Further engineering mathematics: programmes and problems
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basingstoke u.a.
Macmillan
1996
|
| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 1063 graph. Darst. |
| ISBN: | 0333657411 |
Staff View
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| 100 | 1 | |a Stroud, Ken A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Further engineering mathematics |b programmes and problems |c K. A. Stroud |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Basingstoke u.a. |b Macmillan |c 1996 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface to the first edition xi
Preface to the second edition xiii
Preface to the third edition xiv
Hints on using the book xv
Useful background information xvii
Programme 1: Theory of Equations, Part 1 1
Function notation: evaluation by nesting 2
Interpolation: linear and graphical interpolation 5
Gregory Newton formula—forward differences 6
Remainder theorem 13
Equations with given roots 18
Polynomial equations: coefficients and roots 18
Transformation of equations: reciprocal equations 23
Repeated roots 29
Complex roots 32
Programme 2: Theory of Equations, Part 2 37
Cubic equations: Tartaglia s solution for the real root 38
Reduced form of a cubic equation: transformation 41
Trigonometrical solution of x3 + px + q = 0 42
Quartic equations: solution in reduced form 53
Numerical solution of equations: Newton Raphson
iterative method and modified method 63
Programme 3: Partial Differentiation 79
Small increments: Taylor s theorem for one and two
independent variables: rates of change: implicit functions 80
Change of variables: inverse functions 86
Stationary values of a function: maxima and minima:
saddle points 102
Lagrange undetermined multipliers with functions of
two and three independent variables 113
Programme 4: Integral Functions 125
The gamma function: definition: recurrence relation 126
viii Contents
Eigenvalues and eigenvectors 541
Matrix transformation: rotation of axes 550
Diagonalisation of a matrix: modal and spectral matrices 555
Programme 12: Vector Analysis, Part 1 569
Revision of scalar and vector quantities: scalar and vector
products: direction cosines: unit vectors 570
Triple products: scalar and vector triple products:
coplanar vectors 577
Differentiation and integration of vectors, sums
and products 585
Unit tangent vectors 591
Scalar and vector fields 598
Grad, div and curl: unit normal vectors:
directional derivatives 599
Multiple operations of grad, div and curl 616
Programme 13: Vector Analysis, Part 2 627
Line integrals 628
Scalar and vector fields 628
Volume integrals 638
Plane polar, cylindrical and spherical coordinates 642
Surface integrals: conservative vector fields 644
Gauss divergence theorem 660
Stokes theorem 669
Green s theorem 678
Programme 14: Vector Analysis, Part 3 689
Curvilinear coordinates 690
Orthogonal curvilinear coordinates in three dimensions:
base vectors: scale factors 696
Cylindrical polar coordinates 696
Spherical polar coordinates 699
Cartesian rectangular coordinates 702
General curvilinear coordinate system: transformation
equations 705
Elements of arc and volume 708
Grad, div and curl in orthogonal curvilinear coordinates 709
Programme 15: Complex Variable, Part 1 721
Functions of a complex variable 722
Complex mapping: transformation equations 723
Linear transformations 726
Types of transformation: translation, magnification
and rotation 731
Non linear transformation: inversion, bilinear, etc. 743
Contents ix
Mapping of a region 749
Programme 16: Complex Variable, Part 2 773
Differentiation of a complex function 774
Regular (analytic) function: singularities 775
Cauchy Riemann equations 779
Complex integration 782
Contour integration: line integrals in the z plane 782
Cauchy s theorem: deformation of contours at singularities 785
Conformal transformation 801
Schwarz Christoffel transformation 806
Programme 17: Fourier Series 825
Periodic functions: harmonics: non sinusoidal
periodic functions 826
Fourier series; functions of period 2tt 835
Dirichlet conditions: Fourier coefficients 836
Fourier series at a finite discontinuity 851
Odd and even functions, and their products; sine
series and cosine series 854
Half range series 868
Series containing only odd or only even harmonics 873
Periodic functions of period T; half range series 877
Programme 18: Numerical Harmonic Analysis 895
Approximate integration: trapezoidal rule 896
Fourier series coefficients 898
Twelve point analysis: percentage harmonics 898
Functions of period 2tt and T 899
Programme 19: Partial Differential Equations 925
Ordinary second order linear differential equations 926
Partial differential equations 927
Solution by direct integration: initial and boundary
conditions 927
The wave equation 931
Solution by separation of variables 932
The heat conduction equation 945
Laplace s equation 952
Use of Fourier series in fitting boundary conditions 953
Programme 20: Linear Optimisation (Linear Programming) 965
Optimisation: linear programming: objective function and
constraints 966
Linear inequalities: graphical representation 967
Graphical solution of linear programming problems 968
x Contents
The simplex method of solution: slack variables 974
Simplex computation: starting basic solution 977
Artificial variables: removal thereof 990
Minimisation problems 1005
Applications 1011
Appendix 1023
Answers 1033
Index 1064
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed. |
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| spelling | Stroud, Ken A. Verfasser aut Further engineering mathematics programmes and problems K. A. Stroud 3. ed. Basingstoke u.a. Macmillan 1996 XX, 1063 graph. Darst. txt rdacontent n rdamedia nc rdacarrier Engineering mathematics Programmed instruction Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Mathematik (DE-588)4037944-9 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 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007204262&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 |
| spellingShingle | Stroud, Ken A. Further engineering mathematics programmes and problems Engineering mathematics Programmed instruction Ingenieurwissenschaften (DE-588)4137304-2 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4137304-2 (DE-588)4037944-9 (DE-588)4143389-0 |
| title | Further engineering mathematics programmes and problems |
| title_auth | Further engineering mathematics programmes and problems |
| title_exact_search | Further engineering mathematics programmes and problems |
| title_full | Further engineering mathematics programmes and problems K. A. Stroud |
| title_fullStr | Further engineering mathematics programmes and problems K. A. Stroud |
| title_full_unstemmed | Further engineering mathematics programmes and problems K. A. Stroud |
| title_short | Further engineering mathematics |
| title_sort | further engineering mathematics programmes and problems |
| title_sub | programmes and problems |
| topic | Engineering mathematics Programmed instruction Ingenieurwissenschaften (DE-588)4137304-2 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Engineering mathematics Programmed instruction Ingenieurwissenschaften Mathematik Aufgabensammlung |
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