# Methods of Applied Mathematics

#### Jeremy Levesley, University of Leicester

This module aims to introduce the student to fundamental methods in applied mathematics, to give the student experience in using the computer to solve mathematical problems, and to reinforce A level calculus skills.

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Methods of Applied Mathematics
Aug 22, 2013 Jeremy Levesley, Jane Aston, University of Leicester
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Defining convergence and testing for convergence including the alternating series test, ratio test, and comparison test
Methods of Applied Mathematics
Aug 22, 2013 Jeremey Levesley, Jane Aston, University of Leicester
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Explaining absolute convergence with a look at conditional convergence, rearrangements, and product rule
Methods of Applied Mathematics
Aug 22, 2013 Jeremy Levesley, Jane Aston, University of Leicester
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Taylor expansion and examples of finding terms
Methods of Applied Mathematics
Aug 22, 2013 Jeremy Levesley, Jane Aston, University of Leicester
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Definition of power series with explanation of summation; radius of convergence; finding radius of convergence. An understanding of series is necessary before tackling power series.
Methods of Applied Mathematics
Aug 6, 2013 Jeremy Levesley, Jane Aston, University of Leicester
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Official definition and examples, including demonstration of using L'hopital's rule
Methods of Applied Mathematics
Aug 6, 2013 Jeremy Levesley, Jane Aston, University of Leicester
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Differentiation is the process by which we extract the gradient of a line from the formula of a line.
Methods of Applied Mathematics
Aug 5, 2013 Jeremy Levesley, Jane Aston, University of Leicester
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Referring to sequences as a whole; null sequences; can ignore a finite number of sequence terms without affecting anything; domination; bounded sequences; convergent sequences; subsequences
Methods of Applied Mathematics
Aug 5, 2013 Jeremy Levesley, Jane Aston, University of Leicester
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Covers the two types of diverging sequences: sequences tending to infinity, and oscillating sequences
Methods of Applied Mathematics
Aug 5, 2013 Jeremy Levesley, Jane Aston, University of Leicester
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Sequences are understood by first defining convergence: a sequence ends up at a certain value when it gets to infinity. Limits and closeness.
Methods of Applied Mathematics
Aug 2, 2013 Jeremy Levesley, Jane Aston, University of Leicester
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An introduction to series. It is necessary to understand sequences before tackling series. Sigma notation, summation, and geometric series are explained as well.
Methods of Applied Mathematics
Aug 2, 2013 Jeremy Levesley, Jane Aston, University of Leicester
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Bounds are properties of finite and infinite sets. Upper and lower bounds of these sets are explained, along with maximum elements. Least upper bound and greatest lower bound.
Methods of Applied Mathematics
Feb 28, 2013 Jeremy Levesley, University of Leicester
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Prof Jeremy Levesley explains how to compute derivatives in given directions and the maximum slope at a point.
Methods of Applied Mathematics
Feb 28, 2013 Jeremy Levesley, University of Leicester
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Prof Jeremy Levesley explains how to compute the angle between two vectors using the scalar product, the area of a parallelogram included between two vectors, the scalar product, the vector product, and the length of a vector.
Methods of Applied Mathematics
Feb 28, 2013 Jeremy Levesley, University of Leicester
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Prof Jeremy Levesley explains how to find and categorise the local maxima and minima using the second derivative test. He also explains how to find the global maxima and minima by checking for the interior local maxima and minima and then points on the interiors of edges and corners.
Methods of Applied Mathematics
Feb 28, 2013 Jeremy Levesley, University of Leicester
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Prof Jeremy Levesley talks about constructing tangent lines to curves in space and tangent planes to surfaces.
Methods of Applied Mathematics
Feb 28, 2013 Jeremy Levesley, University of Leicester
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Prof Jeremy Levesley explains how to add vectors, multiply vectors by a scalar, compute the scalar (dot) and vector (cross) products of vectors and calculate the length of a vector.
Methods of Applied Mathematics
Feb 28, 2013 Jeremy Levesley, University of Leicester
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Prof Jeremy Levesley talks about partial differentiation and the chain rule for partial differentiation.
Methods of Applied Mathematics
Feb 28, 2013 Jeremy Levesley, University of Leicester
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Prof Jeremy Levesley talks about the solution of differential equations of linear and homogenous types.
Methods of Applied Mathematics
Feb 28, 2013 Jeremy Levesley, University of Leicester
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Prof Jeremy Levesley explains how to calculate the differentiation of vectors which depend on a parameter, the tangent vector to a space curve, the speed and velocity of a particle, and the length of a space curve defined parametrically.
Methods of Applied Mathematics
Feb 28, 2013 Jeremy Levesley, University of Leicester
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Prof Jeremy Levesley talks about the solution of first order differential equations using direct integration and separable equations.
Methods of Applied Mathematics
Feb 28, 2013 Jeremy Levesley, University of Leicester
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Prof Jeremy Levesley explains how to calculate the vector and Cartesian equations of lines and planes, and the scalar and vector products.
Methods of Applied Mathematics
Feb 28, 2013 Jeremy Levesley, University of Leicester
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Prof Jeremy Levesley talks about the solution of second order differential equations with constant coefficients.
Methods of Applied Mathematics
Feb 28, 2013 Jeremy Levesley, University of Leicester
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Prof Jeremy Levesley explains how to compute the Taylor series for a function and how to estimate the error approximating a function with its Taylor series.
Methods of Applied Mathematics
Feb 28, 2013 Jeremy Levesley, University of Leicester
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Prof Jeremy Levesley talks about integration over a rectangle and integration over regions where the range of integration is given. He also explains how to use polar coordinates for regions with circular symmetry.