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1. Title

## Answers: Discrete mathematics: A-Level course material

Description
This resource provides the answers to the exercises included in the 15 chapters dealing with discrete mathematics which are contained within the wider collection of A-Level course material provided by the Centre for Innovation in Mathematics Teaching, University of Plymouth. The individual chapters are also catalogued in the e-library.
Publisher
Centre for Innovation in Mathematics Teaching (CIMT), University of Plymouth
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/discrete_solutions.pdf
2. Title

## Answers: Pure mathematics: A-Level course material

Description
This resource provides the answers to the exercises included in the 21 chapters dealing with pure mathematics which are contained within the wider collection of A-Level course material provided by the Centre for Innovation in Mathematics Teaching, University of Plymouth. The individual chapters are also catalogued in the e-library.
Publisher
Centre for Innovation in Mathematics Teaching (CIMT), University of Plymouth
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/pure_solutions.pdf
3. Title

## Difference equations 1: A-Level course material

Description
This resource introduces difference equations, their use and application. Areas discussed include detection of recursive events, describing associated sequences, and solving first order difference equations. Numerous worked examples are presented, with illustrations where applicable. The resource is chapter 14 of 15 dealing with discrete mathematics, as part of a wider collection of A-Level course material provided by the Centre for Innovation in Mathematics Teaching, University of Plymouth. Answers to the exercises are also catalogued in the e-library.
Publisher
Centre for Innovation in Mathematics Teaching (CIMT), University of Plymouth
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/discrete_ch14.pdf
4. Title

## Difference equations 2: A-Level course material

Description
This resource provides a discussion of second order difference equations, and covers topics such as solving linear homogeneous examples, applying solutions to contextual problems, and solving non-homogeneous cases with generating functions. Numerous worked examples are presented, with illustrations where applicable. The resource is chapter 15 of 15 dealing with discrete mathematics, as part of a wider collection of A-Level course material provided by the Centre for Innovation in Mathematics Teaching, University of Plymouth. Answers to the exercises are also catalogued in the e-library.
Publisher
Centre for Innovation in Mathematics Teaching (CIMT), University of Plymouth
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/discrete_ch15.pdf
5. Title

## Difference equations to differential equations

Description
This book contains sequences, limits and difference equations (Section 1); functions and their properties (Section 2); best affine approximations (Section 3); integration (Section 4); polynomial approximations and Taylor series (Section 5); more transcendental functions (Section 6); the complex plane (Section 7); and differential equations (Section 8).
http://www.synechism.org/wp/difference-equations-to-differential-equations/
6. Title

## Differential equations: LearningSpace: Open University

Description
A description of second order differential equations, which requires some basic knowledge of calculus and complex numbers. Topics include how to solve homogeneous second order equations, construction of solutions to inhomogeneous linear constant-coefficient second order equations, and initial and boundary conditions. This intermediate module is provided by the UK Open University as part of its LearningSpace, a collection of over 800 free online courses (as at July 2016). It is provided as a workbook with a separate document providing answers to the exercises and is expected to take sixteen hours to complete.
Publisher
Open University
http://www.open.edu/openlearn/education/mathematics-education/differential-equations/content-section-0
7. Title

## Dynamical systems

Description
This book introduces the basic concepts and results of dynamical systems including iterations and fixed points, bifurcations, conjugacy, space and time averages, the contraction fixed point theorem, Hutchinson's theorem and fractal images, hyperbolicity, and symbolic dynamics. The book was written by Shlomo Sternberg from the Department of Mathematics, Harvard University, USA.
Publisher
Department of Mathematics, Harvard University
http://www.math.harvard.edu/~shlomo/docs/dynamical_systems.pdf
8. Title

## Even more calculus: A-Level course material

Description
This resource introduces a set of advanced calculus topics, such as differentiation and integration of trigonometric functions, calculating rates of change, solving first order differential equations and integration using substitutions. Numerous worked examples are presented, with illustrations where applicable. The resource is chapter 18 of 21 dealing with pure mathematics, as part of a wider collection of A-Level course material provided by the Centre for Innovation in Mathematics Teaching, University of Plymouth. Answers to the exercises are also catalogued in the e-library.
Publisher
Centre for Innovation in Mathematics Teaching (CIMT), University of Plymouth
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/pure_ch18.pdf
9. Title

## First-order differential equations: LearningSpace: Open University

Description
This module introduces first order differential equations, and assumes a basic knowledge of calculus. The resource describes basic definitions and terminology, teaches the use of Euler's theorem to solve differential equations, and teaches solutions using integration, separation of variables, and the integrating factor method. It is provided as a workbook with a separate document providing answers to the exercises. This intermediate module is provided by the UK Open University as part of its LearningSpace, a collection of over 800 free online courses (as at July 2016). It is expected to take sixteen hours to complete.
Publisher
Open University
http://www.open.edu/openlearn/education/mathematics-education/first-order-differential-equations/content-section-0
10. Title

## Further calculus: A-Level course material

Description
This resource provides an introduction to various concepts in calculus, such as finding the maximum and minimum of functions, applying calculus to sketching curves, finding the second derivative of functions and differentiating composite functions. It requires an understanding of simple mathematical functions and a basic level of calculus knowledge. Several worked examples are presented, with illustrations where applicable. The resource is chapter 14 of 21 dealing with pure mathematics, as part of a wider collection of A-Level course material provided by the Centre for Innovation in Mathematics Teaching, University of Plymouth. Answers to the exercises are also catalogued in the e-library.
Publisher
Centre for Innovation in Mathematics Teaching (CIMT), University of Plymouth
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/pure_ch14.pdf
11. Title

## Further calculus: A-Level course material

Description
This resource describes some advanced concepts and techniques in calculus. These include topics such as using the trapezium rule and Simpson's rule, calculating volumes of revolution, arc lengths, and deriving reduction formulae in integration. Numerous worked examples are presented, with illustrations where applicable. The resource is chapter 8 of 9 dealing with further pure mathematics, as part of a wider collection of A-Level course material provided by the Centre for Innovation in Mathematics Teaching, University of Plymouth. Answers to the exercises are also catalogued in the e-library.
Publisher
Centre for Innovation in Mathematics Teaching (CIMT), University of Plymouth
http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/fpure_ch8.pdf
12. Title

## Lecture 10: Linear equations with additive noise II: Stochastic evolution equations

Description
A discussion of the stochastic abstract Cauchy problem with additive noise, and its possible solutions. A number of worked examples, notes and equations are provided. This is 1 of 15 lectures on stochastic evolution equations produced by Delft University of Technology as part of its OpenCourseWare initiative. The other lectures in this series are also catalogued in the e-library.
Publisher
Delft University of Technology
13. Title

## Lecture 11: Conditional expectations and martingales: Stochastic evolution equations

Description
This resource describes stochastic equations with multiplicative noise, and how to solve them. Topics include conditional expectations and martingales. A number of worked examples, notes and equations are provided. This is 1 of 15 lectures on stochastic evolution equations produced by Delft University of Technology as part of its OpenCourseWare initiative. The other lectures in this series are also catalogued in the e-library.
Publisher
Delft University of Technology
14. Title

## Lecture 12: UMD-spaces: Stochastic evolution equations

Description
This lecture introduces a class of Banach spaces known as UMD-spaces and includes topics such as Haar martingales and the Stein inequality. A number of worked examples, notes and equations are provided. This is 1 of 15 lectures on stochastic evolution equations produced by Delft University of Technology as part of its OpenCourseWare initiative. The other lectures in this series are also catalogued in the e-library.
Publisher
Delft University of Technology
15. Title

## Lecture 13: Stochastic integration II: the Ito integral: Stochastic evolution equations

Description
This lecture discusses extensions to stochastic integration, looking at topics such as UMD Banach spaces, and decoupling. A number of worked examples, notes and equations are provided. This is 1 of 15 lectures on stochastic evolution equations produced by Delft University of Technology as part of its OpenCourseWare initiative. The other lectures in this series are also catalogued in the e-library.
Publisher
Delft University of Technology
16. Title

## Lecture 14: Linear equations with multiplicative noise: Stochastic evolution equations

Description
A resource describing stochastic evolution equations with multiplicative noise and how to formulate and solve them. A number of worked examples, notes and equations are provided. This is 1 of 15 lectures on stochastic evolution equations produced by Delft University of Technology as part of its OpenCourseWare initiative. The other lectures in this series are also catalogued in the e-library.
Publisher
Delft University of Technology
17. Title

## Lecture 15: Applications to stochastic PDE: Stochastic evolution equations

Description
This lecture describes the application of various theories to solving stochastic partial differential equations. Two main examples are provided: the wave equation and the heat equation. A number of worked examples, notes and equations are provided. This is 1 of 15 lectures on stochastic evolution equations produced by Delft University of Technology as part of its OpenCourseWare initiative. The other lectures in this series are also catalogued in the e-library.
Publisher
Delft University of Technology
18. Title

## Lecture 1: Integration in Banach spaces: Stochastic evolution equations

Description
A 14 page discussion of integration in Banach spaces. A number of worked examples, notes and equations are provided. This is 1 of 15 lectures on stochastic evolution equations produced by Delft University of Technology as part of its OpenCourseWare initiative. The other lectures in this series are also catalogued in the e-library.
Publisher
Delft University of Technology
19. Title

## Lecture 2: Random variables in Banach spaces: Stochastic evolution equations

Description
This document describes the study of random variables with values in a Banach space, focusing specifically on the Ito-Nisio theorem. A number of worked examples, notes and equations are provided. This is 1 of 15 lectures on stochastic evolution equations produced by Delft University of Technology as part of its OpenCourseWare initiative. The other lectures in this series are also catalogued in the e-library.
Publisher
Delft University of Technology
20. Title

## Lecture 3: Sums of independent random variables: Stochastic evolution equations

Description
A lecture describing a number of estimates for sums of independent random variables with values in a Banach space. A number of worked examples, notes and equations are provided. This is 1 of 15 lectures on stochastic evolution equations produced by Delft University of Technology as part of its OpenCourseWare initiative. The other lectures in this series are also catalogued in the e-library.
Publisher
Delft University of Technology
21. Title

## Lecture 4: Gaussian random variables: Stochastic evolution equations

Description
This resource concentrates on the general theory of Gaussian random variables with values in a Banach space. A number of worked examples, notes and equations are provided. This is 1 of 15 lectures on stochastic evolution equations produced by Delft University of Technology as part of its OpenCourseWare initiative. The other lectures in this series are also catalogued in the e-library.
Publisher
Delft University of Technology
22. Title

## Lecture 5: Radonifying operators: Stochastic evolution equations

Description
This lecture describes the effect of replacing functions with radonifying or integral operators in Hilbert and Banch spaces. A number of worked examples, notes and equations are provided. This is 1 of 15 lectures on stochastic evolution equations produced by Delft University of Technology as part of its OpenCourseWare initiative. The other lectures in this series are also catalogued in the e-library.
Publisher
Delft University of Technology
23. Title

## Lecture 6: Stochastic integration I: the Wiener integral: Stochastic evolution equations

Description
An introduction to stochastic integration, with specific reference to the Wiener integral. A number of worked examples, notes and equations are provided. This is 1 of 15 lectures on stochastic evolution equations produced by Delft University of Technology as part of its OpenCourseWare initiative. The other lectures in this series are also catalogued in the e-library.
Publisher
Delft University of Technology
24. Title

## Lecture 7: Semigroups of linear operators: Stochastic evolution equations

Description
This lecture describes semigroup theory as applied to stochastic equations. An introduction to semigroups is provided, together with a description of their use in solving the inhomogeneous abstract Cauchy problem. A number of worked examples, notes and equations are provided. This is 1 of 15 lectures on stochastic evolution equations produced by Delft University of Technology as part of its OpenCourseWare initiative. The other lectures in this series are also catalogued in the e-library.
Publisher
Delft University of Technology