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1.

図書
図書
1. Advanced engineering mathematics. 10th ed., International student version (: pbk)
Erwin Kreyszig ; in collaboration with Herbert Kreyszig, Edward J. Norminton
出版情報: Hoboken, N.J. : Wiley, c2011  xv, 1001, 97, 27, 1 p. ; 26 cm
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2.

図書
図書
2. Advanced engineering mathematics : student solutions manual and study guide. 10th ed (v. 1 : [pbk])
Herbert Kreyszig, Erwin Kreyszig
出版情報: Hoboken, NJ : Wiley, c2011  viii, 256 p. ; 28 cm
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3.

電子ブック
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3. Advanced engineering mathematics. 10th ed., International student version (: electronic bk)
Erwin Kreyszig ; in collaboration with Herbert Kreyszig, Edward J. Norminton
出版情報: Hoboken, N.J. : Wiley, c2011  1 online resource
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4.

図書
図書
4. Advanced engineering mathematics. 10th ed
Erwin Kreyszig ; in collaboration with Herbert Kreyszig, Edward J. Norminton
出版情報: Hoboken, N.J. : Wiley, c2011  xxi, 1113, 109, 30, 1 p. ; 27 cm
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目次情報: 続きを見る
Ordinary Differential Equations (ODEs) / Part A：
First-Order ODEs / Chapter 1：
Basic Concepts. Modeling / 1.1：
Geometric Meaning of y' = f(x, y). Direction Fields / 1.2：
Separable ODEs. Modeling / 1.3：
Exact ODEs. Integrating Factors / 1.4：
Linear ODEs. Bernoulli Equation. Population Dynamics / 1.5：
Orthogonal Trajectories. Optional / 1.6：
Existence and Uniqueness of Solutions / 1.7：
Chapter 1 Review Questions and Problems
Summary of Chapter 1
Second-Order Linear ODEs / Chapter 2：
Homogeneous Linear ODEs of Second Order / 2.1：
Homogeneous Linear ODEs with Constant Coefficients / 2.2：
Differential Operators. Optional / 2.3：
Modeling: Free Oscillations. (Mass-Spring System) / 2.4：
Euler-Cauchy Equations / 2.5：
Existence and Uniqueness of Solutions. Wronskian / 2.6：
Nonhomogeneous ODEs / 2.7：
Modeling: Forced Oscillations. Resonance / 2.8：
Modeling: Electric Circuits / 2.9：
Solution by Variation of Parameters / 2.10：
Chapter 2 Review Questions and Problems
Summary of Chapter 2
Higher Order Linear ODEs / Chapter 3：
Homogeneous Linear ODEs / 3.1：
Nonhomogeneous Linear ODEs / 3.2：
Chapter 3 Review Questions and Problems
Summary of Chapter 3
Systems of ODEs. Phase Plane. Qualitative Methods / Chapter 4：
Basics of Matrices and Vectors / 4.0：
Systems of ODEs as Models / 4.1：
Basic Theory of Systems of ODEs / 4.2：
Constant-Coefficient Systems. Phase Plane Method / 4.3：
Criteria for Critical Points. Stability / 4.4：
Qualitative Methods for Nonlinear Systems / 4.5：
Nonhomogeneous Linear Systems of ODEs / 4.6：
Chapter 4 Review Questions and Problems
Summary of Chapter 4
Series Solutions of ODEs. Special Functions / Chapter 5：
Power Series Method / 5.1：
Legendre's Equation. Legendre Polynomials Pn(x) / 5.2：
Frobenius Method / 5.3：
Bessel's Equation. Bessel Functions Jv(x) / 5.4：
Bessel Functions of the Second Kind Yv(x) / 5.5：
Chapter 5 Review Questions and Problems
Summary of Chapter 5
Laplace Transforms / Chapter 6：
Laplace Transform. Inverse Transform. Linearity. ^-Shifting / 6.1：
Transforms of Derivatives and Integrals. ODEs / 6.2：
Unit Step Function. f-Shifting / 6.3：
Short Impulses. Dirac's Delta Function. Partial Fractions / 6.4：
Convolution. Integral Equations / 6.5：
Differentiation and Integration of Transforms / 6.6：
Systems of ODEs / 6.7：
Laplace Transform: General Formulas / 6.8：
Table of Laplace Transforms / 6.9：
Chapter 6 Review Questions and Problems
Summary of Chapter 6
Linear Algebra. Vector Calculus / Part B：
Linear Algebra: Matrices, Vectors, Determinants. Linear Systems / Chapter 7：
Matrices, Vectors: Addition and Scalar Multiplication / 7.1：
Matrix Multiplication / 7.2：
Linear Systems of Equations. Gauss Elimination / 7.3：
Linear Independence. Rank of a Matrix. Vector Space / 7.4：
Solutions of Linear Systems: Existence, Uniqueness / 7.5：
For Reference: Second- and Third-Order Determinants / 7.6：
Determinants. Cramer's Rule / 7.7：
Inverse of a Matrix. Gauss-Jordan Elimination / 7.8：
Vector Spaces, Inner Product Spaces. Linear Transformations Optional / 7.9：
Chapter 7 Review Questions and Problems
Summary of Chapter 7
Linear Algebra: Matrix Eigenvalue Problems / Chapter 8：
Eigenvalues, Eigenvectors / 8.1：
Some Applications of Eigenvalue Problems / 8.2：
Symmetric, Skew-Symmetric, and Orthogonal Matrices / 8.3：
Eigenbases. Diagonalization. Quadratic Forms / 8.4：
Complex Matrices and Forms. Optional / 8.5：
Chapter 8 Review Questions and Problems
Summary of Chapter 8
Vector Differential Calculus. Grad, Div, Curl / Chapter 9：
Vectors in 2-Space and 3-Space / 9.1：
Inner Product / Dot Product9.2：
Vector Product / Cross Product9.3：
Vector and Scalar Functions and Fields. Derivatives / 9.4：
Curves. Arc Length. Curvature. Torsion / 9.5：
Calculus Review: Functions of Several Variables. Optional / 9.6：
Gradient of a Scalar Field. Directional Derivative / 9.7：
Divergence of a Vector Field / 9.8：
Curl of a Vector Field / 9.9：
Chapter 9 Review Questions and Problems
Summary of Chapter 9
Vector Integral Calculus. Integral Theorems / Chapter 10：
Line Integrals / 10.1：
Path Independence of Line Integrals / 10.2：
Calculus Review: Double Integrals. Optional / 10.3：
Green's Theorem in the Plane / 10.4：
Surfaces for Surface Integrals / 10.5：
Surface Integrals / 10.6：
Triple Integrals. Divergence Theorem of Gauss / 10.7：
Further Applications of the Divergence Theorem / 10.8：
Stokes's Theorem / 10.9：
Chapter 10 Review Questions and Problems
Summary of Chapter 10
Fourier Analysis. Partial Differential Equations (PDEs) / Part C：
Fourier Series, Integrals, and Transforms / Chapter 11：
Fourier Series / 11.1：
Functions of Any Period p = 2L. Even and Odd Functions. Half-Range Expansions / 11.2：
Forced Oscillations / 11.3：
Approximation by Trigonometric Polynomials / 11.4：
Sturm-Liouville Problems. Orthogonal Functions / 11.5：
Orthogonal Eigenfunction Expansions / 11.6：
Fourier Integral / 11.7：
Fourier Cosine and Sine Transforms / 11.8：
Fourier Transform. Discrete and Fast Fourier Transforms / 11.9：
Tables of Transforms / 11.10：
Chapter 11 Review Questions and Problems
Summary of Chapter 11
Partial Differential Equations (PDEs) / Chapter 12：
Basic Concepts / 12.1：
Modeling: Vibrating String, Wave Equation / 12.2：
Solution by Separating Variables. Use of Fourier Series / 12.3：
D'Alembert's Solution of the Wave Equation. Characteristics / 12.4：
Introduction to the Heat Equation / 12.5：
Heat Equation: Solution by Fourier Series / 12.6：
Heat Equation: Solution by Fourier Integrals and Transforms / 12.7：
Modeling: Membrane, Two-Dimensional Wave Equation / 12.8：
Rectangular Membrane. Double Fourier Series / 12.9：
Laplacian in Polar Coordinates. Circular Membrane. Fourier-Bessel Series / 12.10：
Laplace's Equation in Cylindrical and Spherical Coordinates. Potential / 12.11：
Solution of PDEs by Laplace Transforms / 12.12：
Chapter 12 Review Questions and Problems
Summary of Chapter 12
Complex Analysis / Part D：
Complex Numbers and Functions / Chapter 13：
Complex Numbers. Complex Plane / 13.1：
Polar Form of Complex Numbers. Powers and Roots / 13.2：
Derivative. Analytic Function / 13.3：
Cauchy-Riemann Equations. Laplace's Equation / 13.4：
Exponential Function / 13.5：
Trigonometric and Hyperbolic Functions / 13.6：
Logarithm. General Power / 13.7：
Chapter 13 Review Questions and Problems
Summary of Chapter 13
Complex Integration / Chapter 14：
Line Integral in the Complex Plane / 14.1：
Cauchy's Integral Theorem / 14.2：
Cauchy's Integral Formula / 14.3：
Derivatives of Analytic Functions / 14.4：
Chapter 14 Review Questions and Problems
Summary of Chapter 14
Power Series, Taylor Series / Chapter 15：
Sequences, Series, Convergence Tests / 15.1：
Power Series / 15.2：
Functions Given by Power Series / 15.3：
Taylor and Maclaurin Series / 15.4：
Uniform Convergence. Optional / 15.5：
Chapter 15 Review Questions and Problems
Summary of Chapter 15
Laurent Series. Residue Integration / Chapter 16：
Laurent Series / 16.1：
Singularities and Zeros. Infinity / 16.2：
Residue Integration Method / 16.3：
Residue Integration of Real Integrals / 16.4：
Review Questions and Problems
Summary of Chapter 16
Conformal Mapping / Chapter 17：
Geometry of Analytic Functions: Conformal Mapping / 17.1：
Linear Fractional Transformations / 17.2：
Special Linear Fractional Transformations / 17.3：
Conformal Mapping by Other Functions / 17.4：
Riemann Surfaces. Optional / 17.5：
Chapter 17 Review Questions and Problems
Summary of Chapter 17
Complex Analysis and Potential Theory / Chapter 18：
Electrostatic Fields / 18.1：
Use of Conformal Mapping. Modeling / 18.2：
Heat Problems / 18.3：
Fluid Flow / 18.4：
Poisson's Integral Formula for Potentials / 18.5：
General Properties of Harmonic Functions / 18.6：
Chapter 18 Review Questions and Problems
Summary of Chapter 18
Numeric Analysis / Part E：
Software
Numerics in General / Chapter 19：
Introduction / 19.1：
Solution of Equations by Iteration / 19.2：
Interpolation / 19.3：
Spline Interpolation / 19.4：
Numeric Integration and Differentiation / 19.5：
Chapter 19 Review Questions and Problems
Summary of Chapter 19
Numeric Linear Algebra / Chapter 20：
Linear Systems: Gauss Elimination / 20.1：
Linear Systems: LU-Factorization, Matrix Inversion / 20.2：
Linear Systems: Solution by Iteration / 20.3：
Linear Systems: Ill-Conditioning, Norms / 20.4：
Least Squares Method / 20.5：
Matrix Eigenvalue Problems: Introduction / 20.6：
Inclusion of Matrix Eigenvalues / 20.7：
Power Method for Eigenvalues / 20.8：
Tridiagonalization and QR-Factorization / 20.9：
Chapter 20 Review Questions and Problems
Summary of Chapter 20
Numerics for ODEs and PDEs / Chapter 21：
Methods for First-Order ODEs / 21.1：
Multistep Methods / 21.2：
Methods for Systems and Higher Order ODEs / 21.3：
Methods for Elliptic PDEs / 21.4：
Neumann and Mixed Problems. Irregular Boundary / 21.5：
Methods for Parabolic PDEs / 21.6：
Method for Hyperbolic PDEs / 21.7：
Chapter 21 Review Questions and Problems
Summary of Chapter 21
Optimization, Graphs / Part F：
Unconstrained Optimization. Linear Programming / Chapter 22：
Basic Concepts. Unconstrained Optimization / 22.1：
Linear Programming / 22.2：
Simplex Method / 22.3：
Ordinary Differential Equations (ODEs) / Part A：
First-Order ODEs / Chapter 1：
Basic Concepts. Modeling / 1.1：
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