Methods of Applied Mathematics

Methods of Applied Mathematics

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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.

Jeremy Levesley, University of Leicester


    • Aug 22, 2013 LATEST EPISODE
    • infrequent NEW EPISODES
    • 6m AVG DURATION
    • 24 EPISODES


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    Latest episodes from Methods of Applied Mathematics

    Power Series 1

    Play Episode Listen Later Aug 22, 2013 6:52


    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.

    Power Series 2

    Play Episode Listen Later Aug 22, 2013 5:36


    Taylor expansion and examples of finding terms

    Series 2

    Play Episode Listen Later Aug 22, 2013 8:19


    Defining convergence and testing for convergence including the alternating series test, ratio test, and comparison test

    Series 3

    Play Episode Listen Later Aug 22, 2013 2:10


    Explaining absolute convergence with a look at conditional convergence, rearrangements, and product rule

    Continuity 1

    Play Episode Listen Later Aug 6, 2013 3:19


    Official definition and examples, including demonstration of using L'hopital's rule

    Differentiation 1

    Play Episode Listen Later Aug 6, 2013 6:33


    Differentiation is the process by which we extract the gradient of a line from the formula of a line.

    Sequences 1

    Play Episode Listen Later Aug 5, 2013 8:59


    Sequences are understood by first defining convergence: a sequence ends up at a certain value when it gets to infinity. Limits and closeness.

    Sequences 3

    Play Episode Listen Later Aug 5, 2013 6:18


    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

    Sequences 2

    Play Episode Listen Later Aug 5, 2013 1:23


    Covers the two types of diverging sequences: sequences tending to infinity, and oscillating sequences

    Series 1

    Play Episode Listen Later Aug 2, 2013 3:37


    An introduction to series. It is necessary to understand sequences before tackling series. Sigma notation, summation, and geometric series are explained as well.

    Bounds

    Play Episode Listen Later Aug 2, 2013 1:31


    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.

    Second Order Liner Differential Equations with Constant Coefficients

    Play Episode Listen Later Feb 28, 2013 17:26


    Prof Jeremy Levesley talks about the solution of second order differential equations with constant coefficients.

    Integration over Regions and the Order of Integration

    Play Episode Listen Later Feb 28, 2013 11:17


    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.

    First Order Differential Equations II

    Play Episode Listen Later Feb 28, 2013 6:49


    Prof Jeremy Levesley talks about the solution of differential equations of linear and homogenous types.

    First Order Differential Equations I

    Play Episode Listen Later Feb 28, 2013 5:20


    Prof Jeremy Levesley talks about the solution of first order differential equations using direct integration and separable equations.

    Taylor Series

    Play Episode Listen Later Feb 28, 2013 6:13


    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.

    Maxima, Minima and Saddle Points

    Play Episode Listen Later Feb 28, 2013 6:08


    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.

    Directional Derivatives

    Play Episode Listen Later Feb 28, 2013 4:19


    Prof Jeremy Levesley explains how to compute derivatives in given directions and the maximum slope at a point.

    Tangent Lines and Planes

    Play Episode Listen Later Feb 28, 2013 7:15


    Prof Jeremy Levesley talks about constructing tangent lines to curves in space and tangent planes to surfaces.

    Partial Differentiation and the Chain Rule

    Play Episode Listen Later Feb 28, 2013 4:50


    Prof Jeremy Levesley talks about partial differentiation and the chain rule for partial differentiation.

    Tangent Vectors, Curves and Lengths of Space Curves

    Play Episode Listen Later Feb 28, 2013 5:46


    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.

    Vector and Cartesian Equations of Lines and Planes in 3D

    Play Episode Listen Later Feb 28, 2013 7:40


    Prof Jeremy Levesley explains how to calculate the vector and Cartesian equations of lines and planes, and the scalar and vector products.

    Angles between Vectors and Areas

    Play Episode Listen Later Feb 28, 2013 5:58


    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.

    Algebra with Vectors

    Play Episode Listen Later Feb 28, 2013 7:37


    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.

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