|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Estep D.J. — Practical Analysis in One Variable |
|
|
|
| Предметный указатель |
Function, right derivative of a 254
Function, right linearization of a 254
Function, second derivative of a 267
Function, strictly monotone 182
Function, strongly differentiable 223
Function, strongly differentiable on an interval 245
Function, strongly differentiable on the left 254
Function, strongly differentiable on the right 254
Function, sum 73
Function, tangent to a 222 238
Function, Taylor polynomial of a 528
Function, uniformly continuous 446
Function, uniformly differentiable 450
Function, uniformly strongly differentiable 251
Function, uniformly strongly differentiable inverse 283
Function, weighted average of a 352
Functional relation 360
Functions, composition of 80
Functions, division of 76
Functions, equicontinuous family of 588
Functions, linear combination of 74
Functions, linearly dependent 75
Functions, linearly independent 75
Functions, Lipschitz continuous 153
Functions, product of 76
Functions, quotient of 76
Functions, sequence of 323 463
Functions, spaces of 570
Fundamental sequence 136
Fundamental theorem of calculus 333 334 343 481 487
Galileo 286
Galileo, Galileo's law 286 296—297 312
Gauss 29 127
General Order Rolle's Theorem 548
General solution of a differential equation 310
Generalized Integral Mean Value Theorem 531
Generalized Mean Value Theorem 499
Geometric series 109 145
Geometric sum 32 62 108
Global behavior 269
Global convergence 408
Global existence 579
Globally convergent method 424
Graph of a function 55 83
Graph of a function of a real variable 156
Graph of a polynomial 68
Graph of an inverse function 180
Greatest lower bound 454
Greeting Card Sales model 192 205
Gronwall 598
Gronwall, Gronwall's Lemma 598
Half-life 375
Half-open interval 48
Harmonic series 62 119
Heine 446
hilbert 149
Hoelder 446
Hoelder continuity 446
HoElder exponent 447
Hooke 387
Hooke, law for a spring 387
Horizontal Line Test 181
Hybrid-Newton method 425
I(t) 69 84
Identify 137
Ill-conditioned root 423
Image 179
Implicit function theorem 581
Indefinite integral 302
Independent variable 53
Indeterminate form 497
INDEX 34 62 100
Induction 31—32
Inductive step 31
inf 454
Infimum 454
Infinite decimal expansion 99
Infinite decimal expansion, uniqueness of 111
Infinite interval 143
Infinite nonperiodic decimal expansion 128
Infinite number 42
Infinite periodic decimal expansion 42
Infinite series 109
Infinitesimal change 240
infinity 18 48
Initial condition 296
Initial population 34
Initial value 559
Initial value problem 316 559
Input 52
Instantaneous rate of change 241
INTEGER 25
Integer equation 571
Integer form of a differential equation 572
Integer form of the remainder of a Taylor polynomial 531
Integer lower limit of a 312
Integer operator 572
Integer, coordinate plane 56
Integer, number line 22
Integer, upper limit of a 312
Integers 22
Integrable function 302
integral 302
integrand 303
Integrating factor 374 375
Integration 302
Integration by parts 309
Integration, linearity of 339
Integration, monotonicity of 340
Integration, power rule 303
Integration, variable 303
Intermediate Value Theorem 170 444
Interpolate 221 317 543
Interpolation nodes 543
Interval, closed 48 142
Interval, endpoint 142
Interval, half-open 48
Interval, infinite 143
Interval, open 48 142
INTO 54
Intrinsic growth rate 371
Intuitionists 19
Inverse function 180 183
Inverse function theorem 183 186 444
Inverse function, graph of a 180
Inverse function, Lipschitz continuous 281
Inverse function, uniformly strongly differentiable 282
Inverse operation 21 23
Invertible function 183
Irrational number 128
Kovalevskaya 107
kronecker 20
L'Hopital 497
l'Hopital's rule 498
Lagrange 246 422 436 539
Lagrange form of the remainder of a Taylor polynomial 532
Lagrange, basis for polynomials 545
Landau 504
Law of conservation of momentum 355
Law of Large Numbers 515
Least upper bound 454
Least Upper Bound Principle 455
Lebesgue 473
Lebesgue integral 473
Left derivative 255
Left linearization 255
Leibniz 51 106 302 307 435 436 539
Length of a curve 489
Lim 102 103
Limit of a function 158 160
| Limit of a sequence 101—103
Limit of a sequence of functions 463
Limit of a series 110
Limit, computing 116 117 148
Limit, indeterminate form 497
Limit, lower 62 312
Limit, one-sided 253
Limit, point of a sequence 452
Limit, uniqueness of a 111
Limit, upper 62 312
linear combination 65
Linear combination of differentiable functions 259
Linear combination of functions 74
Linear combination of integrable functions 303
Linear combination of Lipschitz continuous functions 92
Linear combination, coefficients of a 65 74
Linear combination, unique 75
Linear convergence 207
Linear differential equation 289
Linear model of a function 420
Linear operator 570
Linear polynomial 62
Linear, approximation of a function 223 420
Linearity of Differentiation 260
Linearity of Integration 304
Linearization of a function 223
Linearization, left 255
Linearization, right 254
Linearly, dependent 75
Linearly, independent 75
Liouville 575
Lipschitz 88 599
Lipschitz continuous "at a point" 229
Lipschitz continuous function 85 153 217
Lipschitz continuous functions, composition of 96
Lipschitz continuous functions, linear combination of 92
Lipschitz continuous functions, product of 94
Lipschitz continuous functions, quotient of 95
Lipschitz continuous uniformly 326
Lipschitz, Lipschitz constant 85
Little o 505
Local behavior 269 410
Local convergence 410
Local Convergence for Newton's method 418
Local Convergence for the Fixed Point Iteration 410
Local solution 586
Locally convergent method 424
Locally uniformly Lipschitz continuous 564
LOG 358
Logarithm 358
Logarithmic differentiation 378
Logistic equation 560 562 578 584
Long division 23
Long division of polynomials 79
LONG INTEGER 25
Lower bound 454
lower bound of a 454
Lower Darboux integral 491
Lower limit 62 312
Machine number 124
Maclaurin 539
Malthus 371
Malthus, population growth model 371
Mantissa 118
MAP 53
Map, contraction 203
Mass-spring system 394
Mathematical induction 31—32
Mathematical model 8
Mathematical modeling 11
MAX 455
Maximum 455
Maximum, value of a function 456
Mean value theorem 269 451 456
mesh 318 347 351 478 482 584
Mesh, nested 319
Mesh, nodes 482
Mesh, refinement 485
Mesh, size 319 482
Method of exhaustion 345
Method of Substitution 312
Method of successive approximations 575
MIN 455
Minimum 455
Minimum, value of a function 456
Model, chemical equilibrium 46—47 166 201 205
Model, compound interest 370 380
Model, constant relative rate of change 370 374
Model, continuous 371
Model, Dinner Soup 8—10 54
Model, discrete 370
Model, Einstein's Law of Motion 288
Model, Einstein's Theory of Special Relativity 288
Model, Free Time 194 200 205
Model, Galileo's law 286 296—297 312
Model, Greeting Card 205
Model, Greeting Card Sale 192
Model, Hooke's law for a spring 387
Model, insect population 33—34 231
Model, Law of Conservation of Momentum 355
Model, logistic equation 560 562 578 584
Model, Malthus population growth 371
Model, Mass-spring system 394
Model, Muddy Yard 10—11 54 114 125
Model, Newton's Law of Cooling 370 384
Model, Newton's Law of Motion 286
Model, population growth 370
Model, radioactive decay 370 375
Model, rocket propulsion 357 364—365
Model, spruce budworm 560 585
Model, Verhulst population 45—46 114 115
Modulus of continuity 516
Monomials 65 68 89 248
Monotone function 182 276
Monotonicity of Integration 340
Muddy Yard model 10—11 54 114 125
Napier 355
Natural logarithm 358
Natural number line 18
Natural numbers 15 19
Negative integers 22
Nested meshes 319
Net area, underneath a curve 349
Newton 51 106 435 436
Newton's method 418
Newton's method, hybrid 425
Newton's method, quasi 427
Newton's method, stopping criterion for 424
Newton, Law of Cooling 370 384
Newton, Law of Motion 286
nodes 482 543
Nonlinear differential equation 289
Nonseparable differential equation 290
Normalized weight function 352
nth derivative 267
Number line, integer 22
Number line, natural 18
Number line, rational 47
Numerator 37
o 505
One-sided limit 253
One-to-one 185
Onto 53
Open interval 48 142
Operator 570
Operator, linear 570
Order axioms 149
Order of a differential equation 288
Order of convergence 415
Order Properties of the Real Numbers 142
|
|
|
| Реклама |
|
|
|
|
|
О проекте