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College Level Mathematics II: My Study Notes

Mohamed F. El-Hewie
4.9/5 (34902 ratings)
Read Now Download Now ⏭ listen AudioBook
Description:Special FunctionsFourier TransformsLaplace TransformsChapter 7: SPECIAL FUNCTIONS1. Gamma Functions2. Beta Functions3. Bessel Functions3.1. Bessel equation for zero order3.2. Properties of Bessel functions3.3. Bessel functions of order one (n = 1)3.4. Relationships between Bessel functions of orders zero and one3.5. Lammel’ s integrals3.6. Fourier-Bessel expansions of zero order3.7. Vibration of uniformly stretched membrane3.8. Application of Bessel functions on conduction of heat3.9. Modified Bessel function of zero order3.10. Bessel and Kelvin functions3.11. Bessel functions of any real order3.12. Bessel functions of integral order3.13. Bessel coefficients3.14. Recurrence formulae3.15. Bessel function as integrals3.16. The Bessel functions of order n of the third kind (Hankel functions of order n)4. Legendre functions4.1. Alternative definition of Legendre polynomials4.2. Legendre’s recurrence formulae4.3. Integral properties of Lagendre polynomial4.4. The associated Legendre functions.4.5. Applications of Legendre functions5. Exercises on special functions Chapter 8: Fourier transforms1. Fourier series and harmonic analysis2. Fourier theorem3. Preliminary integrals used in Fourier transforms4. Determination of the coefficients of the Fourier expansion5. Examples of Fourier transformations6. Fourier expansions in cosines only7. Fourier expansions in sines only8. Fourier expansions in even harmonics9. Fourier expansions in odd harmonics10. Summary of common Fourier transforms11. Practical Fourier AnalysisChapter 11: Laplace Transforms1. The Laplace Transformation2. General Theorems on the Laplace Transformation2.1. The unit step function2.2. The second translation or shifting property2.3. Application of the shift theorem to the solution of difference and differential equations2.4. The unit impulse function2.5. The unit doublet2.6. The behavior of f(s) as s →∞2.7. Initial value theorem2.8. Final value theorem2.9. Differentiation of transform2.10. Application of the differentiation of Laplace transform to the solution of linear differential equations with coefficients as polynomials in t.2.11. Integration of transforms2.12. Transforms of periodic functions2.13. The product theorem—Convolution2.14. Application of the product theorem to the solution of differential and integral equations2.15. Power series method for the determination of transforms and inverse transforms2.16. The error function or probability integral2.17. The sine-integral function Si(t)2.18. The Cosine -integral function Ci(t)2.19. The exponential integral function2.20. Evaluation of definite integrals using the Laplace transformation2.21. The Heaviside's expansion formulae2.22. The inversion integral2.23. Formulae for residues2.24. Inversion in the case of branch points2.25. Miscellaneous Examples on Laplace Transform2.26. Exercises on Laplace Transforms3. Electrical Applications of the Laplace Transformation4. Dynamical Applications of Laplace Transforms5. Structural Applications5.1. Deflection of beams5.2. Exercises on Laplace Transform in practical applications6.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with College Level Mathematics II: My Study Notes. To get started finding College Level Mathematics II: My Study Notes, you are right to find our website which has a comprehensive collection of manuals listed.
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College Level Mathematics II: My Study Notes

Mohamed F. El-Hewie
4.4/5 (1290744 ratings)
Read Now Download now ⏭ listen AudioBook
Description: Special FunctionsFourier TransformsLaplace TransformsChapter 7: SPECIAL FUNCTIONS1. Gamma Functions2. Beta Functions3. Bessel Functions3.1. Bessel equation for zero order3.2. Properties of Bessel functions3.3. Bessel functions of order one (n = 1)3.4. Relationships between Bessel functions of orders zero and one3.5. Lammel’ s integrals3.6. Fourier-Bessel expansions of zero order3.7. Vibration of uniformly stretched membrane3.8. Application of Bessel functions on conduction of heat3.9. Modified Bessel function of zero order3.10. Bessel and Kelvin functions3.11. Bessel functions of any real order3.12. Bessel functions of integral order3.13. Bessel coefficients3.14. Recurrence formulae3.15. Bessel function as integrals3.16. The Bessel functions of order n of the third kind (Hankel functions of order n)4. Legendre functions4.1. Alternative definition of Legendre polynomials4.2. Legendre’s recurrence formulae4.3. Integral properties of Lagendre polynomial4.4. The associated Legendre functions.4.5. Applications of Legendre functions5. Exercises on special functions Chapter 8: Fourier transforms1. Fourier series and harmonic analysis2. Fourier theorem3. Preliminary integrals used in Fourier transforms4. Determination of the coefficients of the Fourier expansion5. Examples of Fourier transformations6. Fourier expansions in cosines only7. Fourier expansions in sines only8. Fourier expansions in even harmonics9. Fourier expansions in odd harmonics10. Summary of common Fourier transforms11. Practical Fourier AnalysisChapter 11: Laplace Transforms1. The Laplace Transformation2. General Theorems on the Laplace Transformation2.1. The unit step function2.2. The second translation or shifting property2.3. Application of the shift theorem to the solution of difference and differential equations2.4. The unit impulse function2.5. The unit doublet2.6. The behavior of f(s) as s →∞2.7. Initial value theorem2.8. Final value theorem2.9. Differentiation of transform2.10. Application of the differentiation of Laplace transform to the solution of linear differential equations with coefficients as polynomials in t.2.11. Integration of transforms2.12. Transforms of periodic functions2.13. The product theorem—Convolution2.14. Application of the product theorem to the solution of differential and integral equations2.15. Power series method for the determination of transforms and inverse transforms2.16. The error function or probability integral2.17. The sine-integral function Si(t)2.18. The Cosine -integral function Ci(t)2.19. The exponential integral function2.20. Evaluation of definite integrals using the Laplace transformation2.21. The Heaviside's expansion formulae2.22. The inversion integral2.23. Formulae for residues2.24. Inversion in the case of branch points2.25. Miscellaneous Examples on Laplace Transform2.26. Exercises on Laplace Transforms3. Electrical Applications of the Laplace Transformation4. Dynamical Applications of Laplace Transforms5. Structural Applications5.1. Deflection of beams5.2. Exercises on Laplace Transform in practical applications6.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with College Level Mathematics II: My Study Notes. To get started finding College Level Mathematics II: My Study Notes, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.
Pages
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