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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.
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35. Overview of Course
- Summary
- • 14 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.
- 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.
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.
D'Alembert's solution and derivation of the form of solutions. Classification of PDEs with an example using the wave equation.
- Class notes
- • 5 pages •
D'Alembert's solution and derivation of the form of solutions. Classification of PDEs with an example using the wave equation.
Square Wave example with matlab script to plot solution. Theorem of functions being orthogonal and proving this is the case for different periods. Deriving the value of the coefficients for the fourier series. Square wave Redux.
- Class notes
- • 3 pages •
Square Wave example with matlab script to plot solution. Theorem of functions being orthogonal and proving this is the case for different periods. Deriving the value of the coefficients for the fourier series. Square wave Redux.
Solving systems of equations using matlab and creating a general solution. Shows example of a repeated root problem and how to solve. Goes through the theorem for system of equations and a proof. Gives an example of modelling a system of equations.
- Class notes
- • 5 pages •
Solving systems of equations using matlab and creating a general solution. Shows example of a repeated root problem and how to solve. Goes through the theorem for system of equations and a proof. Gives an example of modelling a system of equations.
Example finished from the end of the last notes. Definitions of linearly independent, linear dependence and linear combination with an example. Existence and uniqueness theorem. Example of solving a third order IVP. Definition of the Wronskian, the Wronskian test with examples and a proof.
- Class notes
- • 5 pages •
Example finished from the end of the last notes. Definitions of linearly independent, linear dependence and linear combination with an example. Existence and uniqueness theorem. Example of solving a third order IVP. Definition of the Wronskian, the Wronskian test with examples and a proof.
Singular solutions for ODEs with examples and a graph. Existence and uniqueness theorem example. Picard's Iteration Method theory and an example.
- Class notes
- • 3 pages •
Singular solutions for ODEs with examples and a graph. Existence and uniqueness theorem example. Picard's Iteration Method theory and an example.
How to make ODEs exact with a integration factor, finding a particular solution for Exact ODEs. Show why integrating factor works. Example finding an integrating factor, finding an exact solution and graphing the solution in Matlab.
- Class notes
- • 2 pages •
How to make ODEs exact with a integration factor, finding a particular solution for Exact ODEs. Show why integrating factor works. Example finding an integrating factor, finding an exact solution and graphing the solution in Matlab.
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Newest Advanced Engineering Mathematics summaries
Separation of variables to solve the Heat equation and represent as a summation solution. Example of copper bar and solving for its solution to transfer of heat over time. Includes matlab code of graphing of solution. Different Boundary conditions: Dirichlet and Neumann boundary conditions, motivation for Fourier series.
- Class notes
- • 5 pages •
Separation of variables to solve the Heat equation and represent as a summation solution. Example of copper bar and solving for its solution to transfer of heat over time. Includes matlab code of graphing of solution. Different Boundary conditions: Dirichlet and Neumann boundary conditions, motivation for Fourier series.
Square Wave example with matlab script to plot solution. Theorem of functions being orthogonal and proving this is the case for different periods. Deriving the value of the coefficients for the fourier series. Square wave Redux.
- Class notes
- • 3 pages •
Square Wave example with matlab script to plot solution. Theorem of functions being orthogonal and proving this is the case for different periods. Deriving the value of the coefficients for the fourier series. Square wave Redux.
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.
Partial Differential Equations and its definition and properties. Some important PDEs are given and an example given of how to solve one. It goes through how to make a well-posed PDE question and the modelling framework. An example is given of modelling car traffic going through the steps of the modelling framework.
- Class notes
- • 4 pages •
Partial Differential Equations and its definition and properties. Some important PDEs are given and an example given of how to solve one. It goes through how to make a well-posed PDE question and the modelling framework. An example is given of modelling car traffic going through the steps of the modelling framework.
Solving systems of equations using matlab and creating a general solution. Shows example of a repeated root problem and how to solve. Goes through the theorem for system of equations and a proof. Gives an example of modelling a system of equations.
- Class notes
- • 5 pages •
Solving systems of equations using matlab and creating a general solution. Shows example of a repeated root problem and how to solve. Goes through the theorem for system of equations and a proof. Gives an example of modelling a system of equations.
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.
General solution for two nonhomogeneous ODE example. How to use matlab to check your solutions. Modelling free and forced oscillations theory and finding the solutions to an undamped system. Example of a harmonic oscillator and looking at the different types of damped systems.
- Class notes
- • 5 pages •
General solution for two nonhomogeneous ODE example. How to use matlab to check your solutions. Modelling free and forced oscillations theory and finding the solutions to an undamped system. Example of a harmonic oscillator and looking at the different types of damped systems.
Proof for multiple roots for solutions. Theory for the general solution for nonhomogeneous linear ODEs and an example. Method of undetermined guessing and an example which is plotted with matlab code. An example of an IVP for nonhomogeneous solutions.
- Class notes
- • 5 pages •
Proof for multiple roots for solutions. Theory for the general solution for nonhomogeneous linear ODEs and an example. Method of undetermined guessing and an example which is plotted with matlab code. An example of an IVP for nonhomogeneous solutions.
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