Advanced engineering mathematics

Title:

Personal Author:

Jeffrey, Alan

Publication Information:

San Diego, Calif. : Academic Press, 2002

ISBN:

9780123825926

Subject Term:

Engineering mathematics

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010025451	TA330 J45 2002	Open Access Book	Book	Searching... Unknown
Searching... PSZ JB	30000004863589	TA330 J45 2002	Open Access Book	Book	Searching... Unknown

When the powerful Lord Takeda's soldiers sweep across the countryside, killing and plundering, they spare the boy Taro's life and take him along with them. Taro becomes a servant in the household of the noble Lord Akiyama, where he meets Togan, a cook, who teaches Taro and makes his new life bearable. But when Togan is murdered, Taro's life takes a new direction: He will become a samurai, and redeem the family legacy that has been stolen from him.

Preface	p. xv
Part 1 Review Material	p. 1
Chapter 1 Review of Prerequisites	p. 3
1.1 Real Numbers, Mathematical Induction, and Mathematical Conventions	p. 4
1.2 Complex Numbers	p. 10
1.3 The Complex Plane	p. 15
1.4 Modulus and Argument Representation of Complex Numbers	p. 18
1.5 Roots of Complex Numbers	p. 22
1.6 Partial Fractions	p. 27
1.7 Fundamentals of Determinants	p. 31
1.8 Continuity in One or More Variables	p. 35
1.9 Differentiability of Functions of One or More Variables	p. 38
1.10 Tangent Line and Tangent Plane Approximations to Functions	p. 40
1.11 Integrals	p. 41
1.12 Taylor and Maclaurin Theorems	p. 43
1.13 Cylindrical and Spherical Polar Coordinates and Change of Variables in Partial Differentiation	p. 46
1.14 Inverse Functions and the Inverse Function Theorem	p. 49
Part 2 Vectors and Matrices	p. 53
Chapter 2 Vectors and Vector Spaces	p. 55
2.1 Vectors, Geometry, and Algebra	p. 56
2.2 The Dot Product (Scalar Product)	p. 70
2.3 The Cross Product (Vector Product)	p. 77
2.4 Linear Dependence and Independence of Vectors and Triple Products	p. 82
2.5 n-Vectors and the Vector Space R[superscript n]	p. 88
2.6 Linear Independence, Basis, and Dimension	p. 95
2.7 Gram-Schmidt Orthogonalization Process	p. 101
Chapter 3 Matrices and Systems of Linear Equations	p. 105
3.1 Matrices	p. 106
3.2 Some Problems That Give Rise to Matrices	p. 120
3.3 Determinants	p. 133
3.4 Elementary Row Operations, Elementary Matrices, and Their Connection with Matrix Multiplication	p. 143
3.5 The Echelon and Row-Reduced Echelon Forms of a Matrix	p. 147
3.6 Row and Column Spaces and Rank	p. 152
3.7 The Solution of Homogeneous Systems of Linear Equations	p. 155
3.8 The Solution of Nonhomogeneous Systems of Linear Equations	p. 158
3.9 The Inverse Matrix	p. 163
3.10 Derivative of a Matrix	p. 171
Chapter 4 Eigenvalues, Eigenvectors, and Diagonalization	p. 177
4.1 Characteristic Polynomial, Eigenvalues, and Eigenvectors	p. 178
4.2 Diagonalization of Matrices	p. 196
4.3 Special Matrices with Complex Elements	p. 205
4.4 Quadratic Forms	p. 210
4.5 The Matrix Exponential	p. 215
Part 3 Ordinary Differential Equations	p. 225
Chapter 5 First Order Differential Equations	p. 227
5.1 Background to Ordinary Differential Equations	p. 228
5.2 Some Problems Leading to Ordinary Differential Equations	p. 233
5.3 Direction Fields	p. 240
5.4 Separable Equations	p. 242
5.5 Homogeneous Equations	p. 247
5.6 Exact Equations	p. 250
5.7 Linear First Order Equations	p. 253
5.8 The Bernoulli Equation	p. 259
5.9 The Riccati Equation	p. 262
5.10 Existence and Uniqueness of Solutions	p. 264
Chapter 6 Second and Higher Order Linear Differential Equations and Systems	p. 269
6.1 Homogeneous Linear Constant Coefficient Second Order Equations	p. 270
6.2 Oscillatory Solutions	p. 280
6.3 Homogeneous Linear Higher Order Constant Coefficient Equations	p. 291
6.4 Undetermined Coefficients: Particular Integrals	p. 302
6.5 Cauchy-Euler Equation	p. 309
6.6 Variation of Parameters and the Green's Function	p. 311
6.7 Finding a Second Linearly Independent Solution from a Known Solution: The Reduction of Order Method	p. 321
6.8 Reduction to the Standard Form u" + f(x)u = 0	p. 324
6.9 Systems of Ordinary Differential Equations: An Introduction	p. 326
6.10 A Matrix Approach to Linear Systems of Differential Equations	p. 333
6.11 Nonhomogeneous Systems	p. 338
6.12 Autonomous Systems of Equations	p. 351
Chapter 7 The Laplace Transform	p. 379
7.1 Laplace Transform: Fundamental Ideas	p. 379
7.2 Operational Properties of the Laplace Transform	p. 390
7.3 Systems of Equations and Applications of the Laplace Transform	p. 415
7.4 The Transfer Function, Control Systems, and Time Lags	p. 437
Chapter 8 Series Solutions of Differential Equations, Special Functions, and Sturm-Liouville Equations	p. 443
8.1 A First Approach to Power Series Solutions of Differential Equations	p. 443
8.2 A General Approach to Power Series Solutions of Homogeneous Equations	p. 447
8.3 Singular Points of Linear Differential Equations	p. 461
8.4 The Frobenius Method	p. 463
8.5 The Gamma Function Revisited	p. 480
8.6 Bessel Function of the First Kind J[subscript n](x)	p. 485
8.7 Bessel Functions of the Second Kind Y[subscript v](x)	p. 495
8.8 Modified Bessel Functions I[subscript v](x) and K[subscript v](x)	p. 501
8.9 A Critical Bending Problem: Is There a Tallest Flagpole?	p. 504
8.10 Sturm-Liouville Problems, Eigenfunctions, and Orthogonality	p. 509
8.11 Eigenfunction Expansions and Completeness	p. 526
Part 4 Fourier Series, Integrals, and the Fourier Transform	p. 543
Chapter 9 Fourier Series	p. 545
9.1 Introduction to Fourier Series	p. 545
9.2 Convergence of Fourier Series and Their Integration and Differentiation	p. 559
9.3 Fourier Sine and Cosine Series on 0 [less than or equal] x [less than or equal] L	p. 568
9.4 Other Forms of Fourier Series	p. 572
9.5 Frequency and Amplitude Spectra of a Function	p. 577
9.6 Double Fourier Series	p. 581
Chapter 10 Fourier Integrals and the Fourier Transform	p. 589
10.1 The Fourier Integral	p. 589
10.2 The Fourier Transform	p. 595
10.3 Fourier Cosine and Sine Transforms	p. 611
Part 5 Vector Calculus	p. 623
Chapter 11 Vector Differential Calculus	p. 625
11.1 Scalar and Vector Fields, Limits, Continuity, and Differentiability	p. 626
11.2 Integration of Scalar and Vector Functions of a Single Real Variable	p. 636
11.3 Directional Derivatives and the Gradient Operator	p. 644
11.4 Conservative Fields and Potential Functions	p. 650
11.5 Divergence and Curl of a Vector	p. 659
11.6 Orthogonal Curvilinear Coordinates	p. 665
Chapter 12 Vector Integral Calculus	p. 677
12.1 Background to Vector Integral Theorems	p. 678
12.2 Integral Theorems	p. 680
12.3 Transport Theorems	p. 697
12.4 Fluid Mechanics Applications of Transport Theorems	p. 704
Part 6 Complex Analysis	p. 709
Chapter 13 Analytic Functions	p. 711
13.1 Complex Functions and Mappings	p. 711
13.2 Limits, Derivatives, and Analytic Functions	p. 717
13.3 Harmonic Functions and Laplace's Equation	p. 730
13.4 Elementary Functions, Inverse Functions, and Branches	p. 735
Chapter 14 Complex Integration	p. 745
14.1 Complex Integrals	p. 745
14.2 Contours, the Cauchy-Goursat Theorem, and Contour Integrals	p. 755
14.3 The Cauchy Integral Formulas	p. 769
14.4 Some Properties of Analytic Functions	p. 775
Chapter 15 Laurent Series, Residues, and Contour Integration	p. 791
15.1 Complex Power Series and Taylor Series	p. 791
15.2 Uniform Convergence	p. 811
15.3 Laurent Series and the Classification of Singularities	p. 816
15.4 Residues and the Residue Theorem	p. 830
15.5 Evaluation of Real Integrals by Means of Residues	p. 839
Chapter 16 The Laplace Inversion Integral	p. 863
16.1 The Inversion Integral for the Laplace Transform	p. 863
Chapter 17 Conformal Mapping and Applications to Boundary Value Problems	p. 877
17.1 Conformal Mapping	p. 877
17.2 Conformal Mapping and Boundary Value Problems	p. 904
Part 7 Partial Differential Equations	p. 925
Chapter 18 Partial Differential Equations	p. 927
18.1 What Is a Partial Differential Equation?	p. 927
18.2 The Method of Characteristics	p. 934
18.3 Wave Propagation and First Order PDEs	p. 942
18.4 Generalizing Solutions: Conservation Laws and Shocks	p. 951
18.5 The Three Fundamental Types of Linear Second Order PDE	p. 956
18.6 Classification and Reduction to Standard Form of a Second Order Constant Coefficient Partial Differential Equation for u(x, y)	p. 964
18.7 Boundary Conditions and Initial Conditions	p. 975
18.8 Waves and the One-Dimensional Wave Equation	p. 978
18.9 The D'Alembert Solution of the Wave Equation and Applications	p. 981
18.10 Separation of Variables	p. 988
18.11 Some General Results for the Heat and Laplace Equation	p. 1025
18.12 An Introduction to Laplace and Fourier Transform Methods for PDEs	p. 1030
Part 8 Numerical Mathematics	p. 1043
Chapter 19 Numerical Mathematics	p. 1045
19.1 Decimal Places and Significant Figures	p. 1046
19.2 Roots of Nonlinear Functions	p. 1047
19.3 Interpolation and Extrapolation	p. 1058
19.4 Numerical Integration	p. 1065
19.5 Numerical Solution of Linear Systems of Equations	p. 1077
19.6 Eigenvalues and Eigenvectors	p. 1090
19.7 Numerical Solution of Differential Equations	p. 1095
Answers	p. 1109
References	p. 1143
Index	p. 1147

Available:*

On Order

Summary

Summary

Table of Contents