Mathematical techniques: an introduction for the engineering, physical, and mathematical sciences
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2008
|
| Edition: | Fourth edition |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Hier auch später erschienene, unveränderte Nachdrucke |
| Physical Description: | XX, 976 Seiten Illustrationen, Diagramme |
| ISBN: | 9780199282012 |
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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 Fourth edition | ||
| 264 | 1 | |a Oxford [u.a.] |b Oxford Univ. Press |c 2008 | |
| 300 | |a XX, 976 Seiten |b Illustrationen, Diagramme | ||
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| _version_ | 1804137695561121792 |
|---|---|
| adam_text | Titel: Mathematical techniques
Autor: Jordan, Dominic W.
Jahr: 2008
Detailed Contents
Elementary methods, differentiation, complex numbers
ndard functions and techniques 3
3
6
7
12
16
17
23
25
28
30
33
35
36
39
43
45
46
51
55
61
2.1 The slope of a graph 62
2.2 The derivative: notation and definition 65
2.3 Rates of change 67
2.4 Derivative of x (n = 0,1,2,3,...) 69
2.5 Derivatives of sums: multiplication by constants 70
2.6 Three important limits 72
2.7 Derivatives of e*, sin x, cos x, In x 74
2.8 A basic table of derivatives 76
2.9 Higher-order derivatives 77
2.10 An interpretation of the second derivative 79
Problems 80
irther techniques for differentiation 82
3.1 The product rule 83
3.2 Quotients and reciprocals 85
3.3 The chain rule 86
3.4 Derivative of x for any value of n 89
3.5 Functions of ax + b 90
3.6 An extension of the chain rule 91
3.7 Logarithmic differentiation 92
1.1 Real numbers, powers, inequalities
1.2 Coordinates in the plane
1.3 Graphs
1.4 Functions
1.5 Radian measure of angles
1.6 Trigonometric functions; properties
1.7 Inverse functions
1.8 Inverse trigonometric functions
1.9 Polar coordinates
1.10 Exponential functions; the number e
1.11 The logarithmic function
1.12 Exponential growth and decay
1.13 Hyperbolic functions
1.14 Partial fractions
1.15 Summation sign: geometric series
1.16 Infinite geometric series
1.17 Permutations and combinations
1.18 The binomial theorem
Problems
MM differentiation
3.8 Implicit differentiation
W 3.9 Derivatives of inverse functions
3.10 Derivative as a function of a parameter
93
94
W Problems 98
Z
O ^QpApplications of differentiation 10°
100
102
106
108
114
116
120
121
124
125
125
128
130
132
134
134
5.8 Indeterminate values; I Hopital s rule 136
4.1 Function notation for derivatives
4.2 Maxima and minima
4.3 Exceptional cases of maxima and minima
4.4 Sketching graphs of functions
4.5 Estimating small changes
4.6 Numerical solution of equations: Newton s method
4.7 The binomial theorem: an alternative proof
Problems
aylor series and approximations
5.1 The index notation for derivatives of any order
5.2 Taylor polynomials
5.3 A note on infinite series
5.4 Infinite Taylor expansions
5.5 Manipulation of Taylor series
5.6 Approximations for large values of x
5.7 Taylor series about other points
Problems
138
omplex numbers 1 °
6.1 Definitions and rules
6.2 The Argand diagram, modulus, conjugate
6.3 Complex numbers in polar coordinates
6.4 Complex numbers in exponential form 14°
6.5 The general exponential form
6.6 Hyperbolic functions 153
6.7 Miscellaneous applications 54
Problems 156
Matrix and vector algebra
Matrix algebra
161
7.1 Matrix definition and notation
7.2 Rules of matrix algebra
168
7.3 Special matrices
7.4 The inverse matrix
Problems 177
i 179
^Determinants
179
8.1 The determinant of a square matrix
182
8.2 Properties of determinants
8.3 The adjoint and inverse matrices
Problems
Elementary operations with vectors
9.1 Displacement along an axis
9.2 Displacement vectors in two dimensions 195
9.3 Axes in three dimensions 198
9.4 Vectors in two and three dimensions 198
9.5 Relative velocity 204
9.6 Position vectors and vector equations 206
9.7 Unit vectors and basis vectors 210
9.8 Tangent vector, velocity, and acceleration 212
9.9 Motion in polar coordinates 214
Problems 216
?Ji The scalar product 219
10.1 The scalar product of two vectors 219
10.2 The angle between two vectors 220
10.3 Perpendicular vectors 222
10.4 Rotation of axes in two dimensions 223
10.5 Direction cosines 225
10.6 Rotation of axes in three dimensions 226
10.7 Direction ratios and coordinate geometry 229
10.8 Properties of a plane 230
10.9 General equation of a straight line 234
10.10 Forces acting at a point 235
10.11 Tangent vector and curvature in two dimensions 238
Problems 240
Vector product 244
11.1 Vector product 244
11.2 Nature of the vectorp=ax6 246
11.3 The scalar triple product 249
11.4 Moment of a force 251
11.5 Vector triple product 255
Problems 256
Linear algebraic equations 259
12.1 Cramer s rule 260
12.2 Elementary row operations 262
12.3 The inverse matrix by Gaussian elimination 265
12.4 Compatible and incompatible sets of equations 267
12.5 Homogeneous sets of equations 271
12.6 Gauss-Seidel iterative method of solution 273
Problems 275
Eigenvalues and eigenvectors 279
13.1 Eigenvalues of a matrix 279
13.2 Eigenvectors 281
189
190 O
O
z
193 m
z
193 H
C/3
13.3 Linear dependence
CO 13.4 Diagonalization of a matrix
Z 13.5 Powers of matrices
UJ 1? 13.6 Quadratic forms
z o o 13.7 Positive-definite matrices
13.8 An application to a vibrating system
Problems
Integration and differential equations
285
286
289
292
295
298
301
(differentiation and area 307
14.1 Reversing differentiation 307
14.2 Constructing a table of antiderivatives 311
14.3 Signed area generated by a graph 314
14.4 Case where the antiderivative is composite 317
Problems 318
definite and indefinite integral 320
15.1 Signed area as the sum of strips 320
15.2 Numerical illustration of the sum formula 321
15.3 The definite integral and area 323
15.4 The indefinite-integral notation 324
15.5 Integrals unrelated to area 326
15.6 Improper integrals 328
15.7 Integration of complex functions: a new type of integral 331
15.8 The area analogy for a definite integral 333
15.9 Symmetric integrals 333
15.10 Definite integrals having variable limits 336
Problems 338
lications involving the integral as a sum 341
16.1 Examples of integrals arising from a sum 341
16.2 Geometrical area in polar coordinates 344
16.3 The trapezium rule 346
16.4 Centre of mass, moment of inertia 348
Problems 353
ematic techniques for integration 356
17.1 Substitution method for j^ax + o)dx 356
17.2 Substitution method for J flax2 + b)x dx 359
17.3 Substitution method for f cc^ax sin ax dx (m or n odd) 360
17.4 Definite integrals and change of variable 362
17.5 Occasional substitutions 364
17.6 Partial fractions for integration 366
17.7 Integration by parts 368
17.8 Integration by parts: definite integrals 371
17.9 Differentiating with respect to a parameter 373
Problems 375
Jnforced linear differential equations with constant coefficients 379
o
18.1 Differential equations and their solutions 380 ^
18.2 Solving first-order linear unforced equations 382 -H
18.3 Solving second-order linear unforced equations 384 z
18.4 Complex solutions of the characteristic equation 388 jjj
18.5 Initial conditions for second-order equations 391
Problems 393
breed linear differential equations 395
19.1 Particular solutions for standard forcing terms 395
19.2 Harmonic forcing term, by using complex solutions 399
19.3 Particular solutions: exceptional cases 403
19.4 The general solution of forced equations 404
19.5 First-order linear equations with a variable coefficient 407
Problems 411
larmonic functions and the harmonic oscillator 413
20.1 Harmonic oscillations 413
20.2 Phase difference: lead and lag 415
20.3 Physical models of a differential equation 417
20.4 Free oscillations of a linear oscillator 419
20.5 Forced oscillations and transients 420
20.6 Resonance 423
20.7 Nearly linear systems 425
20.8 Stationary and travelling waves 427
20.9 Compound oscillations; beats 431
20.10 Travelling waves; beats 434
20.11 Dispersion; group velocity 436
20.12 The Doppler effect 437
Problems 439
ady forced oscillations: phasors, impedance, transfer functions 442
21.1 Phasors 442
21.2 Algebra of phasors 444
21.3 Phasor diagrams 445
21.4 Phasors and complex impedance 446
21.5 Transfer functions in the frequency domain 451
21.6 Phasors and waves; complex amplitude 453
Problems 458
phical, numerical, and other aspects of first-order equations 460
22.1 Graphical features of first-order equations 460
22.2 The Euler method for numerical solution 463
22.3 Nonlinear equations of separable type 466
22.4 Differentials and the solution of first-order equations 469
22.5 Change of variable in a differential equation 473
Problems 476
CO H Z LU -z 23.1 23.2 23.3
o o 23.4 23.5
23.6
23.7
23.8
23.9
onlinear differential equations and the phase plane 480
Autonomous second-order equations 481
Constructing a phase diagram for (x, x) 482
(x, x) phase diagrams for other linear equations; stability 486
The pendulum equation 489
The general phase plane 491
Approximate linearization 494
Classification of linear equilibrium points 496
Limit cycles 497
A numerical method for phase paths 499
Problems 501
Transforms and Fourier Series
e Laplace transform 505
24.1 The Laplace transform 505
24.2 Laplace transforms of r e±(, sin f, cos t 506
24.3 Scale rule; shift rule; factors f and ew 508
24.4 Inverting a Laplace transform 512
24.5 Laplace transforms of derivatives 515
24.6 Application to differential equations 516
24.7 The unit function and the delay rule 519
24.8 The division rule for f(t)/t 524
Problems 525
place and z transforms: applications 527
25.1 Division by s and integration 527
25.2 The impulse function 530
25.3 Impedance in the s domain 533
25.4 Transfer functions in the s domain 535
25.5 The convolution theorem 541
25.6 General response of a system from its impulsive response 543
25.7 Convolution integral in terms of memory 544
25.8 Discrete systems 545
25.9 The z transform 548
25.10 Behaviour of z transforms in the complex plane 552
25.11 z transforms and difference equations 556
Problems 558
rier series 562
26.1 Fourier series for a periodic function 563
26.2 Integrals of periodic functions 564
26.3 Calculating the Fourier coefficients 566
26.4 Examples of Fourier series 569
26.5 Use of symmetry: sine and cosine series 572
26.6 Functions defined on a finite range: half-range series 574
26.7 Spectrum of a periodic function 577
26.8 Obtaining one Fourier series from another 578
26.9 The two-sided Fourier series 579
Problems 582
burier transforms 586
27.1 Sine and cosine transforms
27.2 The exponential Fourier transform
27.3 Short notations: alternative expressions
27.4 Fourier transforms of some basic functions
27.5 Rules for manipulating transforms
27.6 The delta function and periodic functions
27.7 Convolution theorem for Fourier transforms
27.8 The shah function
27.9 Energy in a signal: Rayleigh s theorem
27.10 Diffraction from a uniformly radiating strip
27.11 General source distribution and the inverse transform
27.12 Transforms in radiation problems
Problems
Multivariable calculus
Differentiation of functions of two variables 623
28.1 Depiction of functions of two variables 624
28.2 Partial derivatives 627
28.3 Higher derivatives 629
28.4 Tangent plane and normal to a surface 632
28.5 Maxima, minima, and other stationary points 635
28.6 The method of least squares 638
28.7 Differentiating an integral with respect to a parameter 640
Problems 642
Functions of two variables: geometry and formulae 645
29.1 The incremental approximation 645
29.2 Small changes and errors 648
29.3 The derivative in any direction 651
29.4 Implicit differentiation 654
29.5 Normal to a curve 657
29.6 Gradient vector in two dimensions 659
Problems 662
»n rules, restricted maxima, coordinate systems 664
30.1 Chain rule for a single parameter 664
30.2 Restricted maxima and minima: the Lagrange multiplier 667
30.3 Curvilinear coordinates in two dimensions 672
30.4 Orthogonal coordinates 675
30.5 The chain rule for two parameters 676
30.6 The use of differentials 679
Problems 681
tions of any number of variables 683
31.1 The incremental approximation; errors 683
31.2 Implicit differentiation 686
O
587 O
z
590 H
592 m z
593 -
Cfl
596
599
601
605
607
608
612
613
618
31.3 Chain rules
CO 31.4 The gradient vector in three dimensions
1? z 31.5 Normal to a surface
UJ h- 31.6 Equation of the tangent plane
z 31.7 Directional derivative in terms of gradient
o o 31.8 Stationary points
31.9 The envelope of a family of curves Problems
688
688
690
691
692
696
702
704
uble integration 708
32.1 Repeated integrals with constant limits 709
32.2 Examples leading to repeated integrals with constant limits 710
32.3 Repeated integrals over non-rectangular regions 713
32.4 Changing the order of integration for non-rectangular regions 715
32.5 Double integrals 717
32.6 Polar coordinates 721
32.7 Separable integrals 724
32.8 General change of variable; the Jacobian determinant 727
Problems 732
ine integrals 735
33.1 Evaluation of line integrals 736
33.2 General line integrals in two and three dimensions 739
33.3 Paths parallel to the axes 743
33.4 Path independence and perfect differentials 744
33.5 Closed paths 746
33.6 Green s theorem 748
33.7 Line integrals and work 750
33.8 Conservative fields 752
33.9 Potential for a conservative field 754
33.10 Single-valuedness of potentials 756
Problems 759
or fields: divergence and curl 762
34.1 Vector fields and field lines 762
34.2 Divergence of a vector field 764
34.3 Surface and volume integrals 765
34.4 The divergence theorem; flux of a vector field 770
34.5 Curl of a vector field 773
34.6 Cylindrical polar coordinates 777
34.7 General curvilinear coordinates 779
34.8 Stokes s theorem 781
Problems 785
Discrete mathematics
s 789
35.1 Notation 789
35.2 Equality, union, and intersection 790
35.3 Venn diagrams 792
Problems 799 o
O
z
}olean algebra: logic gates and switching functions 801 ^
z
36.1 Laws of Boolean algebra 801 7*
36.2 Logic gates and truth tables 803
36.3 Logic networks 805
36.4 The inverse truth-table problem 808
36.5 Switching circuits 809
Problems 812
iraph theory and its applications 814
37.1 Examples of graphs 815
37.2 Definitions and properties of graphs 817
37.3 How many simple graphs are there? 818
37.4 Paths and cycles 820
37.5 Trees 821
37.6 Electrical circuits: the cutset method 823
37.7 Signal-flow graphs 827
37.8 Planar graphs 831
37.9 Further applications 834
Problems 837
erence equations 842
38.1 Discrete variables 842
38.2 Difference equations: general properties 845
38.3 First-order difference equations and the cobweb 847
38.4 Constant-coefficient linear difference equations 849
38.5 The logistic difference equation 854
Problems 859
Probability and statistics
liability 865
39.1 Sample spaces, events, and probability 866
39.2 Sets and probability 868
39.3 Frequencies and combinations 872
39.4 Conditional probability 875
39.5 Independent events 877
39.6 Total probability 879
39.7 Bayes theorem 880
Problems 881
m variables and probability distributions 884
40.1 Probability distributions 885
40.2 The binomial distribution 887
40.3 Expected value and variance 889
40.4 Geometric distribution 891
40.5
CO 40.6
t-
z 40.7
LU 1- 40.8
z 40.9
o
Poisson distribution 892
Other discrete distributions 894
Continuous random variables and distributions 895
Mean and variance of continuous random variables 897
The normal distribution 898
Problems 901
escriptive statistics 903
41.1 Representing data 903
41.2 Random samples and sampling distributions 908
41.3 Sample mean and variance, and their estimation 910
41.4 Central limit theorem 911
41.5 Regression 913
Problems 915
Projects
plications projects using symbolic computing 919
42.1 Symbolic computation 919
42.2 Projects 920
Self-tests: Selected answers 931
swers to selected problems 937
Appendices 948
A Some algebraical rules 948
B Trigonometric formulae 949
C Areas and volumes 951
D A table of derivatives 952
E Table of indefinite and definite integrals 953
F Laplace transforms, inverses, and rules 955
G Exponential Fourier transforms and rules 956
H Probability distributions and tables 957
I Dimensions and units 959
Further reading g6i
tlndex
962
|
| adam_txt |
Titel: Mathematical techniques
Autor: Jordan, Dominic W.
Jahr: 2008
Detailed Contents
Elementary methods, differentiation, complex numbers
ndard functions and techniques 3
3
6
7
12
16
17
23
25
28
30
33
35
36
39
43
45
46
51
55
61
2.1 The slope of a graph 62
2.2 The derivative: notation and definition 65
2.3 Rates of change 67
2.4 Derivative of x"(n = 0,1,2,3,.) 69
2.5 Derivatives of sums: multiplication by constants 70
2.6 Three important limits 72
2.7 Derivatives of e*, sin x, cos x, In x 74
2.8 A basic table of derivatives 76
2.9 Higher-order derivatives 77
2.10 An interpretation of the second derivative 79
Problems 80
irther techniques for differentiation 82
3.1 The product rule 83
3.2 Quotients and reciprocals 85
3.3 The chain rule 86
3.4 Derivative of x" for any value of n 89
3.5 Functions of ax + b 90
3.6 An extension of the chain rule 91
3.7 Logarithmic differentiation 92
1.1 Real numbers, powers, inequalities
1.2 Coordinates in the plane
1.3 Graphs
1.4 Functions
1.5 Radian measure of angles
1.6 Trigonometric functions; properties
1.7 Inverse functions
1.8 Inverse trigonometric functions
1.9 Polar coordinates
1.10 Exponential functions; the number e
1.11 The logarithmic function
1.12 Exponential growth and decay
1.13 Hyperbolic functions
1.14 Partial fractions
1.15 Summation sign: geometric series
1.16 Infinite geometric series
1.17 Permutations and combinations
1.18 The binomial theorem
Problems
MM differentiation
3.8 Implicit differentiation
W 3.9 Derivatives of inverse functions
3.10 Derivative as a function of a parameter
93
94
W Problems 98
Z
O ^QpApplications of differentiation 10°
100
102
106
108
114
116
120
121
124
125
125
128
130
132
134
134
5.8 Indeterminate values; I'Hopital's rule 136
4.1 Function notation for derivatives
4.2 Maxima and minima
4.3 Exceptional cases of maxima and minima
4.4 Sketching graphs of functions
4.5 Estimating small changes
4.6 Numerical solution of equations: Newton's method
4.7 The binomial theorem: an alternative proof
Problems
aylor series and approximations
5.1 The index notation for derivatives of any order
5.2 Taylor polynomials
5.3 A note on infinite series
5.4 Infinite Taylor expansions
5.5 Manipulation of Taylor series
5.6 Approximations for large values of x
5.7 Taylor series about other points
Problems
138
omplex numbers 1 °
6.1 Definitions and rules
6.2 The Argand diagram, modulus, conjugate
6.3 Complex numbers in polar coordinates
6.4 Complex numbers in exponential form 14°
6.5 The general exponential form
6.6 Hyperbolic functions 153
6.7 Miscellaneous applications 54
Problems 156
Matrix and vector algebra
Matrix algebra
161
7.1 Matrix definition and notation
7.2 Rules of matrix algebra
168
7.3 Special matrices
7.4 The inverse matrix
Problems 177
i 179
^Determinants
179
8.1 The determinant of a square matrix
182
8.2 Properties of determinants
8.3 The adjoint and inverse matrices
Problems
Elementary operations with vectors
9.1 Displacement along an axis
9.2 Displacement vectors in two dimensions 195
9.3 Axes in three dimensions 198
9.4 Vectors in two and three dimensions 198
9.5 Relative velocity 204
9.6 Position vectors and vector equations 206
9.7 Unit vectors and basis vectors 210
9.8 Tangent vector, velocity, and acceleration 212
9.9 Motion in polar coordinates 214
Problems 216
?Ji The scalar product 219
10.1 The scalar product of two vectors 219
10.2 The angle between two vectors 220
10.3 Perpendicular vectors 222
10.4 Rotation of axes in two dimensions 223
10.5 Direction cosines 225
10.6 Rotation of axes in three dimensions 226
10.7 Direction ratios and coordinate geometry 229
10.8 Properties of a plane 230
10.9 General equation of a straight line 234
10.10 Forces acting at a point 235
10.11 Tangent vector and curvature in two dimensions 238
Problems 240
Vector product 244
11.1 Vector product 244
11.2 Nature of the vectorp=ax6 246
11.3 The scalar triple product 249
11.4 Moment of a force 251
11.5 Vector triple product 255
Problems 256
Linear algebraic equations 259
12.1 Cramer's rule 260
12.2 Elementary row operations 262
12.3 The inverse matrix by Gaussian elimination 265
12.4 Compatible and incompatible sets of equations 267
12.5 Homogeneous sets of equations 271
12.6 Gauss-Seidel iterative method of solution 273
Problems 275
Eigenvalues and eigenvectors 279
13.1 Eigenvalues of a matrix 279
13.2 Eigenvectors 281
189
190 O
O
z
193 m
z
193 H
C/3
13.3 Linear dependence
CO 13.4 Diagonalization of a matrix
Z 13.5 Powers of matrices
UJ 1? 13.6 Quadratic forms
z o o 13.7 Positive-definite matrices
13.8 An application to a vibrating system
Problems
Integration and differential equations
285
286
289
292
295
298
301
(differentiation and area 307
14.1 Reversing differentiation 307
14.2 Constructing a table of antiderivatives 311
14.3 Signed area generated by a graph 314
14.4 Case where the antiderivative is composite 317
Problems 318
definite and indefinite integral 320
15.1 Signed area as the sum of strips 320
15.2 Numerical illustration of the sum formula 321
15.3 The definite integral and area 323
15.4 The indefinite-integral notation 324
15.5 Integrals unrelated to area 326
15.6 Improper integrals 328
15.7 Integration of complex functions: a new type of integral 331
15.8 The area analogy for a definite integral 333
15.9 Symmetric integrals 333
15.10 Definite integrals having variable limits 336
Problems 338
lications involving the integral as a sum 341
16.1 Examples of integrals arising from a sum 341
16.2 Geometrical area in polar coordinates 344
16.3 The trapezium rule 346
16.4 Centre of mass, moment of inertia 348
Problems 353
ematic techniques for integration 356
17.1 Substitution method for j^ax + o)dx 356
17.2 Substitution method for J flax2 + b)x dx 359
17.3 Substitution method for f cc^ax sin"ax dx (m or n odd) 360
17.4 Definite integrals and change of variable 362
17.5 Occasional substitutions 364
17.6 Partial fractions for integration 366
17.7 Integration by parts 368
17.8 Integration by parts: definite integrals 371
17.9 Differentiating with respect to a parameter 373
Problems 375
Jnforced linear differential equations with constant coefficients 379
o
18.1 Differential equations and their solutions 380 ^
18.2 Solving first-order linear unforced equations 382 -H
18.3 Solving second-order linear unforced equations 384 z
18.4 Complex solutions of the characteristic equation 388 jjj
18.5 Initial conditions for second-order equations 391
Problems 393
breed linear differential equations 395
19.1 Particular solutions for standard forcing terms 395
19.2 Harmonic forcing term, by using complex solutions 399
19.3 Particular solutions: exceptional cases 403
19.4 The general solution of forced equations 404
19.5 First-order linear equations with a variable coefficient 407
Problems 411
larmonic functions and the harmonic oscillator 413
20.1 Harmonic oscillations 413
20.2 Phase difference: lead and lag 415
20.3 Physical models of a differential equation 417
20.4 Free oscillations of a linear oscillator 419
20.5 Forced oscillations and transients 420
20.6 Resonance 423
20.7 Nearly linear systems 425
20.8 Stationary and travelling waves 427
20.9 Compound oscillations; beats 431
20.10 Travelling waves; beats 434
20.11 Dispersion; group velocity 436
20.12 The Doppler effect 437
Problems 439
ady forced oscillations: phasors, impedance, transfer functions 442
21.1 Phasors 442
21.2 Algebra of phasors 444
21.3 Phasor diagrams 445
21.4 Phasors and complex impedance 446
21.5 Transfer functions in the frequency domain 451
21.6 Phasors and waves; complex amplitude 453
Problems 458
phical, numerical, and other aspects of first-order equations 460
22.1 Graphical features of first-order equations 460
22.2 The Euler method for numerical solution 463
22.3 Nonlinear equations of separable type 466
22.4 Differentials and the solution of first-order equations 469
22.5 Change of variable in a differential equation 473
Problems 476
CO H Z LU \-z 23.1 23.2 23.3
o o 23.4 23.5
23.6
23.7
23.8
23.9
onlinear differential equations and the phase plane 480
Autonomous second-order equations 481
Constructing a phase diagram for (x, x) 482
(x, x) phase diagrams for other linear equations; stability 486
The pendulum equation 489
The general phase plane 491
Approximate linearization 494
Classification of linear equilibrium points 496
Limit cycles 497
A numerical method for phase paths 499
Problems 501
Transforms and Fourier Series
e Laplace transform 505
24.1 The Laplace transform 505
24.2 Laplace transforms of r\ e±(, sin f, cos t 506
24.3 Scale rule; shift rule; factors f" and ew 508
24.4 Inverting a Laplace transform 512
24.5 Laplace transforms of derivatives 515
24.6 Application to differential equations 516
24.7 The unit function and the delay rule 519
24.8 The division rule for f(t)/t 524
Problems 525
place and z transforms: applications 527
25.1 Division by s and integration 527
25.2 The impulse function 530
25.3 Impedance in the s domain 533
25.4 Transfer functions in the s domain 535
25.5 The convolution theorem 541
25.6 General response of a system from its impulsive response 543
25.7 Convolution integral in terms of memory 544
25.8 Discrete systems 545
25.9 The z transform 548
25.10 Behaviour of z transforms in the complex plane 552
25.11 z transforms and difference equations 556
Problems 558
rier series 562
26.1 Fourier series for a periodic function 563
26.2 Integrals of periodic functions 564
26.3 Calculating the Fourier coefficients 566
26.4 Examples of Fourier series 569
26.5 Use of symmetry: sine and cosine series 572
26.6 Functions defined on a finite range: half-range series 574
26.7 Spectrum of a periodic function 577
26.8 Obtaining one Fourier series from another 578
26.9 The two-sided Fourier series 579
Problems 582
burier transforms 586
27.1 Sine and cosine transforms
27.2 The exponential Fourier transform
27.3 Short notations: alternative expressions
27.4 Fourier transforms of some basic functions
27.5 Rules for manipulating transforms
27.6 The delta function and periodic functions
27.7 Convolution theorem for Fourier transforms
27.8 The shah function
27.9 Energy in a signal: Rayleigh's theorem
27.10 Diffraction from a uniformly radiating strip
27.11 General source distribution and the inverse transform
27.12 Transforms in radiation problems
Problems
Multivariable calculus
Differentiation of functions of two variables 623
28.1 Depiction of functions of two variables 624
28.2 Partial derivatives 627
28.3 Higher derivatives 629
28.4 Tangent plane and normal to a surface 632
28.5 Maxima, minima, and other stationary points 635
28.6 The method of least squares 638
28.7 Differentiating an integral with respect to a parameter 640
Problems 642
Functions of two variables: geometry and formulae 645
29.1 The incremental approximation 645
29.2 Small changes and errors 648
29.3 The derivative in any direction 651
29.4 Implicit differentiation 654
29.5 Normal to a curve 657
29.6 Gradient vector in two dimensions 659
Problems 662
»n rules, restricted maxima, coordinate systems 664
30.1 Chain rule for a single parameter 664
30.2 Restricted maxima and minima: the Lagrange multiplier 667
30.3 Curvilinear coordinates in two dimensions 672
30.4 Orthogonal coordinates 675
30.5 The chain rule for two parameters 676
30.6 The use of differentials 679
Problems 681
tions of any number of variables 683
31.1 The incremental approximation; errors 683
31.2 Implicit differentiation 686
O
587 O
z
590 H
592 m z
593 -\
Cfl
596
599
601
605
607
608
612
613
618
31.3 Chain rules
CO 31.4 The gradient vector in three dimensions
1? z 31.5 Normal to a surface
UJ h- 31.6 Equation of the tangent plane
z 31.7 Directional derivative in terms of gradient
o o 31.8 Stationary points
31.9 The envelope of a family of curves Problems
688
688
690
691
692
696
702
704
uble integration 708
32.1 Repeated integrals with constant limits 709
32.2 Examples leading to repeated integrals with constant limits 710
32.3 Repeated integrals over non-rectangular regions 713
32.4 Changing the order of integration for non-rectangular regions 715
32.5 Double integrals 717
32.6 Polar coordinates 721
32.7 Separable integrals 724
32.8 General change of variable; the Jacobian determinant 727
Problems 732
ine integrals 735
33.1 Evaluation of line integrals 736
33.2 General line integrals in two and three dimensions 739
33.3 Paths parallel to the axes 743
33.4 Path independence and perfect differentials 744
33.5 Closed paths 746
33.6 Green's theorem 748
33.7 Line integrals and work 750
33.8 Conservative fields 752
33.9 Potential for a conservative field 754
33.10 Single-valuedness of potentials 756
Problems 759
or fields: divergence and curl 762
34.1 Vector fields and field lines 762
34.2 Divergence of a vector field 764
34.3 Surface and volume integrals 765
34.4 The divergence theorem; flux of a vector field 770
34.5 Curl of a vector field 773
34.6 Cylindrical polar coordinates 777
34.7 General curvilinear coordinates 779
34.8 Stokes's theorem 781
Problems 785
Discrete mathematics
s 789
35.1 Notation 789
35.2 Equality, union, and intersection 790
35.3 Venn diagrams 792
Problems 799 o
O
z
}olean algebra: logic gates and switching functions 801 ^
z
36.1 Laws of Boolean algebra 801 7*
36.2 Logic gates and truth tables 803
36.3 Logic networks 805
36.4 The inverse truth-table problem 808
36.5 Switching circuits 809
Problems 812
iraph theory and its applications 814
37.1 Examples of graphs 815
37.2 Definitions and properties of graphs 817
37.3 How many simple graphs are there? 818
37.4 Paths and cycles 820
37.5 Trees 821
37.6 Electrical circuits: the cutset method 823
37.7 Signal-flow graphs 827
37.8 Planar graphs 831
37.9 Further applications 834
Problems 837
'erence equations 842
38.1 Discrete variables 842
38.2 Difference equations: general properties 845
38.3 First-order difference equations and the cobweb 847
38.4 Constant-coefficient linear difference equations 849
38.5 The logistic difference equation 854
Problems 859
Probability and statistics
liability 865
39.1 Sample spaces, events, and probability 866
39.2 Sets and probability 868
39.3 Frequencies and combinations 872
39.4 Conditional probability 875
39.5 Independent events 877
39.6 Total probability 879
39.7 Bayes' theorem 880
Problems 881
m variables and probability distributions 884
40.1 Probability distributions 885
40.2 The binomial distribution 887
40.3 Expected value and variance 889
40.4 Geometric distribution 891
40.5
CO 40.6
t-
z 40.7
LU 1- 40.8
z 40.9
o
Poisson distribution 892
Other discrete distributions 894
Continuous random variables and distributions 895
Mean and variance of continuous random variables 897
The normal distribution 898
Problems 901
escriptive statistics 903
41.1 Representing data 903
41.2 Random samples and sampling distributions 908
41.3 Sample mean and variance, and their estimation 910
41.4 Central limit theorem 911
41.5 Regression 913
Problems 915
Projects
plications projects using symbolic computing 919
42.1 Symbolic computation 919
42.2 Projects 920
Self-tests: Selected answers 931
swers to selected problems 937
Appendices 948
A Some algebraical rules 948
B Trigonometric formulae 949
C Areas and volumes 951
D A table of derivatives 952
E Table of indefinite and definite integrals 953
F Laplace transforms, inverses, and rules 955
G Exponential Fourier transforms and rules 956
H Probability distributions and tables 957
I Dimensions and units 959
Further reading g6i
tlndex
962 |
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| author | Jordan, Dominic W. Smith, Peter 1935- |
| author_GND | (DE-588)115172602 (DE-588)141762349 |
| author_facet | Jordan, Dominic W. Smith, Peter 1935- |
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| author_sort | Jordan, Dominic W. |
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| callnumber-first | Q - Science |
| callnumber-label | QA300 |
| callnumber-raw | QA300 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 110 SK 950 |
| ctrlnum | (OCoLC)191732532 (DE-599)BVBBV023342161 |
| dewey-full | 510 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics 515 - Analysis |
| dewey-raw | 510 515 |
| dewey-search | 510 515 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | Fourth edition |
| format | Book |
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| index_date | 2024-07-02T21:01:58Z |
| indexdate | 2024-07-09T21:16:23Z |
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| isbn | 9780199282012 |
| language | English |
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| 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 Fourth edition Oxford [u.a.] Oxford Univ. Press 2008 XX, 976 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Analyse mathématique Mathematical analysis Mathematica Programm (DE-588)4268208-3 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf 1\p (DE-588)4143389-0 Aufgabensammlung gnd-content 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=016525909&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 Mathematical analysis Mathematica Programm (DE-588)4268208-3 gnd Mathematik (DE-588)4037944-9 gnd Mathematische Physik (DE-588)4037952-8 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
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| 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_exact_search_txtP | 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 Mathematical analysis Mathematica Programm (DE-588)4268208-3 gnd Mathematik (DE-588)4037944-9 gnd Mathematische Physik (DE-588)4037952-8 gnd Ingenieurwissenschaften (DE-588)4137304-2 gnd |
| topic_facet | Analyse mathématique Mathematical analysis Mathematica Programm Mathematik Mathematische Physik Ingenieurwissenschaften Aufgabensammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016525909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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