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Woods F.S. — Advanced Calculus
Woods F.S. — Advanced Calculus

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Название: Advanced Calculus

Автор: Woods F.S.

Аннотация:

The course in advanced calculus contained in this book has for many years been given by the author to students in the Massachusetts Institute of Technology. The choice of the subject matter and the arrangement of the material are the result of the experience thus gained. The students to whom the course has been given have been chiefly interested in the applications of the calculus and have felt the need of a more extensive knowledge than that gained in the elementary courses, but they have not been primarily concerned with theoretical questions. Hence there is no attempt to make this course one in analysis. However, some knowledge of theory is certainly necessary if correct use is to be made of the science; therefore the author has endeavored to introduce the students to theoretical questions and possibly to incite in some a desire for more thorough study. As an example of the method used, a proof of the existence of the definite integral in one variable has been given; for the multiple integral the proof has been omitted and simply the result stated. The student who has mastered the simpler case is in a position to rvad the more difficult case in easily accessible texts.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1934

Количество страниц: 403

Добавлена в каталог: 16.07.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Addition formulas, elliptic functions      372
Amplitude, function      368
Arc, element of      106 125 128
Arc, infinitesimal      23
Area, curved surface      187
Area, element of      126
Area, line integral      177
Area, vector      209
Argument of complex number      334
Bernoulli's equation      221
Bessel functions      275 360
Bessel's equation      275
beta function      166
Binormal      119
Calculus of variations      317
Cauchy's theorem      352
Characteristics      293
Circle of convergence      355
Circulation      200
Clairaut's equation      227
Continuity, defined      2
Continuity, equation of      195
Continuity, uniform      4
convergence of integrals      147 151
Convergence of series      38
Convergence, absolute      39
Convergence, circle of      355
Convergence, comparison test for      40
Convergence, conditional      58
Convergence, ratio test for      41
Convergence, region of      42
Convergence, uniform      45 149 150 152
Coordinates, curvilinear      124
Coordinates, cylindrical      129
Coordinates, generalized      329
Coordinates, polar      130
Cosines, direction      106
Curl      212
Curvature      121
Curve, equations of      118
Curve, length of      23 107
Curve, vector equation of      208
De Moivre's theorem      55
DEL      211
Derivative of a complex function      345
Derivative, defined      5
Derivative, directional      74
Derivative, partial      66
Determinant, functional      99
Differential equation, Bessel's      275
Differential equation, complete      253
Differential equation, first degree      219
Differential equation, first order      216
Differential equation, higher degree      225
Differential equation, higher order      252
Differential equation, Laplace's      301 306
Differential equation, Legendre's      268
Differential equation, linear      220 253
Differential equation, partial      292
Differential equation, reduced      253
Differential equation, second order      264
Differential equation, simultaneous      243 268
Differential of function of one variable      28
Differential of function of several variables      78
Differential, exact      81 185
Differential, higher      29 84
Differentiation of definite integral      141 148
Differentiation of elliptic functions      371
Differentiation, partial      65
Direction cosines      106
Direction of a line      108
Dirichlet's integrals      167
Divergence      211
Duhamel's theorem      23
Element, of arc      106 125 128
Element, of area      126
Element, of volume      129 159
Envelope      229
Euler's constant      171
Euler's theorem      73
Evolute      233
Expansion of elliptic functions      371
Expansion, asymptotic      363
Factor, integrating      222 238
Fluid, flow of      176 191 212
Force, conservative      84
Forms, indeterminate      15 16 18
Fourier series      295
Function      1
Function of a complex variable      332 344
Function of several variables      65
Function, analytic      347
Function, Bessel      275 360
Function, Beta      166
Function, complementary      254 259
Function, composite      7 69
Function, conjugate      347
Function, defined by power series      45
Function, dominant      57 87
Function, elliptic      366 367
Function, exponential      53 339
Function, Gamma      164
Function, harmonic      310
Function, homogeneous      73
Function, hyperbolic      55 341
Function, implicit      91
Function, inverse      343
Function, logarithmic      342
Function, regular      355
Function, trigonometric      53 339
Function, vector      209
Gamma functions      164
Geodesics      323 327
Gradient      77 210
Green's theorem      181 192
Hamilton's principle      328
Heat, flow of      303
Helix      133
Imaginary, conjugate      333
Imaginary, pure      332
Indicatrix      114 115
Infinitesimal      19 22
Integral, definite      134
Integral, elliptic      365 376 379 381
Integral, line      174
Integral, multiple      156
Integral, of a complex function      361
Integral, particular      254 261
Integral, surface      190
Integrand, infinite      151
Integration under the integral sign      145 148
interval      2
Involute      235
Jacobians      99
l'Hospital's rule      16
Lagrange's equations      329
Laplace's equation      301 306
Legendre's associated polynomial      272
Legendre's equation      268
Legendre's integrals      367
Legendre's polynomials      270
Lemniscate      382
Length of curve      23 107
Limit, infinite      146
Line integrals      174
Line, contour      76
Line, straight      108
Loxodrome      133
Maclaurin's series      13
Maxima and minima      116
Mean, theorem of      8
Mercator's projection      133 351
Modulus of complex number      333
Modulus of elliptic function      367
Normal, principal      120
Normal, to plane      111
Normal, to surface      110 127
Number, complex      332
Operations on scries      46 51
Operator      257
Operator del      211
Order of infinitesimals      19
Orthogonality      107 126
Oscillation of a function      5
Osgood's Theorem      23
Parallelism, condition for      206
Part, principal      20
Path of integration      183
Pendulum      330 369
Pendulum, spherical      383
periods      373
Perpendicularity, condition for      107 126 206
Plane      110
Plane, osculating      119
Point, elliptic      114
Point, hyperbolic      115
Point, parabolic      116
Point, singular      231
Pole      355
Polynomial, Legendre's      270
Polynomial, Legendre's associated      272
Potential      199 308
Power of complex number      335
Projection, Mercator's      133 351
Projection, stereographic      133 351
Region of convergence      42
Remainder, Taylor's series      10
Representation, conformal      348
Residue      355
Rolle's theorem      7
Roots, of Bessel functions      279
Roots, of complex numbers      335
Roots, square      337
Scalar product      205
Series, Fourier      295
Series, operations on      46 51
Series, power      38
Simpson's rule      139
Solution, singular      232
Stokes's theorem      197
Surface integrals      190
Surfaces      109 112
Surfaces of revolution      133
Surfaces, area of      187
Systems, orthogonal      348
Tangent line      119
Tangent plane      111 112
Taylor's series      10 48 353
Torsion      122
Trajectory      236
Triangle, infinitesimal      26
Value, absolute      333
Variable, complex      332
Variation of constants      255
Variation, constrained      324
Variation, first      318
Variations, calculus of      317
Vector      203
Vector function      209
Vector product      206
Velocity potential      200
Volume, element of      129 159
Vortex Motion      200 212
Weierstrass      5
Weierstrass's elliptic function      381
Work      176 200
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