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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
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
- • 9 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...
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
- • 4 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...
Frobenius ODEs, and looking at special cases. Using the indicial equation to find what type of solution the Frobenius ODEs. Edge Waves redux finding a power series solution.
- Class notes
- • 5 pages •
Frobenius ODEs, and looking at special cases. Using the indicial equation to find what type of solution the Frobenius ODEs. Edge Waves redux finding a power series solution.
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.
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.
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.
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.
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.
Existence and completeness theorem and a general proof (not complete), Characteristic Equation derivation and the different types with an example. Theory of linear independent solutions and a basis, using Wronksian for linear independence and basis- partial proof. Complex roots theory and an example with a graph and matlab code. Multiple roots theory of the number of linearly independent solutions and an example.
- Class notes
- • 5 pages •
Existence and completeness theorem and a general proof (not complete), Characteristic Equation derivation and the different types with an example. Theory of linear independent solutions and a basis, using Wronksian for linear independence and basis- partial proof. Complex roots theory and an example with a graph and matlab code. Multiple roots theory of the number of linearly independent solutions and an example.
Looking at the steps to Modelling Ordinary Differential Equations and the different types of forms: first order ODEs in explicit form, implicit form. How to solve Separable ODEs using a Chauvet Cave example. Lastly looking at the Concepts of a particular solution and a general solution.
- Class notes
- • 3 pages •
Looking at the steps to Modelling Ordinary Differential Equations and the different types of forms: first order ODEs in explicit form, implicit form. How to solve Separable ODEs using a Chauvet Cave example. Lastly looking at the Concepts of a particular solution and a general solution.
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Newest Advanced Engineering Mathematics summaries
35. Overview of Course
- Summary
- • 14 pages •
Further Fourier Series looking at a Maclaurin Series, inner product, weight function, orthogonal and norm. These have definitions equations and examples. Define an orthogonal set and examples of these. Legrendre Polynomials, Bessel functions and generalised fourier series. Definition for completeness of functions. Complex Fourier series and example.
- Class notes
- • 6 pages •
Further Fourier Series looking at a Maclaurin Series, inner product, weight function, orthogonal and norm. These have definitions equations and examples. Define an orthogonal set and examples of these. Legrendre Polynomials, Bessel functions and generalised fourier series. Definition for completeness of functions. Complex Fourier series and example.
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.
Frobenius ODEs, and looking at special cases. Using the indicial equation to find what type of solution the Frobenius ODEs. Edge Waves redux finding a power series solution.
- Class notes
- • 5 pages •
Frobenius ODEs, and looking at special cases. Using the indicial equation to find what type of solution the Frobenius ODEs. Edge Waves redux finding a power series solution.
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.
Looking at the steps to Modelling Ordinary Differential Equations and the different types of forms: first order ODEs in explicit form, implicit form. How to solve Separable ODEs using a Chauvet Cave example. Lastly looking at the Concepts of a particular solution and a general solution.
- Class notes
- • 3 pages •
Looking at the steps to Modelling Ordinary Differential Equations and the different types of forms: first order ODEs in explicit form, implicit form. How to solve Separable ODEs using a Chauvet Cave example. Lastly looking at the Concepts of a particular solution and a general solution.
Example of solving the time it takes for water to flow out of a tank and its Matlab code. Solving Exact ODEs with example.
- Class notes
- • 3 pages •
Example of solving the time it takes for water to flow out of a tank and its Matlab code. Solving Exact ODEs with 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.
Solving Linear ODEs: definition of linear/nonlinear and homogeneous/nonhomogeneous. General solution to first order ODE with integrating factor. Example of a first order linear IVP. Explanation to why the General solution formula works. Example of Hormone levels and their rates of changes. Using Matlab to solve ODEs.
- Class notes
- • 4 pages •
Solving Linear ODEs: definition of linear/nonlinear and homogeneous/nonhomogeneous. General solution to first order ODE with integrating factor. Example of a first order linear IVP. Explanation to why the General solution formula works. Example of Hormone levels and their rates of changes. Using Matlab to solve ODEs.
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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