Mathematical techniques: an introduction for the engineering, physical, and mathematical sciences
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
1997
|
| Ausgabe: | 2. ed. |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 788 S. graph. Darst. |
| ISBN: | 0198564627 0198564619 |
Internformat
MARC
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| 245 | 1 | 0 | |a Mathematical techniques |b an introduction for the engineering, physical, and mathematical sciences |c D. W. Jordan and P. Smith |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 1997 | |
| 300 | |a XVIII, 788 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804126129878990848 |
|---|---|
| adam_text | Contents
1 Standard functions and techniques
1.1 Number line, intervals /
1.2 Coordinates in the plane 2
1.3 Straight lines and curves^ 3
1.4 Functions 6
1.5 Radian measure of angles 8
1.6 Trigonometric functions 9
1.7 Inverse functions 12
1.8 Exponential functions 14
1.9 The logarithmic function 15
1.10 Exponential growth and decay 17
1.11 Hyperbolic functions 18
1.12 Partial fractions 20
1.13 Summation sign; geometric series 24
Problems 26
1 Differentiation
2.1 The slope of a graph 30
2.2 The derivative: notation and definition 32
2.3 Rates of change 34
2.4 Derivative of x (m = 0, 1,2, 3,...) 36
2.5 Derivatives of sums: multiplication by constants 37
2.6 Three important limits 39
2.7 Derivatives of e*, sin x, cos x, In x 41
2.8 A basic table of derivatives 43
2.9 Higher order derivatives 44
2.10 An interpretation of the second derivative 44
Problems 45
3 Further techniques for differentiation
3.1 The product rule 48
3.2 Quotients and reciprocals 50
3.3 The chain rule 52
3.4 Derivative of x for any value of n 55
3.5 Functions of ax + b 56
3.6 An extension of the chain rule 56
3.7 Logarithmic differentiation 57
3.8 Implicit differentiation 58
3.9 Derivatives of inverse functions 59
3.10 Derivative as a function of a parameter 60
Problems 62
Contents
4 Applications of differentiation
4.1 Function notation for derivatives 64
4.2 Maxima and minima 66
4.3 Exceptional cases of maxima and minima 69
4.4 Sketching graphs of functions 70
4.5 Estimating small changes 75
4.6 Numerical solution of equations: Newton s method 77
Problems 81
5 Taylor series and approximations
5.1 The index notation for derivatives of any order 83
5.2 Taylor polynomials 83
5.3 A note on infinite series 86
5.4 Infinite Taylor expansions 88
5.5 Manipulation of Taylor series 89
5.6 Approximations for large values of x 92
5.7 Taylor series about other points 92
Problems 94
6 Complex numbers
6.1 Definitions and rules 96
6.2 The Argand diagram and complex numbers 700
6.3 Complex numbers in polar coordinates 102
6.4 Complex numbers in exponential form 103
6.5 The general exponential form 105
6.6 Hyperbolic functions 107
6.7 Miscellaneous applications 108
Problems 109
7 Matrix algebra
7.1 Matrix definition and notation 112
7.2 Rules of matrix algebra 113
7.3 Special matrices 118
7.4 The inverse matrix 122
Problems 126
8 Determinants
8.1 The determinant of a square matrix 129
8.2 Properties of determinants 132
8.3 The adjoint and inverse matrices 137
Problems 139
9 Elementary operations with vectors
9.1 Displacement along an axis 142
9.2 Displacement vectors in two dimensions 144
9.3 Axes in three dimensions 146
9.4 Vectors in two and three dimensions 146
9.5 Relative velocity 150
9.6 Position vectors and vector equations 152
Contents xi
9.7 Unit vectors and basis vectors 155
9.8 Tangent vector, velocity, and acceleration 157
9.9 Motion in polar coordinates 158
Problems 160
10 The scalar product
10.1 The scalar product of two vectors 163
10.2 The angle between two vectors 164
10.3 Perpendicular vectors 165
10.4 Rotation of axes in two dimensions 167
10.5 Direction cosines 167
10.6 Rotation of axes in three dimensions 169
10.7 Direction ratios and coordinate geometry 171
10.8 Properties of a plane 173
10.9 General equation of a straight line 175
10.10 Forces acting at a point 176
10.11 Curvature in two dimensions 17H
Problems I HO
11 Vector product and derivatives of vectors
11.1 Vector product 183
11.2 Nature of the vector p = a x b 1S5
11.3 The scalar triple product 187
11.4 Moment of a force 190
11.5 Vector triple product 192
Problems 193
12 Linear equations
12.1 Solution of linear equations by elimination 196
12.2 The inverse matrix by Gaussian elimination 201
12.3 Compatible and incompatible sets of equations 202
12.4 Homogeneous sets of equations 205
12.5 Gauss Seidel iterative method of solution 208
Problems 210
13 Eigenvalues and eigenvectors
13.1 Eigenvalues of a matrix 214
13.2 Eigenvectors 215
13.3 Linear dependence 220
13.4 Diagonalization of a matrix 221
13.5 Powers of matrices 224
13.6 Quadratic forms 227
13.7 Positive definite matrices 229
13.8 An application to a vibrating system 233
Problems 235
Contents
14 Antidifferentiation and area
14.1 Reversing differentiation 238
14.2 Constructing a table of antiderivatives 241
12.3 Signed area generated by a graph 244
Problems 246
1 5 The definite and indefinite integral
15.1 Signed area as the sum of strips 248
15.2 Numerical illustration of the sum formula 249
15.3 The definite integral and area 250
15.4 The indefinite integral notation 251
15.5 Integrals unrelated to area 252
15.6 Improper integrals 255
15.7 Integration of complex functions: a new type of integral 256
15.8 The area analogy for a definite integral 258
15.9 Using the area analogy 259
15.10 Definite integrals having variable limits 261
Problems 263
16 Applications involving the integral as a sum
16.1 Examples of integrals arising from a sum 265
16.2 Geometrical area in polar coordinates 267
16.3 The trapezium rule 268
16.4 Centre of mass, moment of inertia 270
Problems 274
17 Systematic techniques for integration
17.1 Substitution method for J f(ax + b) dx 277
17.2 Substitution method for J f(ax2 + b)x dx 279
17.3 Substitution method for j cosm ax sin ax dx (m or n odd) 280
17.4 Definite integrals and change of variable 282
17.5 Occasional substitutions 283
17.6 Partial fractions for integration 285
17.7 Integration by parts 286
17.8 Integration by parts: definite integrals 289
Problems 291
1 8 Unforced linear differential equations with
constant coefficients
18.1 Differential equations and their solutions 295
18.2 Solving first order linear unforced equations 298
18.3 Solving second order linear unforced equations 301
18.4 Complex roots of the characteristic equation 304
18.5 Initial conditions for second order equations 307
Problems 308
Contents xiii
19 Forced linear differential equations
19.1 Particular solutions for standard forcing terms 3 JO
19.2 Harmonic forcing term by using complex solutions 314
19.3 Particular solutions: exceptional cases 317
19.4 The general solution of forced equations 318
19.5 First order linear equations with a variable coefficient 321
Problems 324
20 Harmonic functions and the harmonic
oscillator
20.1 Harmonic oscillations 326
20.2 Phase difference: lead and lag 328
20.3 Physical models of a differential equation 329
20.4 Free oscillations of a linear oscillator 330
20.5 Forced oscillations and transients 331
20.6 Resonance 333
20.7 Nearly linear systems 335
Problems 337
21 Steady forced oscillations: phasors,
impedance, transfer functions
21.1 Phasors 339
21.2 Algebra of phasors 341
21.3 Phasor diagrams 342
21.4 Phasors and complex impedance 343
21.5 Transfer functions in the frequency domain 346
Problems 348
11 Graphical, numerical and other aspects of
first order equations
22.1 Graphical features of first order equations 350
22.2 The Euler method for numerical solution 351
22.3 Nonlinear equations of separable type 354
22.4 Differentials and the solution of first order equations 356
22.5 Change of variable in a differential equation 360
Problems 363
23 Nonlinear differential equations and the
phase plane
23.1 Autonomous second order equations 367
23.2 Constructing a phase diagram for (x, x) 368
23.3 (x, x) phase diagrams for other linear equations; stability 371
23.4 The pendulum equation 373
23.5 The general phase plane 375
23.6 Approximate linearization 377
23.7 Limit cycles 379
23.8 A numerical method for x = P, y = Q 380
Problems 381
Contents
24 The Laplace transform
24.1 The Laplace transform 384
24.2 Laplace transforms of f , e±r, sin t, cos t 385
24.3 Scale rule; shift rule; factors t and ekt 387
24.4 Inverting a Laplace transform 390
24.5 Laplace transforms of derivatives 392
24.6 Application to differentia! equations 394
24.7 The unit function and the delay rule 396
Problems 400
25 Applications of the Laplace transform
25.1 Division by s and integration 402
25.2 The impulse function 404
25.3 Impedance in the s domain 406
25.4 Transfer functions in the s domain 408
25.5 The convolution theorem 413
25.6 General response of a system from its impulsive response 415
25.7 Convolution integral in terms of memory 416
25.8 Discrete systems 417
25.9 The z transform 419
25.10 Behaviour of z transforms in the complex plane 424
25.11 Difference equations 428
Problems 430
26 Fourier series and Fourier transforms
26.1 The composition of vibrations 434
26.2 Fourier series for a periodic function 435
26.3 Integrals of periodic functions 436
26.4 Calculating the Fourier coefficients 438
26.5 Examples of Fourier series 440
26.6 Use of symmetry: sine and cosine series 442
26.7 Functions defined on a finite range: half range series 444
26.8 Spectrum of a periodic function 447
26.9 Obtaining one Fourier series from another 448
26.10 The two sided Fourier series 449
26.11 Nonperiodic functions and the Fourier transform 451
26.12 Short notations 454
26.13 Fourier transforms of some basic functions 454
26.14 Rules for manipulating transforms 456
26.15 The delta function and periodic functions 458
26.16 Convolutions 460
26.17 The shah function 464
26.18 Energy in a signal: Rayleigh s theorem 465
Problems 466
27 Differentiation of functions of two variables
27.1 Functions of more than one variable 470
27.2 Depiction of functions of two variables 471
27.3 Partial derivatives 473
27.4 Higher derivatives 476
27.5 Tangent plane and normal to a surface 478
Contents xv
27.6 Maxima, minima, and other stationary points 480
27.7 The method of least squares 483
27.8 Differentiating an integral with respect to a parameter 484
Problems 486
28 Functions of two variables: geometry and
formulae
28.1 The incremental approximation 488
28.2 Small changes and errors 490
28.3 The derivative in any direction 493
28.4 Implicit differentiation 496
28.5 Normal to a curve 498
28.6 Gradient vector in two dimensions 499
Problems 502
29 Chain rules, restricted maxima, coordinate
systems
29.1 Chain rule for a single parameter 504
29.2 Restricted maxima and minima: the Lagrange multiplier 506
29.3 Curvilinear coordinates in two dimensions 511
29.4 Orthogonal coordinates 513
29.5 The chain rule for two parameters 514
29.6 The use of differentials 517
Problems 519
30 Functions of any number of variables
30.1 The incremental approximation; errors 521
30.2 Implicit differentiation 523
30.3 Chain rules 525
30.4 The gradient vector in three dimensions 525
30.5 Normal to a surface 527
30.6 Equation of the tangent plane 528
30.7 Directional derivative in terms of gradient 529
30.8 Stationary points 532
30.9 The envelope of a family of curves 537
Problems 538
31 Double integration
31.1 Repeated integrals with constant limits 543
31.2 Examples leading to repeated integrals with constant limits 544
31.3 Repeated integrals over nonrectangular regions 546
31.4 Changing the order of integration for nonrectangular regions 548
31.5 Double integrals 550
31.6 Polar coordinates 553
31.7 Separable integrals 555
31.8 General change of variable; the Jacobian determinant 557
Problems 561
Contents
32 Line integrals
32.1 Illustrating a line integral 564
32.2 General line integrals in two and three dimensions 567
32.3 Paths parallel to the axes 570
32.4 Path independence and perfect differentials 571
32.5 Closed paths 572
32.6 Green s theorem 574
32.7 Line integrals and work 576
32.8 Conservative fields 578
32.9 Potential for a conservative field 580
32.10 Single valuedness of potentials 581
Problems 584
33 Vector fields: divergence and curl
33.1 Vector fields and field lines 587
33.2 Divergence of a vector field 588
33.3 Surface and volume integrals 589
33.4 The divergence theorem 593
33.5 Curl of a vector field 595
33.6 Cylindrical polar coordinates 599
33.7 Curvilinear coordinates 601
Problems 602
34 Sets
34.1 Notation 605
34.2 Equality, union, and intersection 606
34.3 Venn diagrams 608
Problems 612
35 Boolean algebra: logic gates and switching
functions
35.1 Laws of Boolean algebra 615
35.2 Logic gates and truth tables 617
35.2 Logic networks 619
35.4 The inverse truth table problem 621
35.5 Switching circuits 622
Problems 623
36 Graph theory and its applications
36.1 Examples of graphs 626
36.2 Definitions and properties of graphs 627
36.3 How many simple graphs are there? 629
36.4 Paths and cycles 629
36.5 Trees 631
36.6 Electrical circuits: the cutset method 632
36.7 Signal flow graphs 635
36.8 Planar graphs 638
36.9 Further applications 640
Problems 643
Contents xvii
37 Difference equations
37.1 Discrete variables 648
37.2 Difference equations: general properties 650
37.3 First order difference equations and the cobweb 652
37.4 Constant coefficient linear difference equations 65.?
37.5 The logistic difference equation 658
Problems 662
38 Probability
PART VII 3g j introcjuctjon 666
Probability and 38 2 Sample spaces, events and probability 667
. .. ,. 38.3 Sets and probability 669
statistics _ . F , ...
38.4 Counting and combinations 673
38.5 Conditional probability 675
38.6 Independent events 677
38.7 Total probability 678
38.8 Bayes theorem 679
Problems 680
39 Random variables and probability distributions
39.1 Random variables 683
39.2 Probability distributions 684
39.3 The binomial distribution 685
39.4 Expected value and variance 687
39.5 Geometric distribition 689
39.6 Poisson distribution 691
39.7 Other discrete distributions 693
39.8 Continuous random variables and distributions 694
39.9 Mean and variance of continuous random variables 695
39.10 The normal distribution 696
Problems 698
40 Descriptive statistics
40.1 Representing data 701
40.2 Random samples and sampling distributions 705
40.3 Sample mean and variance, and their estimation 707
40.4 Central limit theorem 708
40.5 Regression 710
Problems 713
41 Applications projects using symbolic computing
PART VIII 41.1 Symbolic computation 715
Projects 41.2 Pr°Jects 716
Contents
Answers to selected problems 736
Appendices
A Some algebraical rules 767
B Trigonometric formulae 769
C Areas and volumes 770
D A table of derivatives 771
E A table of integrals 772
F A table of Laplace transforms, inverses and general rules 773
G A table of Fourier transforms and general rules 774
H Probability distributions and tables 776
Index 779
|
| any_adam_object | 1 |
| author | Jordan, Dominic W. Smith, Peter 1935- |
| author_GND | (DE-588)115172602 (DE-588)141762349 |
| author_facet | Jordan, Dominic W. Smith, Peter 1935- |
| author_role | aut aut |
| author_sort | Jordan, Dominic W. |
| author_variant | d w j dw dwj p s ps |
| building | Verbundindex |
| bvnumber | BV011599937 |
| callnumber-first | Q - Science |
| callnumber-label | QA300 J82 1997 |
| callnumber-raw | QA300 J82 1997 |
| callnumber-search | QA300 J82 1997 |
| callnumber-sort | QA 3300 J82 41997 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 950 |
| ctrlnum | (OCoLC)610755089 (DE-599)BVBBV011599937 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| genre | 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Matériel didactique |
| genre_facet | Aufgabensammlung Matériel didactique |
| id | DE-604.BV011599937 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:12:33Z |
| institution | BVB |
| isbn | 0198564627 0198564619 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007814440 |
| oclc_num | 610755089 |
| open_access_boolean | |
| owner | DE-20 DE-1050 DE-11 |
| owner_facet | DE-20 DE-1050 DE-11 |
| physical | XVIII, 788 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| spelling | Jordan, Dominic W. Verfasser (DE-588)115172602 aut Mathematical techniques an introduction for the engineering, physical, and mathematical sciences D. W. Jordan and P. Smith 2. ed. Oxford [u.a.] Oxford Univ. Press 1997 XVIII, 788 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Analyse mathématique Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content Matériel didactique Mathematik (DE-588)4037944-9 s Ingenieurwissenschaften (DE-588)4137304-2 s DE-604 Mathematische Physik (DE-588)4037952-8 s 2\p DE-604 Mathematica Programm (DE-588)4268208-3 s 3\p DE-604 Smith, Peter 1935- Verfasser (DE-588)141762349 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007814440&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Jordan, Dominic W. Smith, Peter 1935- Mathematical techniques an introduction for the engineering, physical, and mathematical sciences Analyse mathématique Ingenieurwissenschaften (DE-588)4137304-2 gnd Mathematica Programm (DE-588)4268208-3 gnd Mathematische Physik (DE-588)4037952-8 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4137304-2 (DE-588)4268208-3 (DE-588)4037952-8 (DE-588)4037944-9 (DE-588)4143389-0 |
| title | Mathematical techniques an introduction for the engineering, physical, and mathematical sciences |
| title_auth | Mathematical techniques an introduction for the engineering, physical, and mathematical sciences |
| title_exact_search | Mathematical techniques an introduction for the engineering, physical, and mathematical sciences |
| title_full | Mathematical techniques an introduction for the engineering, physical, and mathematical sciences D. W. Jordan and P. Smith |
| title_fullStr | Mathematical techniques an introduction for the engineering, physical, and mathematical sciences D. W. Jordan and P. Smith |
| title_full_unstemmed | Mathematical techniques an introduction for the engineering, physical, and mathematical sciences D. W. Jordan and P. Smith |
| title_short | Mathematical techniques |
| title_sort | mathematical techniques an introduction for the engineering physical and mathematical sciences |
| title_sub | an introduction for the engineering, physical, and mathematical sciences |
| topic | Analyse mathématique Ingenieurwissenschaften (DE-588)4137304-2 gnd Mathematica Programm (DE-588)4268208-3 gnd Mathematische Physik (DE-588)4037952-8 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Analyse mathématique Ingenieurwissenschaften Mathematica Programm Mathematische Physik Mathematik Aufgabensammlung Matériel didactique |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007814440&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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