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Essential mathematics for the physical sciences. Volume I, Homogeneous boundary value problems, Fourier methods, and special functions / Brett Borden, James Luscombe.

Κατά: Συντελεστής(ές): Τύπος υλικού: ΚείμενοΚείμενοΣειρά: IOP concise physicsΛεπτομέρειες δημοσίευσης: San Rafael [Καλιφόρνια] : Morgan & Claypool Publishers, c2017.Περιγραφή: 1 ηλεκτρονική πηγή (ποικίλες σελιδαριθμήσεις) : εικ. (μερ. έγχρ.)ISBN:
  • 9781681744858
  • 9781681744872
Άλλος τίτλος:
  • Homogeneous boundary value problems, Fourier methods, and special functions
Θέμα(τα): Ταξινόμηση DDC:
  • 530.15 23
Πηγές στο διαδίκτυο:
Περιεχόμενα:
1. Partial differential equations -- 2. Separation of variables -- 2.1. Helmholtz equation -- 2.2. Helmholtz equation in rectangular coordinates -- 2.3. Helmholtz equation in cylindrical coordinates -- 2.4. Helmholtz equation in spherical coordinates -- 2.5. Roadmap : where we are headed
3. Power-series solutions of ODEs -- 3.1. Analytic functions and the Frobenius method -- 3.2. Ordinary points -- 3.3. Regular singular points -- 3.4. Wronskian method for obtaining a second solution -- 3.5. Bessel and Neumann functions -- 3.6. Legendre polynomials
4. Sturm-Liouville theory -- 4.1. Differential equations as operators -- 4.2. Sturm-Liouville systems -- 4.3. The SL eigenvalue problem, L[y] = -[lambda]wy -- 4.4. Dirac delta function -- 4.5. Completeness -- 4.6. Hilbert space : a brief introduction
5. Fourier series and integrals -- 5.1. Fourier series -- 5.2. Complex form of Fourier series -- 5.3. General intervals -- 5.4. Parseval's theorem -- 5.5. Back to the delta function -- 5.6. Fourier transform -- 5.7. Convolution integral
6. Spherical harmonics and friends -- 6.1. Properties of the Legendre polynomials, Pl(x) -- 6.2. Associated Legendre functions, Pl m(x) -- 6.3. Spherical harmonic functions, Yl m([theta], [phi]) -- 6.4. Addition theorem for Yl m([theta], [phi]) -- 6.5. Laplace equation in spherical coordinates
7. Bessel functions and friends -- 7.1. Small-argument and asymptotic forms -- 7.2. Properties of the Bessel functions, Jn(x) -- 7.3. Orthogonality -- 7.4. Bessel series -- 7.5. Fourier-Bessel transform -- 7.6. Spherical Bessel functions -- 7.7. Expansion of plane waves in spherical coordinates
Appendices -- A. Topics in linear algebra -- B. Vector calculus -- C. Power series -- D. Gamma function, [Gamma](x).
Περίληψη: Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced. A study of the mathematics used in science is thus a sound intellectual investment for training as scientists and engineers. This first volume of two is centered on methods of solving partial differential equations and the special functions introduced. This text is based on a course offered at the Naval Postgraduate School (NPS) and while produced for NPS needs, it will serve other universities well.
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Περιλαμβάνει βιβλιογραφικές παραπομπές.

1. Partial differential equations -- 2. Separation of variables -- 2.1. Helmholtz equation -- 2.2. Helmholtz equation in rectangular coordinates -- 2.3. Helmholtz equation in cylindrical coordinates -- 2.4. Helmholtz equation in spherical coordinates -- 2.5. Roadmap : where we are headed

3. Power-series solutions of ODEs -- 3.1. Analytic functions and the Frobenius method -- 3.2. Ordinary points -- 3.3. Regular singular points -- 3.4. Wronskian method for obtaining a second solution -- 3.5. Bessel and Neumann functions -- 3.6. Legendre polynomials

4. Sturm-Liouville theory -- 4.1. Differential equations as operators -- 4.2. Sturm-Liouville systems -- 4.3. The SL eigenvalue problem, L[y] = -[lambda]wy -- 4.4. Dirac delta function -- 4.5. Completeness -- 4.6. Hilbert space : a brief introduction

5. Fourier series and integrals -- 5.1. Fourier series -- 5.2. Complex form of Fourier series -- 5.3. General intervals -- 5.4. Parseval's theorem -- 5.5. Back to the delta function -- 5.6. Fourier transform -- 5.7. Convolution integral

6. Spherical harmonics and friends -- 6.1. Properties of the Legendre polynomials, Pl(x) -- 6.2. Associated Legendre functions, Pl m(x) -- 6.3. Spherical harmonic functions, Yl m([theta], [phi]) -- 6.4. Addition theorem for Yl m([theta], [phi]) -- 6.5. Laplace equation in spherical coordinates

7. Bessel functions and friends -- 7.1. Small-argument and asymptotic forms -- 7.2. Properties of the Bessel functions, Jn(x) -- 7.3. Orthogonality -- 7.4. Bessel series -- 7.5. Fourier-Bessel transform -- 7.6. Spherical Bessel functions -- 7.7. Expansion of plane waves in spherical coordinates

Appendices -- A. Topics in linear algebra -- B. Vector calculus -- C. Power series -- D. Gamma function, [Gamma](x).

Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced. A study of the mathematics used in science is thus a sound intellectual investment for training as scientists and engineers. This first volume of two is centered on methods of solving partial differential equations and the special functions introduced. This text is based on a course offered at the Naval Postgraduate School (NPS) and while produced for NPS needs, it will serve other universities well.

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