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Advanced Engineering Mathematics notes
Erwin Kreyszig - ISBN: 9780470458365
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View all 41 notes for Advanced Engineering Mathematics, written by Erwin Kreyszig. All Advanced Engineering Mathematics notes, flashcards, summaries and study guides are written by your fellow students or tutors. Get yourself a Advanced Engineering Mathematics summary or other study material that matches your study style perfectly, and studying will be a breeze.
Best selling Advanced Engineering Mathematics notes
This is for electrical engineering student related subjects for you references in your subjects. Please analyze carefully the solutions. Email me at if you have questions. Thank you
- Class notes
- • 1 pages •
This is for electrical engineering student related subjects for you references in your subjects. Please analyze carefully the solutions. Email me at if you have questions. Thank you
The aim of this course unit is to enable a student to: 1. Demonstrate an understanding of methods used to solve partial differential equations and their engineering areas of application, 2. Apply mathematical skills from partial differentiation to solve problems that require partial differentiation methods, 3. Appreciate the role of partial differentiation in solving problems that are related to science and engineering. At the end of this course unit, the student should be able to: 1. Apply par...
- Class notes
- • 6 pages •
The aim of this course unit is to enable a student to: 1. Demonstrate an understanding of methods used to solve partial differential equations and their engineering areas of application, 2. Apply mathematical skills from partial differentiation to solve problems that require partial differentiation methods, 3. Appreciate the role of partial differentiation in solving problems that are related to science and engineering. At the end of this course unit, the student should be able to: 1. Apply par...
Looking at the wave equation and solving using polar coordinates for a wave propagating on the surface of a circular pool. Special case with no angular dependence and finding solutions.
- Class notes
- • 6 pages •
Looking at the wave equation and solving using polar coordinates for a wave propagating on the surface of a circular pool. Special case with no angular dependence and finding solutions.
Graph and solve fourier series for square wave with arbitrary period. Fourier Cosine and Sine series with matlab example. Half-range expansion with examples.
- Class notes
- • 4 pages •
Graph and solve fourier series for square wave with arbitrary period. Fourier Cosine and Sine series with matlab example. Half-range expansion with examples.
Example of Near constant car density continued with interpretation. D'Alembert's solutions with an example of some cars being able to pass other cars. Heat equation and solving it with separation of variables coming to the full general solution.
- Class notes
- • 5 pages •
Example of Near constant car density continued with interpretation. D'Alembert's solutions with an example of some cars being able to pass other cars. Heat equation and solving it with separation of variables coming to the full general solution.
Looking at steady state solution for modelling the populations of predators and prey with graphs. Constructing systems of equations for different stages of life to model the population of a species.
- Class notes
- • 4 pages •
Looking at steady state solution for modelling the populations of predators and prey with graphs. Constructing systems of equations for different stages of life to model the population of a species.
Reduction of order method to find all terms of the homogeneous solution. Euler Cauchy Equations and the types of solution for the roots of the characteristic equation. Example using Reduction of order finding the general solution. Modelling Mathematical ecology, by looking at a fish example, finding solutions to a system of equations of how different factors affect fish populations.
- Class notes
- • 5 pages •
Reduction of order method to find all terms of the homogeneous solution. Euler Cauchy Equations and the types of solution for the roots of the characteristic equation. Example using Reduction of order finding the general solution. Modelling Mathematical ecology, by looking at a fish example, finding solutions to a system of equations of how different factors affect fish populations.
Damped system and the different scenarios and their solutions. Solutions plotted in matlab and graphed. Looked at Resonance in forced oscillations and the particular solution for this equation. Graph the solution of types of solution for the particular solution for different constant values and interpreted the results. Looked at more general methods of solving ODEs: finding a solution that is a factor multiple of a known solution.
- Class notes
- • 5 pages •
Damped system and the different scenarios and their solutions. Solutions plotted in matlab and graphed. Looked at Resonance in forced oscillations and the particular solution for this equation. Graph the solution of types of solution for the particular solution for different constant values and interpreted the results. Looked at more general methods of solving ODEs: finding a solution that is a factor multiple of a known solution.
Picard's Iteration method with example and using matlab to solve. Classification of ODEs: order and linearity. Initial value problem theory: autonomy, deterministism, homogeneous linear ODEs and superposition with proof. Different cases of equation giving examples of the different types and features.
- Class notes
- • 5 pages •
Picard's Iteration method with example and using matlab to solve. Classification of ODEs: order and linearity. Initial value problem theory: autonomy, deterministism, homogeneous linear ODEs and superposition with proof. Different cases of equation giving examples of the different types and features.
Example of a separable solution. Existence and Uniqueness Theorem (no proof) with two example questions. Showing how to work out the integrating factor to make exact ODEs exact.
- Class notes
- • 5 pages •
Example of a separable solution. Existence and Uniqueness Theorem (no proof) with two example questions. Showing how to work out the integrating factor to make exact ODEs exact.
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Gamma Function and solving the integral. Gamma Function for half integers and Matlab Script. Bessel Function series and plot with different values for nu. Bessel functions, special cases and the Bessel equation General Solution. Indicial Equation and its derivation. Frobenius Theorem and the different cases for different solutions.
- Class notes
- • 4 pages •
Gamma Function and solving the integral. Gamma Function for half integers and Matlab Script. Bessel Function series and plot with different values for nu. Bessel functions, special cases and the Bessel equation General Solution. Indicial Equation and its derivation. Frobenius Theorem and the different cases for different solutions.
Bessel equation and looking at Frobenius solution when using cylindrical coordinates. Show how nu is a solution a Frobenius solution to the Bessel Equation. Finding a recurrence relation for the coefficients of the Bessel functions. Plotting Bessel functions of the first kind. Generalising the Bessel series solution of first kind of order nu where half integers can used.
- Class notes
- • 5 pages •
Bessel equation and looking at Frobenius solution when using cylindrical coordinates. Show how nu is a solution a Frobenius solution to the Bessel Equation. Finding a recurrence relation for the coefficients of the Bessel functions. Plotting Bessel functions of the first kind. Generalising the Bessel series solution of first kind of order nu where half integers can used.
Legrendre polynomials and ODE, finding a power series to solve creating a recurrence relation for the coefficients. Convergence for power series. Method of Frobenius for circular and cylindrical geometries. Singular points and an example. Bessel's equation with singular points. Frobenius method and its solutions.
- Class notes
- • 5 pages •
Legrendre polynomials and ODE, finding a power series to solve creating a recurrence relation for the coefficients. Convergence for power series. Method of Frobenius for circular and cylindrical geometries. Singular points and an example. Bessel's equation with singular points. Frobenius method and its solutions.
Series Solution and how they can be found. Modelling of shallow water and finding solutions. Variation of Parameters and an example. Variation of parameters general solution and deriving it. Power Series method and using is to solve ODEs creating a recurrence relationship.
- Class notes
- • 7 pages •
Series Solution and how they can be found. Modelling of shallow water and finding solutions. Variation of Parameters and an example. Variation of parameters general solution and deriving it. Power Series method and using is to solve ODEs creating a recurrence relationship.
27. Power Series Method process of solving and example. Picard iteration method for second order ODE using Matlab. Power series solution for nonlinear ODEs. Power series properties (Radius of convergence). Existence of power series.
- Class notes
- • 7 pages •
27. Power Series Method process of solving and example. Picard iteration method for second order ODE using Matlab. Power series solution for nonlinear ODEs. Power series properties (Radius of convergence). Existence of power series.
Water Waves in 2D. Using Dirichlet Boundary conditions in an example to solve the wave equation for a rectangular region. Procedure how to solve Wave equation in this way using Fourier series.
- Class notes
- • 5 pages •
Water Waves in 2D. Using Dirichlet Boundary conditions in an example to solve the wave equation for a rectangular region. Procedure how to solve Wave equation in this way using Fourier series.
Linearising wave equation for a water column. Using separation of variables to create a general solution to the wave equation.
- Class notes
- • 4 pages •
Linearising wave equation for a water column. Using separation of variables to create a general solution to the wave equation.
Matlab Script graphing Wave Equation solution of separation of variables with Fourier series. Heat Flow equation example solving and graphing with Matlab. PDEs and waves, shows part way through deriving the PDE for the wave equation.
- Class notes
- • 5 pages •
Matlab Script graphing Wave Equation solution of separation of variables with Fourier series. Heat Flow equation example solving and graphing with Matlab. PDEs and waves, shows part way through deriving the PDE for the wave equation.
Graph and solve fourier series for square wave with arbitrary period. Fourier Cosine and Sine series with matlab example. Half-range expansion with examples.
- Class notes
- • 4 pages •
Graph and solve fourier series for square wave with arbitrary period. Fourier Cosine and Sine series with matlab example. Half-range expansion with examples.
Theorem for Fourier series, the fourier series and the integrals to solve the coefficients. Forced oscillation example and graphing of solution. Generalising Fourier series to an Arbitrary period and derivation.
- Class notes
- • 3 pages •
Theorem for Fourier series, the fourier series and the integrals to solve the coefficients. Forced oscillation example and graphing of solution. Generalising Fourier series to an Arbitrary period and derivation.
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