Oxford User's Guide to Mathematics

Contents......Page file5_0011.djvu
Introduction......Page file5_0023.djvu
0.1.1 Mathematical constants......Page file5_0025.djvu
0.1.2 Measuring angles......Page file5_0027.djvu
0.1.3 Area and circumference of plane figures......Page file5_0029.djvu
0.1.4 Volume and surface area of solids......Page file5_0032.djvu
0.1.5 Volumes and surface areas of regular polyhedra......Page file5_0035.djvu
0.1.6 Volume and surface area of n-dimensional balls......Page file5_0037.djvu
0.1.7 Basic formulas for analytic geometry in the plane......Page file5_0038.djvu
0.1.8 Basic formulas of analytic geometry of space......Page file5_0047.djvu
0.1.9 Powers, roots and logarithms......Page file5_0048.djvu
0.1.10 Elementary algebraic formulas......Page file5_0050.djvu
0.1.11 Important inequalities......Page file5_0058.djvu
0.1.12 Application to the motion of the planets......Page file5_0063.djvu
0.2 Elementary functions and graphs......Page file5_0067.djvu
0.2.1 Transformation of functions......Page file5_0069.djvu
0.2.2 Linear functions......Page file5_0070.djvu
0.2.3 Quadratic functions......Page file5_0071.djvu
0.2.5 The Euler e-function......Page file5_0072.djvu
0.2.6 The logarithm......Page file5_0074.djvu
0.2.8 Sine and cosine......Page file5_0075.djvu
0.2.9 Tangent and cotangent......Page file5_0081.djvu
0.2.10 The hyperbolic functions sinh x and cosh x......Page file5_0085.djvu
0.2.11 The hyperbolic functions tanh x and coth x......Page file5_0086.djvu
0.2.12 The inverse trigonometric functions......Page file5_0088.djvu
0.2.13 The inverse hyperbolic functions......Page file5_0090.djvu
0.2.14 Polynomials......Page file5_0092.djvu
0.2.15 Rational functions......Page file5_0093.djvu
0.3 Mathematics and computers - a revolution in mathematics......Page file5_0096.djvu
0.4.1 Empirical data for sequences of measurements (trials)......Page file5_0097.djvu
0.4.2 The theoretical distribution function......Page file5_0099.djvu
0.4.3 Checking for a normal distribution......Page file5_0101.djvu
0.4.5 The statistical comparison of two sequences of measurements......Page file5_0102.djvu
0.4.6 Tables of mathematical statistics......Page file5_0105.djvu
0.5.1 The gamma functions Γ(x) and 1/Γ(x)......Page file5_0120.djvu
0.5.2 Cylinder functions (also known as Bessel functions)......Page file5_0121.djvu
0.5.3 Spherical functions (Legendre polynomials)......Page file5_0125.djvu
0.5.4 Elliptic integrals......Page file5_0126.djvu
0.5.5 Integral trigonometric and exponential functions......Page file5_0128.djvu
0.5.7 The function [Equation Omitted]......Page file5_0130.djvu
0.5.8 Changing from degrees to radians......Page file5_0131.djvu
0.6 Table of prime numbers ≤ 4000......Page file5_0132.djvu
0.7.1 Special series......Page file5_0133.djvu
0.7.2 Power series......Page file5_0136.djvu
0.7.3 Asymptotic series......Page file5_0146.djvu
0.7.4 Fourier series......Page file5_0149.djvu
0.7.5 Infinite products......Page file5_0154.djvu
0.8.1 Differentiation of elementary functions......Page file5_0155.djvu
0.8.2 Rules for differentiation of functions of one variable......Page file5_0157.djvu
0.8.3 Rules for differentiating functions of several variables......Page file5_0158.djvu
0.9.1 Integration of elementary functions......Page file5_0160.djvu
0.9.2 Rules for integration......Page file5_0162.djvu
0.9.3 Integration of rational functions......Page file5_0166.djvu
0.9.4 Important substitutions......Page file5_0167.djvu
0.9.5 Tables of indefinite integrals......Page file5_0171.djvu
0.9.6 Tables of definite integrals......Page file5_0208.djvu
0.10.1 Fourier transformation......Page file5_0214.djvu
0.10.2 Laplace transformation......Page file5_0227.djvu
1. Analysis......Page file5_0243.djvu
1.1.1 Real numbers......Page file5_0244.djvu
1.1.2 Complex numbers......Page file5_0250.djvu
1.1.3 Applications to oscillations......Page file5_0255.djvu
1.1.4 Calculations with equalities......Page file5_0256.djvu
1.1.5 Calculations with inequalities......Page file5_0258.djvu
1.2.1 Basic ideas......Page file5_0260.djvu
1.2.2 The Hilbert axioms for the real numbers......Page file5_0261.djvu
1.2.3 Sequences of real numbers......Page file5_0264.djvu
1.2.4 Criteria for convergence of sequences......Page file5_0267.djvu
1.3.1 Functions of a real variable......Page file5_0271.djvu
1.3.2 Metric spaces and point sets......Page file5_0276.djvu
1.3.3 Functions of several variables......Page file5_0281.djvu
1.4.1 The derivative......Page file5_0284.djvu
1.4.2 The chain rule......Page file5_0286.djvu
1.4.3 Increasing and decreasing functions......Page file5_0287.djvu
1.4.4 Inverse functions......Page file5_0288.djvu
1.4.5 Taylor\'s theorem and the local behavior of functions......Page file5_0290.djvu
1.4.6 Complex valued functions......Page file5_0299.djvu
1.5.1 Partial derivatives......Page file5_0300.djvu
1.5.2 The Fréchet derivative......Page file5_0301.djvu
1.5.3 The chain rule......Page file5_0304.djvu
1.5.4 Applications to the transformation of differential operators......Page file5_0307.djvu
1.5.5 Application to the dependency of functions......Page file5_0309.djvu
1.5.6 The theorem on implicit functions......Page file5_0310.djvu
1.5.7 Inverse mappings......Page file5_0312.djvu
1.5.8 The nth variation and Taylor\'s theorem......Page file5_0314.djvu
1.5.9 Applications to estimation of errors......Page file5_0315.djvu
1.5.10 The Fréchet differential......Page file5_0317.djvu
1.6 Integration of functions of a real variable......Page file5_0328.djvu
1.6.1 Basic ideas......Page file5_0329.djvu
1.6.2 Existence of the integral......Page file5_0332.djvu
1.6.3 The fundamental theorem of calculus......Page file5_0334.djvu
1.6.4 Integration by parts......Page file5_0335.djvu
1.6.5 Substitution......Page file5_0336.djvu
1.6.6 Integration on unbounded intervals......Page file5_0339.djvu
1.6.8 The Cauchy principal value......Page file5_0340.djvu
1.6.9 Application to arc length......Page file5_0341.djvu
1.6.10 A standard argument from physics......Page file5_0342.djvu
1.7.1 Basic ideas......Page file5_0343.djvu
1.7.2 Existence of the integral......Page file5_0351.djvu
1.7.3 Calculations with integrals......Page file5_0354.djvu
1.7.4 The principle of Cavalieri (iterated integration)......Page file5_0355.djvu
1.7.6 The fundamental theorem of calculus (theorem of Gauss-Stokes)......Page file5_0357.djvu
1.7.7 The Riemannian surface measure......Page file5_0363.djvu
1.7.8 Integration by parts......Page file5_0365.djvu
1.7.9 Curvilinear coordinates......Page file5_0366.djvu
1.7.10 Applications to the center of mass and center of inertia......Page file5_0370.djvu
1.7.11 Integrals depending on parameters......Page file5_0372.djvu
1.8.1 Linear combinations of vectors......Page file5_0373.djvu
1.8.2 Coordinate systems......Page file5_0375.djvu
1.8.3 Multiplication of vectors......Page file5_0376.djvu
1.9.1 Velocity and acceleration......Page file5_0379.djvu
1.9.2 Gradient, divergence and curl......Page file5_0381.djvu
1.9.3 Applications to deformations......Page file5_0383.djvu
1.9.4 Calculus with the nabla operator......Page file5_0385.djvu
1.9.5 Work, potential energy and integral curves......Page file5_0388.djvu
1.9.6 Applications to conservation laws in mechanics......Page file5_0390.djvu
1.9.7 Flows, conservation laws and the integral theorem of Gauss......Page file5_0392.djvu
1.9.8 The integral theorem of Stokes......Page file5_0394.djvu
1.9.9 Main theorem of vector analysis......Page file5_0395.djvu
1.9.10 Application to Maxwell\'s equations in electromagnetism......Page file5_0396.djvu
1.10 Infinite series......Page file5_0398.djvu
1.10.1 Criteria for convergence......Page file4.djvu
1.10.2 Calculations with infinite series......Page file4_0003.djvu
1.10.3 Power series......Page file4_0005.djvu
1.10.4 Fourier series......Page file4_0008.djvu
1.10.6 Infinite products:......Page file4_0012.djvu
1.11 Integral transformations......Page file4_0014.djvu
1.11.1 The Laplace transformation......Page file4_0016.djvu
1.11.2 The Fourier transformation......Page file4_0021.djvu
1.11.3 The Z-transformation......Page file4_0026.djvu
1.12.1 Introductory examples......Page file4_0030.djvu
1.12.2 Basic notions......Page file4_0038.djvu
1.12.3 The classification of differential equations......Page file4_0047.djvu
1.12.4 Elementary methods of solution......Page file4_0057.djvu
1.12.5 Applications......Page file4_0073.djvu
1.12.6 Systems of linear differential equations and the propagator......Page file4_0077.djvu
1.12.7 Stability......Page file4_0080.djvu
1.12.8 Boundary value problems and Green\'s functions......Page file4_0082.djvu
1.12.9 General theory......Page file4_0087.djvu
1.13 Partial differential equations......Page file4_0091.djvu
1.13.1 Equations of first order of mathematical physics......Page file4_0092.djvu
1.13.2 Equations of mathematical physics of the second order......Page file4_0119.djvu
1.13.3 The role of characteristics......Page file4_0134.djvu
1.13.4 General principles for uniqueness......Page file4_0144.djvu
1.13.5 General existence results......Page file4_0145.djvu
1.14 Complex function theory......Page file4_0155.djvu
1.14.1 Basic ideas......Page file4_0156.djvu
1.14.2 Sequences of complex numbers......Page file4_0157.djvu
1.14.3 Differentiation......Page file4_0158.djvu
1.14.4 Integration......Page file4_0160.djvu
1.14.5 The language of differential forms......Page file4_0164.djvu
1.14.6 Representations of functions......Page file4_0166.djvu
1.14.7 The calculus of residues and the calculation of integrals......Page file4_0172.djvu
1.14.8 The mapping degree......Page file4_0174.djvu
1.14.9 Applications to the fundamental theorem of algebra......Page file4_0175.djvu
1.14.10 Biholomorphic maps and the Riemann mapping theorem......Page file4_0177.djvu
1.14.11 Examples of conformal maps......Page file4_0178.djvu
1.14.12 Applications to harmonic functions......Page file4_0186.djvu
1.14.13 Applications to hydrodynamics......Page file4_0189.djvu
1.14.14 Applications in electrostatics and magnetostatics......Page file4_0191.djvu
1.14.15 Analytic continuation and the identity principle......Page file4_0192.djvu
1.14.16 Applications to the Euler gamma function......Page file4_0195.djvu
1.14.17 Elliptic functions and elliptic integrals......Page file4_0197.djvu
1.14.18 Modular forms and the inversion problem for the ℘-function......Page file4_0204.djvu
1.14.19 Elliptic integrals......Page file4_0207.djvu
1.14.20 Singular differential equations......Page file4_0215.djvu
1.14.22 Application to the Bessel differential equation......Page file4_0216.djvu
1.14.23 Functions of several complex variables......Page file4_0218.djvu
2.1.1 Combinatorics......Page file4_0222.djvu
2.1.2 Determinants......Page file4_0225.djvu
2.1.3 Matrices......Page file4_0228.djvu
2.1.4 Systems of linear equations......Page file4_0233.djvu
2.1.5 Calculations with polynomials......Page file4_0238.djvu
2.1.6 The fundamental theorem of algebra according to Gauss......Page file4_0241.djvu
2.1.7 Partial fraction decomposition......Page file4_0247.djvu
2.2.1 The spectrum of a matrix......Page file4_0249.djvu
2.2.2 Normal forms for matrices......Page file4_0251.djvu
2.2.3 Matrix functions......Page file4_0258.djvu
2.3.1 Basic ideas......Page file4_0260.djvu
2.3.2 Linear spaces......Page file4_0261.djvu
2.3.3 Linear operators......Page file4_0264.djvu
2.3.4 Calculating with linear spaces......Page file4_0268.djvu
2.3.5 Duality......Page file4_0271.djvu
2.4.1 Algebras......Page file4_0273.djvu
2.4.2 Calculations with multilinear forms......Page file4_0274.djvu
2.4.3 Universal products......Page file4_0280.djvu
2.4.4 Lie algebras......Page file4_0284.djvu
2.4.5 Superalgebras......Page file4_0285.djvu
2.5.1 Groups......Page file4_0286.djvu
2.5.2 Rings......Page file4_0292.djvu
2.5.3 Fields......Page file4_0295.djvu
2.6.2 The main theorem of Galois theory......Page file4_0298.djvu
2.6.3 The generalized fundamental theorem of algebra......Page file4_0301.djvu
2.6.4 Classification of field extensions......Page file4_0302.djvu
2.6.5 The main theorem on equations which can be solved by radicals......Page file4_0303.djvu
2.6.6 Constructions with a ruler and a compass......Page file4_0305.djvu
2.7 Number theory......Page file4_0308.djvu
2.7.1 Basic ideas......Page file4_0309.djvu
2.7.2 The Euclidean algorithm......Page file4_0310.djvu
2.7.3 The distribution of prime numbers......Page file4_0313.djvu
2.7.4 Additive decompositions......Page file4_0319.djvu
2.7.5 The approximation of irrational numbers by rational numbers and continued fractions......Page file4_0322.djvu
2.7.6 Transcendental numbers......Page file4_0328.djvu
2.7.7 Applications to the number π......Page file4_0331.djvu
2.7.8 Gaussian congruences......Page file4_0335.djvu
2.7.9 Minkowski\'s geometry of numbers......Page file4_0338.djvu
2.7.10 The fundamental local-global principle in number theory......Page file4_0339.djvu
2.7.11 Ideals and the theory of divisors......Page file4_0340.djvu
2.7.12 Applications to quadratic number fields......Page file4_0342.djvu
2.7.14 Hilbert\'s class field theory for general number fields......Page file4_0345.djvu
3.1 The basic idea of geometry epitomized by Klein\'s Erlanger Program......Page file4_0348.djvu
3.2.1 Plane trigonometry......Page file4_0349.djvu
3.2.2 Applications to geodesy......Page file4_0356.djvu
3.2.3 Spherical geometry......Page file4_0359.djvu
3.2.4 Applications to sea and air travel......Page file4_0364.djvu
3.2.5 The Hilbert axioms of geometry......Page file4_0365.djvu
3.2.6 The parallel axiom of Euclid......Page file4_0368.djvu
3.2.7 The non-Euclidean elliptic geometry......Page file4_0369.djvu
3.2.8 The non-Euclidean hyperbolic geometry......Page file4_0370.djvu
3.3 Applications of vector algebra in analytic geometry......Page file4_0372.djvu
3.3.1 Lines in the plane......Page file4_0373.djvu
3.3.2 Lines and planes in space......Page file4_0374.djvu
3.3.3 Volumes......Page file4_0375.djvu
3.4.1 The group of Euclidean motions......Page file4_0376.djvu
3.4.2 Conic sections......Page file4_0377.djvu
3.4.3 Quadratic surfaces......Page file4_0378.djvu
3.5.1 Basic ideas......Page file4_0383.djvu
3.5.2 Projective maps......Page file4_0385.djvu
3.5.3 The n-dimensional real projective space......Page file4_0386.djvu
3.5.5 The classification of plane geometries......Page file4_0388.djvu
3.6 Differential geometry......Page file4_0392.djvu
3.6.1 Plane curves......Page file4_0393.djvu
3.6.2 Space curves......Page file4_0398.djvu
3.6.3 The Gaussian local theory of surfaces......Page file4_0401.djvu
3.7.1 Envelopes and caustics......Page file4_0411.djvu
3.7.2 Evolutes......Page file4_0412.djvu
3.7.4 Huygens\' tractrix and the catenary curve......Page file4_0413.djvu
3.7.5 The lemniscate of Jakob Bernoulli and Cassini\'s oval......Page file4_0414.djvu
3.7.7 Spirals......Page file4_0416.djvu
3.7.8 Ray curves (chonchoids)......Page file4_0417.djvu
3.7.9 Wheel curves......Page file4_0419.djvu
3.8.1 Basic ideas......Page file4_0422.djvu
3.8.2 Examples of plane curves......Page file4_0431.djvu
3.8.3 Applications to the calculation of integrals......Page file4_0436.djvu
3.8.4 The projective complex form of a plane algebraic curve......Page file4_0437.djvu
3.8.5 The genus of a curve......Page file4_0441.djvu
3.8.6 Diophantine Geometry......Page file4_0445.djvu
3.8.7 Analytic sets and the Weierstrass preparation theorem......Page file4_0451.djvu
3.8.8 The resolution of singularities......Page file4_0452.djvu
3.8.9 The algebraization of modern algebraic geometry......Page file4_0454.djvu
3.9.1 Basic ideas......Page file4_0460.djvu
3.9.2 Unitary geometry, Hilbert spaces and elementary particles......Page file4_0463.djvu
3.9.3 Pseudo-unitary geometry......Page file4_0470.djvu
3.9.4 Minkowski geometry......Page file4_0473.djvu
3.9.5 Applications to the special theory of relativity......Page file4_0477.djvu
3.9.6 Spin geometry and fermions......Page file4_0483.djvu
3.9.8 Symplectic geometry......Page file4_0492.djvu
4.1.1 True and false statements......Page file4_0496.djvu
4.1.2 Implications......Page file4_0497.djvu
4.1.3 Tautological and logical laws......Page file4_0499.djvu
4.2.2 Induction proofs......Page file5_1.djvu
4.2.4 Proofs of existence......Page file5_0002_1.djvu
4.2.5 The necessity of proofs in the age of computers......Page file5_0004_1.djvu
4.2.6 Incorrect proofs......Page file5_0005_1.djvu
4.3.1 Basic ideas......Page file5_0007_1.djvu
4.3.2 Calculations with sets......Page file5_0009_1.djvu
4.3.3 Maps......Page file5_0012_1.djvu
4.3.4 Cardinality of sets......Page file5_0014_1.djvu
4.3.5 Relations......Page file5_0015_1.djvu
4.4 Mathematical logic......Page file5_0018_1.djvu
4.4.1 Propositional calculus......Page file5_0019_1.djvu
4.4.2 Predicate logic......Page file5_0022_1.djvu
4.4.3 The axioms of set theory......Page file5_0023_1.djvu
4.4.4 Cantor\'s structure at infinity......Page file5_0024_1.djvu
4.5 The history of the axiomatic method......Page file5_0028_1.djvu
5. Calculus of Variations and Optimization......Page file5_0032_1.djvu
5.1.1 The Euler-Lagrange equations......Page file5_0033_1.djvu
5.1.2 Applications......Page file5_0036_1.djvu
5.1.3 Hamilton\'s equations......Page file5_0042_1.djvu
5.1.4 Applications......Page file5_0048_1.djvu
5.1.5 Sufficient conditions for a local minimum......Page file5_0050_1.djvu
5.1.6 Problems with constraints and Lagrange multipliers......Page file5_0053_1.djvu
5.1.7 Applications......Page file5_0054_1.djvu
5.1.8 Natural boundary conditions......Page file5_0057_1.djvu
5.2.1 The Euler-Lagrange equations......Page file5_0058_1.djvu
5.2.2 Applications......Page file5_0059_1.djvu
5.2.3 Problems with constraints and Lagrange multipliers......Page file5_0062_1.djvu
5.3 Control problems......Page file5_0063_1.djvu
5.3.1 Bellman dynamical optimization......Page file5_0064_1.djvu
5.3.2 Applications......Page file5_0065_1.djvu
5.3.3 The Pontryagin maximum principle......Page file5_0066_1.djvu
5.3.4 Applications......Page file5_0067_1.djvu
5.4.1 Local minimization problems......Page file5_0069_1.djvu
5.4.3 Applications to Gauss\' method of least squares......Page file5_0070_1.djvu
5.4.5 Problems with constraints and Lagrange multipliers......Page file5_0071_1.djvu
5.4.6 Applications to entropy......Page file5_0073_1.djvu
5.4.8 Duality theory and saddle points......Page file5_0074_1.djvu
5.5.1 Basic ideas......Page file5_0075_1.djvu
5.5.2 The general linear optimization problem......Page file5_0078_1.djvu
5.5.3 The normal form of an optimization problem and the minimal test......Page file5_0080_1.djvu
5.5.5 The minimal test......Page file5_0081_1.djvu
5.5.6 Obtaining the normal form......Page file5_0084_1.djvu
5.5.7 Duality in linear optimization......Page file5_0085_1.djvu
5.6.1 Capacity utilization......Page file5_0086_1.djvu
5.6.3 Distributing resources or products......Page file5_0087_1.djvu
5.6.4 Design and shift planing......Page file5_0088_1.djvu
5.6.5 Linear transportation problems......Page file5_0089_1.djvu
6. Stochastic Calculus - Mathematics of Chance......Page file5_0098_1.djvu
6.1 Elementary stochastics......Page file5_0099_1.djvu
6.1.1 The classical probability model......Page file5_0100_1.djvu
6.1.2 The law of large numbers due to Jakob Bernoulli......Page file5_0102_1.djvu
6.1.4 The Gaussian normal distribution......Page file5_0103_1.djvu
6.1.5 The correlation coefficient......Page file5_0106_1.djvu
6.1.6 Applications to classical statistical physics......Page file5_0109_1.djvu
6.2 Kolmogorov\'s axiomatic foundation of probability theory......Page file5_0112_1.djvu
6.2.1 Calculations with events and probabilities......Page file5_0115_1.djvu
6.2.2 Random variables......Page file5_0118_1.djvu
6.2.3 Random vectors......Page file5_0124_1.djvu
6.2.4 Limit theorems......Page file5_0128_1.djvu
6.2.5 The Bernoulli model for successive independent trials......Page file5_0130_1.djvu
6.3 Mathematical statistics......Page file5_0138_1.djvu
6.3.1 Basic ideas......Page file5_0139_1.djvu
6.3.2 Important estimators......Page file5_0140_1.djvu
6.3.3 Investigating normally distributed measurements......Page file5_0141_1.djvu
6.3.4 The empirical distribution function......Page file5_0144_1.djvu
6.3.5 The maximal likelihood method......Page file5_0150_1.djvu
6.3.6 Multivariate analysis......Page file5_0152_1.djvu
6.4 Stochastic processes......Page file5_0154_1.djvu
6.4.1 Time series......Page file5_0156_1.djvu
6.4.2 Markov chains and stochastic matrices......Page file5_0162_1.djvu
6.4.3 Poisson processes......Page file5_0164_1.djvu
6.4.4 Brownian motion and diffusion......Page file5_0165_1.djvu
6.4.5 The main theorem of Kolmogorov for general stochastic processes......Page file5_0169_1.djvu
7. Numerical Mathematics and Scientific Computing......Page file5_0172_1.djvu
7.1.1 The notion of algorithm......Page file5_0173_1.djvu
7.1.2 Representing numbers on computers......Page file5_0174_1.djvu
7.1.3 Sources of error, finding errors, condition and stability......Page file5_0175_1.djvu
7.2.1 Linear systems of equations - direct methods......Page file5_0178_1.djvu
7.2.2 Iterative solutions of linear systems of equations......Page file5_0185_1.djvu
7.2.3 Eigenvalue problems......Page file5_0188_1.djvu
7.2.4 Fitting and the method of least squares......Page file5_0192_1.djvu
7.3.1 Interpolation polynomials......Page file5_0198_1.djvu
7.3.2 Numerical differentiation......Page file5_0207_1.djvu
7.3.3 Numerical integration......Page file5_0208_1.djvu
7.4.1 Non-linear equations......Page file5_0216_1.djvu
7.4.2 Non-linear systems of equations......Page file5_0217_1.djvu
7.4.3 Determination of zeros of polynomials......Page file5_0220_1.djvu
7.5.1 Approximation in quadratic means......Page file5_0225_1.djvu
7.5.2 Uniform approximation......Page file5_0229_1.djvu
7.5.3 Approximate uniform approximation......Page file5_0231_1.djvu
7.6.1 Initial value problems......Page file5_0232_1.djvu
7.6.2 Boundary value problems......Page file5_0241_1.djvu
7.7.1 Basic ideas......Page file5_0244_1.djvu
7.7.2 An overview of discretization procedures......Page file5_0245_1.djvu
7.7.3 Elliptic differential equations......Page file5_0250_1.djvu
7.7.4 Parabolic differential equations......Page file5_0261_1.djvu
7.7.5 Hyperbolic differential equations......Page file5_0264_1.djvu
7.7.6 Adaptive discretization procedures......Page file5_0272_1.djvu
7.7.7 Iterative solutions of systems of equations......Page file5_0275_1.djvu
7.7.8 Boundary element methods......Page file5_0286_1.djvu
7.7.9 Harmonic analysis......Page file5_0288_1.djvu
7.7.10 Inverse problems......Page file5_0299_1.djvu
Sketch of the history of mathematics......Page file5_0302_1.djvu
Bibliography......Page file5_0326_1.djvu
List of Names......Page file5_0354_1.djvu
A......Page file5_0358_1.djvu
C......Page file5_0360_1.djvu
D......Page file5_0364_1.djvu
E......Page file5_0366_1.djvu
F......Page file5_0369_1.djvu
G......Page file5_0373_1.djvu
H......Page file5_0374_1.djvu
I......Page file5_0375_1.djvu
L......Page file5_0377_1.djvu
M......Page file5_0379_1.djvu
N......Page file5_0382_1.djvu
P......Page file5_0383_1.djvu
R......Page file5_0387_1.djvu
S......Page file5_0389_1.djvu
T......Page file5_0392_1.djvu
V......Page file5_0396_1.djvu
Z......Page file5_0397_1.djvu
Mathematical symbols......Page file5_0398_1.djvu
Dimensions of physical quantities......Page file5_0402.djvu
Tables of physical constants......Page file5_0404.djvu