05602cam a2200445 a 4500 7817502 BD-DhUL 20150203082536.0 m d cr n 100615s2007 caua ab 000 0 eng d 1598291874 (electronic bk.) 9781598291872 (electronic bk.) 1598291866 (pbk.) 9781598291865 (pbk.) 10.2200/S00082ED1V01Y200612ENG003 doi (WaSeSS)ssj0000328540 CaBNvSL CaBNvSL CaBNvSL WaSeSS BD-DhUL TA330 .W274 2007 515.353 22 WAE Watts, Robert G. Essentials of applied mathematics for scientists and engineers Essentials of applied mathematics for scientists and engineers / Robert G. Watts. 1st ed. San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2007. ix, 169 p. : ill. ; 23 cm. US$ 40.90 Synthesis lectures on engineering sequence in series, 1559-8128 ; #3 Part of: Synthesis digital library of engineering and computer science. Title from PDF t.p. (viewed on October 13, 2008). Series from website. Includes bibliographical references. Partial differential equations in engineering -- Introductory comments -- Fundamental concepts -- Problems -- The heat conduction (or diffusion) equation -- Rectangular Cartesian coordinates -- Cylindrical coordinates -- Spherical coordinates -- The Laplacian operator -- Boundary conditions -- The vibrating string -- Boundary conditions -- Vibrating membrane -- Longitudinal displacements of an elastic bar -- Further reading -- The Fourier method: Separation of variables -- Heat conduction -- Scales and dimensionless variables -- Separation of variables -- Superposition -- Orthogonality -- Lessons -- Problems -- Scales and dimensionless variables -- Separation of variables -- Choosing the sign of the separation constant -- Superposition -- Orthogonality -- Lessons -- Scales and dimensionless variables -- Getting to one nonhomogeneous condition -- Separation of variables -- Choosing the sign of the separation constant -- Superposition -- Orthogonality -- Lessons -- Scales and dimensionless variables -- Relocating the nonhomogeneity -- Separating variables -- Superposition -- Orthogonality -- Lessons -- Problems -- Vibrations -- Scales and dimensionless variables -- Separation of variables -- Orthogonality -- Lessons -- Problems -- Further reading -- Orthogonal sets of functions -- Vectors -- Orthogonality of vectors -- Orthonormal sets of vectors -- Functions -- Orthonormal sets of functions and Fourier series -- Best approximation -- Convergence of Fourier series -- Examples of Fourier series -- Problems -- Sturm-Liouville problems: Orthogonal functions -- Orthogonality of Eigenfunctions -- Problems -- Further reading -- Series solutions of ordinary differential equations -- General series solutions -- Definitions -- Ordinary points and series solutions -- Lessons: Finding series solutions for differential equations with ordinary points -- Problems -- Regular singular points and the method of Frobenius -- Lessons: Finding series solution for differential equations with regular singular points -- Logarithms and second solutions -- Problems -- Bessel functions -- Solutions of Bessel's equation -- Here are the rules -- Fourier-Bessel series -- Problems -- Legendre functions -- Associated Legendre functions -- Problems -- Further reading -- Solutions using Fourier series and integrals -- Conduction (or diffusion) problems -- Time-dependent boundary conditions -- Vibrations problems -- Problems -- Fourier integrals -- Problem -- Further reading -- Integral transforms: The Laplace transform -- The Laplace transform -- Some important transforms -- Exponentials -- Shifting in the S-domain -- Shifting in the time domain -- Sine and cosine -- Hyperbolic functions -- Powers of t: tm -- Heaviside step -- The Dirac delta function -- Transforms of derivatives -- Laplace transforms of integrals -- Derivatives of transforms -- Linear ordinary differential equations with constant coefficients -- Some important theorems -- Initial value theorem -- Final value theorem -- Convolution -- Partial fractions -- Nonrepeating roots -- Repeated roots -- Quadratic factors: Complex roots -- Problems -- Further reading -- Complex variables and the Laplace inversion integral -- Basic properties -- Limits and differentiation of complex variables analytic functions -- Integrals -- The Cauchy integral formula -- Problems -- Solutions with Laplace transforms -- Mechanical vibrations -- Problems -- Diffusion or conduction problems -- Problems -- Duhamel's theorem -- Problems -- Further reading -- Sturm-Liouville Transforms -- A Preliminary Example: Fourier Sine Transform -- Generalization: The Sturm-Liouville Transform: Theory -- The Inverse Transform -- Problems -- Further Reading -- Introduction to Perturbation methods -- Examples from algebra -- Regular perturbation -- Singular perturbation -- Appendix A: The roots of certain transcendental equations. Differential equations, Partial Numerical solutions. Differential equations, Linear Numerical solutions. Engineering mathematics. Synthesis lectures on engineering (Online) ; #3. Serials Solutions original record ddc BK 6763 6763 0 0 ddc 0 515_353000000000000_WAE 0 NFIC 11771 DUSL DUSL GEN 2014-04-15 Purchased 515.353 WAE 481186 2014-09-01 2014-09-01 BK