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Canuto C., Tabacco A. — Mathematical analysis
Canuto C., Tabacco A. — Mathematical analysis

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Название: Mathematical analysis

Авторы: Canuto C., Tabacco A.

Аннотация:

The purpose of the volume is to provide a support for a first course in Mathematical Analysis, along the lines of the recent Programme Specifications for mathematical teaching in European universities. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. Definitions and properties are furnished with substantial examples to stimulate the learning process. Over 350 solved exercises complete the text, at least half of which guide the reader to the solution.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2008

Количество страниц: 435

Добавлена в каталог: 20.04.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute value      13
Antiderivative      300
ARC      280
Arc, closed      280
Arc, Jordan      280
Arc, length      375
Arc, simple      280
Arccosine      56 114
Archimedean property      16
Arcsine      56 114 174 334
Arctangent      114 174 334
Argument      273
Asymptote      135
Asymptote, horizontal      135
Asymptote, oblique      135
Asymptote, vertical      136
Binomial coefficient      19 232
Binomial expansion      20
Bisection method      111
Cardinality      2
Colatitude      259
Combination      20
Conjunction      5
Connective      5
Coordinates, cylindrical      259
Coordinates, polar      257
Coordinates, spherical      259
Corner      176
Cosine      52 101 171 174 231
Cosine, hyperbolic      195 236
Cotangent      54
Curve      279
Curve, congruent      370
Curve, equivalent      370
Curve, integral      388
Curve, opposite      370
Curve, piecewise regular      282
Curve, plane      279
Curve, regular      282
Curve, simple      280
De Morgan laws      4
Degree      50 52
Derivative      168 187
Derivative, backward      176
Derivative, forward      176
Derivative, left      176
Derivative, logarithmic      174
Derivative, partial      286 288
Derivative, right      176
Difference      4
Difference, quotient      167
Difference, symmetric      4
Differential equation with separable variables      392
Differential equation, autonomous      388
Differential equation, homogeneous      394 397 404
Differential equation, linear      394 404
Differential equation, ordinary      387
Differential equation, solution      387
Discontinuity of first kind      84
Discontinuity of second kind      84
Discontinuity, removable      78
Disjunction      5
Domain      31
Equation, characteristic      405
Equivalence, logic      6
Expansion, asymptotic      241
Expansion, Maclaurin      227 233
Expansion, Taylor      226
Exponential      50 171 227
Factorial      18
Form, algebraic      270
Form, Cartesian      270
Form, exponential      274
Form, indeterminate      99 107
Form, normal      388
Form, polar      273
Form, trigonometric      273
Formula      5
Formula, addition      54
Formula, contrapositive      6
Formula, de Moivre      275
Formula, duplication      54
Formula, Euler      274
Formula, finite increment      183
Formula, Stirling      141
Formula, subtraction      54
Formula, Taylor      226
Function      31
Function of class $C^{k}$      189
Function of class $C^{\infty}$      189
Function of real variable      32
Function of same order of magnitude      124
Function of several variables      284
Function, absolute value      33 34
Function, absolutely integrable      360
Function, arccosine      56 114
Function, arcsine      56 114 174 334
Function, arctangent      114 174 334
Function, asymptotic      136
Function, big o      123
Function, bijective      40
Function, bounded      37 95
Function, bounded from above      37
Function, composite      103 173 239
Function, composition      43
Function, concave      189
Function, continuous      76 80 285
Function, continuous on the right      83
Function, convex      189
Function, cosine      52 101 171 174 231
Function, cotangent      54
Function, decreasing      42
Function, differentiable      168 187
Function, equivalent      124
Function, even      47 175 227
Function, exponential      50 171 227
Function, hyperbolic      195
Function, hyperbolic cosine      195 236
Function, hyperbolic sine      195 236
Function, hyperbolic tangent      196
Function, increasing      41
Function, infinite      130
Function, infinite of bigger order      131
Function, infinite of same order      131
Function, infinite of smaller order      131
Function, infinitesimal      130 242
Function, injective      38
Function, integer part      33 34
Function, integrable      324
Function, integral      331
Function, inverse      38 114 173
Function, inverse, cosine      56
Function, inverse, hyperbolic cosine      197
Function, inverse, hyperbolic sine      197
Function, inverse, hyperbolic tangent      197
Function, inverse, sine      55
Function, inverse, tangent      56
Function, invertible      39
Function, little o      124
Function, logarithm      51 114 174 229
Function, mantissa      34
Function, monotone      41 85 114 185
Function, negative part      359
Function, negligible      124
Function, odd      47 175 227
Function, one-to-one      38 114
Function, onto      38
Function, periodic      47
Function, piecewise      32
Function, piecewise-continuous      317
Function, polynomial      50 98 100 172 313
Function, positive part      359
Function, power      48 231
Function, primitive      300
Function, rational      50 98 100 101 310
Function, real      32
Function, real-valued      32
Function, sign      33 34
Function, sine      52 79 93 106 171 230
Function, step      321
Function, surjective      38
Function, tangent      54 173 239
Function, trigonometric      51
Gap      84
Gradient      286
Graph      31
Image      31 36
Image of a curve      279
Implication      5
Inequality of Bernoulli      139
Inequality, Cauchy — Schwarz      264
Inequality, triangle      13
Infimum of a function      37
Infimum of a set      17
Infinite      200
Infinite of bigger order      131
Infinite of same order      131
Infinite of smaller order      131
Infinite, test function      131
Infinitesimal      130 200
Infinitesimal of bigger order      130
Infinitesimal of same order      130
Infinitesimal of smaller order      130
Infinitesimal, test function      131
Inflection      190 244
Inflection, ascending      190
Inflection, descending      190
Integral, Cauchy      318
Integral, definite      317 319 321 324
Integral, general      389
Integral, improper      356 363 367
Integral, indefinite      300 301
Integral, line      368 376
Integral, lower      323
Integral, mean value      328
Integral, particular      389
Integral, Riemann      320
Integral, singular      392
Integral, upper      323
Integration by parts      305 335
Integration by substitution      307 315 336
Intersection      3 7
interval      14
Interval of monotonicity      42 185
Inverse, cosine      56 114
Inverse, sine      55 114
Inverse, tangent      56 114
Landau symbols      123
Latitude      259
Length of a curve      373 374
Length of a vector      261
LIMIT      68 70 72 73 76 81
limit, left      82
limit, right      82
Logarithm      51 106 114 174 229
Logarithm, natural      72
longitude      259
Lower bound      15
Lower bound, greatest      17 113
MAP      31
Map, identity      45
Maximum      16 37
Maximum, absolute      178
Maximum, relative      178
Minimum      16 37
Modulus      272
Negation      5
Neighbourhood      65 285
Neighbourhood, left      82
Neighbourhood, right      82
Norm of a vector      261
Number, complex      270
Number, integer      9
Number, Napier      72 106 171
Number, natural      8
Number, rational      9
Number, real      10
Order      242
Order of a differential equation      387
Order of an infinite function      132
Order of an infinitesimal function      132
Order of magnitude      200
Pair, ordered      21
Part, imaginary      270
Part, negative      359
Part, positive      359
Part, principal      133 242
Part, real      270
Partition      320
Partition, adapted      321
Period      10 47
Period, minimum      48
Permutation      19
Point of discontinuity      84
Point with vertical tangent      177
Point, corner      176
Point, critical      179 243
Point, cusp      177
Point, extremum      178
Point, inflection      190 244
Point, interior      15
Point, jump      84
Point, Lagrange      182
Point, maximum      178
Point, minimum      178
Polynomial      50 98 100 172 313
Polynomial, characteristic      405
Polynomial, Taylor      226
Pre-image      36
Predicate      2 6
primitive      300
Problem, boundary value      391
Problem, Cauchy      390
Problem, initial value      390
Product, cartesian      21
Product, dot      264
Product, scalar      264
Prolongation      78
Proof by contradiction      6
Quantifier, existential      7
Quantifier, universal      7
Radian      52
RADIUS      65
RANGE      31 36
refinement      320
Region under the curve      317
Relation      23
Remainder of a series      145
Remainder, Lagrange      225 227
Remainder, Peano      225 226
Restriction      40
SEQUENCE      32 66 104 137
Sequence of partial sums      141
Sequence, convergent      68
Sequence, divergent      70
Sequence, geometric      138
Sequence, indeterminate      71
Sequence, monotone      71
Series      141
Series, absolutely convergent      150
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