Mathematical Methods for Physics and Engineering: A Comprehensive Guide
The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. Further tabulations, of relevance in statistics and numerical integration, have been added. In this edition, half of the exercises are provided with hints and answers and, in a separate manual available to both students and their teachers, complete worked solutions. The remaining exercises have no hints, answers or worked solutions and can be used for unaided homework; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.
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Complex numbers and hyperbolic functions
Series and limits
Matrices and vector spaces
general and particular solutions
separation of variables
Calculus of variations
Applications of complex variables
Line surface and volume integrals
Firstorder ordinary diﬀerential equations
Higherorder ordinary diﬀerential equations
Series solutions of ordinary diﬀerential equations
Eigenfunction methods for diﬀerential equations
Preface to the third edition page
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axis basis vectors boundary conditions Cartesian coordinates Cartesian tensor chapter coeﬃcients complex numbers components consider constant contour convergence coordinate system corresponding curve deﬁned deﬁnition denote determinant diﬀerent diﬀerential equations discussed divergence theorem eigenfunctions eigenvalues eigenvectors equal evaluate example expression ﬁeld ﬁnd ﬁnding ﬁnite ﬁrst ﬁrst-order ﬁxed follows Fourier series Fourier transform given gives Green’s function hence Hermitian Hermitian operator inﬁnite integrand inverse Laplace transform Legendre Legendre polynomials line integral linearly independent matrix method multiplying non-zero normalised obtain orthogonal particular plane polar coordinates polynomial properties prove radius recurrence relation respect result roots saddle point satisﬁes scalar second-order shown in ﬁgure singular sinx solution solve speciﬁc spherical polar stationary points subsection substitution surface tensor theorem variable vector field write written zero
Side 45 - The derivative of the product of two functions is equal to the first function times the derivative of the second plus the second times the derivative of the first.
Side 47 - This can now be rearranged into the more convenient and memorisable form This can be expressed in words as the derivative of a quotient is equal to the bottom times the derivative of the top minus the top times the derivative of the bottom, all over the bottom squared.
Side xix - I know the kings of England, and I quote the fights historical, From Marathon to Waterloo, in order categorical ; I'm very well acquainted too with matters mathematical, I understand equations, both the simple and quadratical, About binomial theorem I'm teeming with a lot o' news, With many cheerful facts about the square of the hypotenuse. I'm very good at integral and differential calculus, I know the scientific names of beings animalculous, In short, in matters vegetable, animal and mineral, I...