how simultaneous linear equations can be solved by calculating the inverse of an appropriate matrix. (Engineering Maths First Aid Kit 5.6)
Trigonometric functionsThe sine, cosine and tangent of an angle are all defined in terms of trigonometry, but they can also be expressed as functions. In this unit we examine these functions and their graphs. We also see how to restrict the domain of each function in order to define an inverse function. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
The inverse of a matrixThis leaflet explains what is meant by the inverse of a matrix and how this can be calculated. (Engineering Maths First Aid Kit 5.5)
Trigonometric functionsThe sine, cosine and tangent of an angle are all defined in terms of trigonometry, but they can also be expressed as functions. In this unit we examine these functions and their graphs. We also see how to restrict the domain of each function in order to define an inverse function. (Mathtutor Video Tutorial)
The video is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Matrix inversion of a 3x3 matrixMatrices 11: This leaflet explains how to calculate the inverse of a 3x3 matrix. There is an accompanying video tutorial.
Matrix inversion of a 3x3 matrixMatrices 11: This video tutorial explains how to calculate the inverse of a 3x3 matrix. There is an accompanying help leaflet.
Matrix inversion of a 3x3 matrixMatrices 11: This video tutorial explains how to calculate the inverse of a 3x3 matrix. There is an accompanying help leaflet.
Systems of linear equations - Numbas3 questions. First, two equations in two unknowns; second 3 equations in 3 unknowns, solved by Gauss elimination. The third, two equations in 2 unknowns solved by putting into matrix form and finding the inverse of the coefficient matrix. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Basic complex numbers - Numbas6 questions on complex numbers, multiplication, inverse, division and modulus. Finding the distance between complex numbers. Numbas resources have been made available under a Creative Commons licence by Bill Foster and Christian Perfect, School of Mathematics & Statistics at Newcastle University.
Complex Numbers Arithmetic - Numbas6 questions on complex numbers, multiplication, inverse, division and modulus and finding the distance between complex numbers.
Numbas resources have been made available under a Creative Commons licence by the School of Mathematics & Statistics at Newcastle University.
Composition of functionsWe can build up complicated functions from simple functions by using the
process of composition, where the output of one function becomes the input of another. It is also sometimes necessary to carry out the reverse process, decomposing a complicated function into two or more simple functions. This unit explains how. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Composition of functionsWe can build up complicated functions from simple functions by using the
process of composition, where the output of one function becomes the input of another. It is also sometimes necessary to carry out the reverse process, decomposing a complicated function into two or more simple functions. This unit explains how. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Exponential and logarithm functionsExponential functions and logarithm functions are important in both theory and practice. In this unit we look at the graphs of exponential and logarithm
functions, and see how they are related. (Mathtutor Video Tutorial)
This resource is released under a Creative Commons license Attribution-Non-Commercial-No Derivative Works and the copyright is held by Skillbank Solutions Ltd.
Polynomial functionsMany common functions are polynomial functions. In this unit we describe
polynomial functions and look at some of their properties.
