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Mauch S. — Introduction to Methods of Applied Mathematics or Advanced Mathematical Methods for Scientists and Engineers
Mauch S. — Introduction to Methods of Applied Mathematics or Advanced Mathematical Methods for Scientists and Engineers

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Название: Introduction to Methods of Applied Mathematics or Advanced Mathematical Methods for Scientists and Engineers

Автор: Mauch S.

Язык: en

Рубрика: Математика/Анализ/Учебники по элементарному анализу/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 1421

Добавлена в каталог: 12.12.2004

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
a + i b form      113
Abel's formula      547
Absolute convergence      320
adjoint of a differential operator      550
adjoint of operators      787
Analytic      219
Analytic continuation      263
analytic continuation Fourier integrals      933
Analytic functions      1367
Anti-derivative      285
Argand diagram      113
Argument of a complex number      114
argument theorem      303
Asymptotic expansions      747
asymptotic integration by parts      754
asymptotic relations      747
autonomous D.E.      593
Autonomous differential equations      593
average value theorem      302
behavior of Fourier coefficients      811
Bernoulli equations      589
Bessel functions      979
Bessel generating function      983
Bessel generating function of the first kind      983
Bessel generating function second kind      992
Bessel's equation      979
Bessel's inequality      774
Bijective function      5
Bilinear concomitant      551
Binomial coefficients      1409
Binomial formula      1409
Boundary value problems      664
Branch point      165
branch point singularity      229
branch principal      6
Branches      6
Calculus of variations      1261
canonical forms constant coefficient equation      609
canonical forms of differential equations      609
Cardinality of a set      4
Cartesian form      113
Cartesian product of sets      4
Cauchy convergence      319
Cauchy principal value      384 932
Cauchy's inequality      301
Cauchy—Riemann equations      223 1367
clockwise      148
Closed curve      147
Closed interval      3
closure relation and Fourier transform      934
closure relation discrete sets of functions      775
Codomain      4
Comparison Test      321
comparison test series      321
completeness of sets of functions      774
completeness of sets of vectors      24
Complex conjugate      112 113
complex derivative      219
complex infinity      149
Complex line integral      280
complex magnitude      113
complex modulus      113
Complex number      112
complex numbers      111
complex numbers arithmetic      118
Complex plane      113
components of vector      18
computer games      1413
connected region      147
constant coefficient differential equations      557
Continuity      36
Continuity uniform      37
continuous curve      147
Continuous functions      36 325 327
continuous piecewise      37
contour      147
Contour integral      280
convergence comparison test      321
Convergence in the mean      774
convergence integral test      322
convergence of integrals      885
Convergence of sequences      319
Convergence of series      319
convergence, Raabe's test      325
convergence, ratio test      323
convergence, root test      324
convolution theorem and Fourier transform      936
Convolution theorem for Laplace transforms      898
convolution theorem of Laplace transforms      898
Convolutions      898
counter-clockwise      148
Curve      147
Definite integral      76
definition of power series      328
degree of a differential equation      467
DEL      95
derivative complex      219
derivative of determinant      544
difference constant coefficient equations      699
difference exact equations      696
difference first order homogeneous      697
difference first order inhomogeneous      698
Difference of sets      4
Differential calculus      33
differential equations constant coefficient      557
differential equations degree      467
differential equations equidimensional-in-x      595
differential equations equidimensional-in-y      596
differential equations first order      467 476
differential equations order      467
differentiation of power series      332
Dirac delta function      625 775
Directional derivative      95
discontinuous functions      36 802
discrete derivative      695
discrete integral      695
Disjoint sets      4
Domain      4
Economics      1413
Eigenfunctions      799
eigenvalue problems      799
Eigenvalues      799
Elements of a set      3
Empty set      3
Entire      219
equidimensional differential equations      563
equidimensional-in-x D.E.      595
equidimensional-in-y D.E.      596
Euler differential equations      563
Euler's formula      116
Euler's formula of Gamma function      967
Euler's notation i      112
Euler's theorem      473
Euler—Mascheroni constant      970
exact differential equations      469 566
exact equations      469
exchanging dep. and indep. var.      592
Extended complex plane      149
extremum modulus theorem      303
Fibonacci sequence      703
first order differential equations      484
fluid flow ideal      232
formally self-adjoint operators      788
Fourier coefficients      771 802
Fourier convolution theorem      936
Fourier cosine series      808
Fourier cosine transform      940
Fourier cosine transform of derivatives      942
Fourier series      799
Fourier series and Fourier transform      927
Fourier series uniform convergence      814
Fourier sine series      809
Fourier sine transform      941
Fourier sine transform of derivatives      942
Fourier transform alternate definitions      929
Fourier transform closure relation      934
Fourier transform convolution theorem      936
Fourier transform of a derivative      935
Fourier transform shift property      938
Fredholm alternative theorem      664
Fredholm equations      614
Frobenius series first order differential equation      487
function elements      263
Functional equation      236
fundamental set of solutions of a differential equation      549
Fundamental theorem of algebra      302
Fundamental theorem of calculus      78
Gambler's ruin problem      695 700
Gamma function      967
Gamma function difference equation      967
Gauss' formula of Gamma function      969
Gauss' test      325
Gauss' test convergence      325
Gauss' test series      325
generating function for Bessel functions      983
Geometric series      320
Gibb's phenomenon      817
Gradient      95
Gramm—Schmidt orthogonalization      766
Greatest integer function      5
Green's formula      551 787
Hankel's formula of Gamma function      968
Harmonic conjugate      226
Harmonic series      321 342
Heaviside function      479 625
Holomorphic      219
homogeneous coefficient differential equations      473
homogeneous coefficient equations      473
homogeneous differential equations      467
homogeneous functions      473
homogeneous solution      477
homogeneous solutions of differential equations      542
i Euler's notation      112
ideal fluid flow      232
identity map      4
ill-posed problems      482
image of a mapping      4
Imaginary number      112
Imaginary part      112
Improper integrals      81
Indefinite integral      73 285
Indicial equation      718
infinity complex      149
infinity first order differential equation      490
inhomogeneous differential equations      467
Initial conditions      478
Injective function      5
inner product of functions      769
integral bound maximum modulus      282
Integral calculus      73
Integral equations      614
integral equations of boundary value problems      614
integral equations of initial value problems      614
integral test series      322
Integrals improper      81
Integrating factor      477
integration of power series      332
Intermediate Value Theorem      37
Intersection of sets      4
Inverse function      5
Inverse image      4
inverse of function      5
irregular first order differential equations      489
irregular singular points      726
j electrical engineering      112
Jordan curve      148
Jordan's lemma      1367
Kramer's rule      1403
Kronecker delta function      24
l'Hospital's rule      49
Lagrange's identity      551 568 787
Laplace transform inverse      890
Laplace transform pairs      892
Laplace transforms      889
Laplace transforms of derivatives      898
Laurent expansions      379 1367
Laurent series      337 1368
Laurent series first order differential equation      486
leading order behavior for differential equations      749
Least integer function      5
least squares fit Fourier series      803
Legendre polynomials      767
limit left and right      34
limits of functions      33
Line integral      280
Linear differential equations      467 547
Linear differential operator      542
Linear space      763
Liouville's theorem      301
Magnitude      113
maximum modulus integral bound      282
Maximum modulus theorem      303
Mellin inversion formula      890
minimum modulus theorem      303
Modulus      113
multi-valued function      5
multiply-connected region      147
nabla      95
Natural boundary      263
negative direction      148
Newton's binomial formula      1409
norm of functions      769
normal form of differential equations      611
Null vector      18
One-to-one mapping      5
Open interval      3
Opportunity cost      1413
optimal asymptotic approximations      757
Order of a differential equation      467
Order of a set      4
Ordinary differential equations      467
ordinary points first order differential equations      484
ordinary points of linear differential equations      707
orthogonal series      771
orthogonality weighting functions      770
Orthonormal      769
Parseval's equality      805
Parseval's theorem for Fourier transform      938
Partial derivative      94
Particular solution      477
particular solution of an ODE      635
particular solutions of differential equations      542
periodic extension      802
Piecewise continuous      37
Piecewise smooth curve      147
Point at infinity      149
point differential equations      726
Polar form      115
Positive direction      148
potential flow      232
principal argument      114
Principal branch      6
principal root      122
Principal value      384 932
properties of regular Sturm—Liouville problems      860
pure imaginary number      112
Raabe's test      325
Raabe's test series      325
radius of convergence power series      328
range of a mapping      4
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