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1.

図書
図書
1. Discrete numerical methods in physics and engineering
Donald Greenspan
出版情報: New York : Academic Press, 1974  xi, 312 p. ; 24 cm
シリーズ名: Mathematics in science and engineering : a series of monographs and textbooks ; v. 107
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2.

図書
図書
2. Advanced engineering mathematics. 8th ed (: hc ; : pbk)
Erwin Kreyszig
出版情報: New York : John Wiley & Sons, c1999  xvi, 1156, 97, 20 p. ; 26-27 cm
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目次情報: 続きを見る
How to Use this Student Solutions Manual and Study Guide
Ordinary Differential Equations (ODEs) / Part A：
First-Order ODEs / Chapter 1：
Second-Order Linear ODEs / Chapter 2：
Ordinary Differential Equations (Ode's)
First-Order ODE's / Chapter 3：
Higher Order Linear ODEs
Second Order Linear ODE's / Chapter 4：
Systems of ODEs. Phase Plane. Qualitative Methods
Higher Order Linear ODE's
Systems of ODE's Phase Plane, Qualitative Methods / Chapter 5：
Series Solutions of ODEs. Special Functions
Series Solutions of ODE's Special Functions / Chapter 6：
Laplace Transforms
Linear Algebra, Vector Calculus / Part B：
Linear Algebra: Matrices, Vectors, Determinants: Linear Systems / Chapter 7：
Matrices, Vectors, Determinants. Linear Systems / Chapter 8：
Linear Algebra: Matrix Eigenvalue Problems
Vector Differential Calculus: Grad, Div, Curl / Chapter 9：
Vector Integral Calculus: Integral Theorems / Chapter 10：
Vector Differential Calculus. Grad, Div, Curl / Part C：
Fourier Analysis, Partial Differential Equations
Fourier Series, Integrals, and Transforms / Chapter 11：
Vector Integral Calculus. Integral Theorems
Partial Differential Equations (PDE 's) / Chapter 12：
Fourier Analysis. Partial Differential Equations / Chapter 13：
Complex Numbers and Functions
Complex Integration / Chapter 14：
Power Series, Taylor Series / Chapter 15：
Partial Differential Equations (PDEs) / Chapter 16：
Laurent Series: Residue Integration
Conformal Mapping / Part D：
Complex Analysis
Complex Analysis and Potential Theory / Chapter 18：
Numerical Analysis Software / Part E：
Numerics in General / Chapter 19：
Numerical Linear Algebra / Chapter 20：
Numerics for ODE 's and PDE 's / Chapter 21：
Optimization, Graphs / Part F：
Laurent Series. Residue Integration
Unconstrained Optimization: Linear Programming / Chapter 22：
Graphs, Combinatorial Optimization / Chapter 23：
Probability / Part G：
Statistics
Data Analysis / Chapter 24：
Numeric Analysis
Probability Theory
Mathematical Statistics / Chapter 25：
References / Appendix 1：
Numeric Linear Algebra / Appendix 2：
Answers to Odd-Numbered Problems
Auxiliary Material / Appendix 3：
Numerics for ODEs and PDEs
Additional Proofs / Appendix 4：
Tables / Appendix 5：
Index
Unconstrained Optimization. Linear Programming
Graphs and Combinatorial Optimization
Probability, Statistics
Data Analysis. Probability Theory
Photo Credits
How to Use this Student Solutions Manual and Study Guide
Ordinary Differential Equations (ODEs) / Part A：
First-Order ODEs / Chapter 1：
3.

図書
図書
3. Integral methods in science and engineering (v. 1 ; v. 2)
C. Constanda, J. Saranen and S. Seikkala (editors)
出版情報: Harlow, Essex : Longman, 1997  2 v. ; 25 cm
シリーズ名: Pitman research notes in mathematics series ; 374-375
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4.

図書
図書
4. Multigrid methods for finite elements
V.V. Shaidurov
出版情報: Dordrecht ; Boston : Kluwer Academic Publishers, c1995  xiv, 331 p. ; 25 cm
シリーズ名: Mathematics and its applications ; v. 318
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5.

図書
図書
5. Advanced engineering mathematics. 2nd ed
Erwin Kreyszig
出版情報: New York : John Wiley & Sons, 1967  xvii, 898 p. ; 24 cm
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6.

図書
図書
6. Topics in physical geometry
Robert Hermann
出版情報: Brookline, Mass. : Math Sci Press, c1988  xv, 595 p. ; 24 cm
シリーズ名: Interdisciplinary mathematics ; v. 24
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7.

図書
図書
7. Mathematical methods in engineering and physics
David E. Johnson, Johnny R. Johnson
出版情報: Englewood Cliffs, NJ : Prentice-Hall, c1982  x, 273 p. ; 24 cm
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8.

図書
図書
8. Advanced engineering mathematics. 9th ed (: [pbk.])
Erwin Kreyszig
出版情報: Hoboken, NJ : John Wiley, c2006  1 v. (various pagings) ; 26 cm
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目次情報: 続きを見る
Ordinary Differential Equations (Ode's) / Part A：
First-Order ODE's / Chapter 1：
Second Order Linear ODE's / Chapter 2：
Higher Order Linear ODE's / Chapter 3：
Systems of ODE's Phase Plane, Qualitative Methods / Chapter 4：
Series Solutions of ODE's Special Functions / Chapter 5：
Laplace Transforms / Chapter 6：
Linear Algebra, Vector Calculus / Part B：
Linear Algebra: Matrices, Vectors, Determinants: Linear Systems / Chapter 7：
Linear Algebra: Matrix Eigenvalue Problems / Chapter 8：
Vector Differential Calculus: Grad, Div, Curl / Chapter 9：
Vector Integral Calculus: Integral Theorems / Chapter 10：
Fourier Analysis, Partial Differential Equations / Part C：
Fourier Series, Integrals, and Transforms / Chapter 11：
Partial Differential Equations (PDE 's) / Chapter 12：
Complex Numbers and Functions / Chapter 13：
Complex Integration / Chapter 14：
Power Series, Taylor Series / Chapter 15：
Laurent Series: Residue Integration / Chapter 16：
Conformal Mapping / Chapter 17：
Complex Analysis and Potential Theory / Chapter 18：
Numerical Analysis Software / Part E：
Numerics in General / Chapter 19：
Numerical Linear Algebra / Chapter 20：
Numerics for ODE 's and PDE 's / Chapter 21：
Optimization, Graphs / Part F：
Unconstrained Optimization: Linear Programming / Chapter 22：
Graphs, Combinatorial Optimization / Chapter 23：
Probability / Part G：
Statistics
Data Analysis / Chapter 24：
Probability Theory
Mathematical Statistics / Chapter 25：
References / Appendix 1：
Answers to Odd-Numbered Problems / Appendix 2：
Auxiliary Material / Appendix 3：
Additional Proofs / Appendix 4：
Tables / Appendix 5：
Index
Ordinary Differential Equations (ODEs)
First-Order ODEs
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
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
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
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
Power Series Method / 5.1：
Theory of the Power Series Method / 5.2：
Legendre's Equation. Legendre Polynomials P[subscript n](x) / 5.3：
Frobenius Method / 5.4：
Bessel's Equation. Bessel Functions J[subscript v](x) / 5.5：
Bessel Functions of the Second Kind Y[subscript v](x) / 5.6：
Sturm-Liouville Problems. Orthogonal Functions / 5.7：
Orthogonal Eigenfunction Expansions / 5.8：
Chapter 5 Review Questions and Problems
Summary of Chapter 5
Laplace Transform. Inverse Transform. Linearity. s-Shifting / 6.1：
Transforms of Derivatives and Integrals. ODEs / 6.2：
Unit Step Function. t-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
Linear Algebra: Matrices, Vectors, Determinants, Linear Systems
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
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
Vectors in 2-Space and 3-Space / 9.1：
Inner Product (Dot Product) / 9.2：
Vector Product (Cross Product) / 9.3：
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
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)
Fourier Series / 11.1：
Functions of Any Period p = 2L / 11.2：
Even and Odd Functions. Half-Range Expansions / 11.3：
Complex Fourier Series. Optional / 11.4：
Forced Oscillations / 11.5：
Approximation by Trigonometric Polynomials / 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)
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：
Heat Equation: Solution by Fourier Series / 12.5：
Heat Equation: Solution by Fourier Integrals and Transforms / 12.6：
Modeling: Membrane, Two-Dimensional Wave Equation / 12.7：
Rectangular Membrane. Double Fourier Series / 12.8：
Laplacian in Polar Coordinates. Circular Membrane. Fourier-Bessel Series / 12.9：
Laplace's Equation in Cylindrical and Spherical Coordinates. Potential / 12.10：
Solution of PDEs by Laplace Transforms / 12.11：
Chapter 12 Review Questions and Problems
Summary of Chapter 12
Complex Analysis / Part D：
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
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
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
Laurent Series / 16.1：
Singularities and Zeros. Infinity / 16.2：
Residue Integration Method / 16.3：
Residue Integration of Real Integrals / 16.4：
Chapter 16 Review Questions and Problems
Summary of Chapter 16
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
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
Software
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
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
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
Unconstrained Optimization. Linear Programming
Basic Concepts. Unconstrained Optimization / 22.1：
Linear Programming / 22.2：
Simplex Method / 22.3：
Simplex Method: Difficulties / 22.4：
Chapter 22 Review Questions and Problems
Summary of Chapter 22
Graphs. Combinatorial Optimization
Graphs and Digraphs / 23.1：
Shortest Path Problems. Complexity / 23.2：
Bellman's Principle. Dijkstra's Algorithm / 23.3：
Shortest Spanning Trees: Greedy Algorithm / 23.4：
Shortest Spanning Trees: Prim's Algorithm / 23.5：
Flows in Networks / 23.6：
Maximum Flow: Ford-Fulkerson Algorithm / 23.7：
Bipartite Graphs. Assignment Problems / 23.8：
Chapter 23 Review Questions and Problems
Summary of Chapter 23
Probability, Statistics
Data Analysis. Probability Theory
Data Representation. Average. Spread / 24.1：
Experiments, Outcomes, Events / 24.2：
Permutations and Combinations / 24.3：
Random Variables. Probability Distributions / 24.5：
Mean and Variance of a Distribution / 24.6：
Binomial, Poisson, and Hypergeometric Distributions / 24.7：
Normal Distribution / 24.8：
Distributions of Several Random Variables / 24.9：
Chapter 24 Review Questions and Problems
Summary of Chapter 24
Introduction. Random Sampling / 25.1：
Point Estimation of Parameters / 25.2：
Confidence Intervals / 25.3：
Testing Hypotheses. Decisions / 25.4：
Quality Control / 25.5：
Acceptance Sampling / 25.6：
Goodness of Fit. x[superscript 2]-Test / 25.7：
Nonparametric Tests / 25.8：
Regression. Fitting Straight Lines. Correlation / 25.9：
Chapter 25 Review Questions and Problems
Summary of Chapter 25
Formulas for Special Functions / A3.1：
Partial Derivatives / A3.2：
Sequences and Series / A3.3：
Grad, Div, Curl, [down triangle, open] [superscript 2] in Curvilinear Coordinates / A3.4：
Photo Credits
Ordinary Differential Equations (Ode's) / Part A：
First-Order ODE's / Chapter 1：
Second Order Linear ODE's / Chapter 2：
9.

図書
図書
9. Mathematical methods for physics and engineering. 3rd ed (: hbk ; : pbk)
K.F. Riley, M.P. Hobson and S.J. Bence
出版情報: Cambridge : Cambridge University Press, c2006  xxvii, 1333 p. ; 25 cm
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目次情報: 続きを見る
Preliminary algebra / 1：
Preliminary calculus / 2：
Complex numbers and hyperbolic functions / 3：
Series and limits / 4：
Partial differentiation / 5：
Multiple integrals / 6：
Vector algebra / 7：
Matrices and vector spaces / 8：
Normal modes 10. Vector calculus / 9：
Line, surface and volume integrals / 11：
Fourier series / 12：
Integral transforms / 13：
First-order ordinary differential equations / 14：
Higher ordinary differential equations / 15：
Series solutions of ordinary differential equations / 16：
Eigenfunction methods for differential equations / 17：
Partial differential equations: general and particular / 18：
Partial differential equations: separation of variables and other methods / 19：
Complex variables / 20：
Tensors / 21：
Calculus of variations / 22：
Integral equations / 23：
Group theory / 24：
Representation theory / 25：
Probability / 26：
Statistics / 27：
Numerical methods / 28：
Appendix
Index
Preliminary algebra / 1：
Preliminary calculus / 2：
Complex numbers and hyperbolic functions / 3：
10.

図書
図書
10. Mathematics of physics and modern engineering. 2nd ed. International student ed
I.S. Sokolnikoff, R.M. Redheffer
出版情報: Singapore ; Tokyo : McGraw-Hill International Book Co., 1966  xi, 752 p. ; 25 cm
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