[PDF] Advanced Engineering Mathematics - Erwin Kreyszig - 3rd Edition

Advanced Engineering Mathematics – Erwin Kreyszig – 3rd Edition

Descripción

Este libro pretende introducir a los estudiantes de ingeniería y física en aquellas áreas de las matemáticas que, desde un punto de vista moderno, parecen ser las más importantes en relación con los problemas prácticos. Los temas se eligen de acuerdo con la frecuencia de aparición en las aplicaciones. Se tomaron en cuenta las nuevas ideas de la formación matemática moderna, expresadas en simposios recientes sobre educación en ingeniería.

Advanced Engineering Mathematics, puede adaptarse a aquellas instituciones que han ofrecido una formación matemática extendida durante mucho tiempo, así como a aquellas que pretenden seguir la tendencia general de ampliar el programa de instrucción en matemáticas.

Este texto de matemáticas de ingeniería, ha sido el líder en el mercado desde sus inicios por su cobertura integral, matemáticas cuidadosas y correctas, ejercicios sobresalientes y partes temáticas independientes para una máxima flexibilidad.

Esta edición clásica, la tercera edición, expone la tradición que brindó a los instructores y estudiantes un recurso integral y para la enseñanza y el aprendizaje de las matemáticas de ingeniería, es decir, matemáticas aplicadas para ingenieros y físicos, matemáticos e informáticos, así como para miembros de otras disciplinas.

Ver más
  • Chapter 1: Ordinary Differential Equations of the First Order

    1.1 Basic Concepts and Ideas
    1.2 Geometrical Considerations. Isoclines
    1.3 Separable Equations
    1.4 Equations Reducible to Separable Form
    1.5 Exact Differential Equations
    1.6 Integrating Factors
    1.7 Linear First-Order Differential Equations
    1.8 Variation of Parameters
    1.9 Electric Circuits
    1.10 Families of Curves. Orthogonal Trajectories
    1.11 Picard's Iteration Method
    1.12 Existence and Uniqueness of Solutions

    Chapter 2: Ordinary Linear Differential Equations

    2.1 Homogeneous Linear Equations of the Second Order
    2.2 Homogeneous Second-Order Equations with Constant Coefficients
    2.3 General Solution. Fundamental System
    2.4 Complex Roots of the Characteristic Equation. Initial Value Problem
    2.5 Double Root of the Characteristic Equation
    2.6 Free Oscillations
    2.7 Cauchy Equation
    2.8 Existence and Uniqueness of Solutions
    2.9 Homogeneous Linear Equations of Arbitrary Order
    2.10 Homogeneous Linear Equations of Arbitrary Order with Constant Coefficients
    2.11 Nonhomogeneous Linear Equations
    2.12 A Method for Solving Nonhomogeneous Linear Equations
    2.13 Forced Oscillations. Resonance
    2.14 Electric Circuits
    2.15 Complex Method for Obtaining Particular Solutions
    2.16 General Method for Solving Nonhomogeneous Equations

    Chapter 3: Power Series Solutions of Differential Equations

    3.1 The Power Series Method
    3.2 Theoretical Basis of the Power Series Method
    3.3 Legendre's Equation. Legendre Polynomials
    3.4 Extended Power Series Method. Indicial Equation
    3.5 Bessel's Equation. Bessel Functions of the First Kind
    3.6 Bessel Functions of the Second Kind
    3.7 Orthogonal Sets of Functions
    3.8 Sturm-Liouville Problem
    3.9 Orthogonality of Legendre Polynomials and Bessel Functions

    Chapter 4: Laplace Transformation

    4.1 Laplace Transform. Inverse Transform. Linearity
    4.2 Laplace Transforms of Derivatives and Integrals
    4.3 Transformation of Ordinary Differential Equations
    4.4 Partial Fractions
    4.5 Examples and Applications
    4.6 Differentiation and Integration of Transforms
    4.7 Unit Step Function
    4.8 Shifting on the r-axis
    4.9 Periodic Functions
    4.10 Table of Some Laplace Transforms

    Chapter 5: Linear Algebra Part I: Vectors

    5.1 Scalars and Vectors
    5.2 Components of a Vector
    5.3 Addition of VectorsMultiplication by Scalars
    5.4 Vector Spaces. Linear Dependence and Independence
    5.5 Inner Product (Dot Product)
    5.6 Inner Product Spaces
    5.7 Vector Product (Cross Product)
    5.8 Vector Products in Terms of Components
    5.9 Scalar Triple Product. Other Repeated Products

    Chapter 6: Linear Algebra Part II: Matrices and Determinants

    6.1 Basic Concepts
    6.2 Addition of MatricesMultiplication by Numbers
    6.3 Transpose of a Matrix. Special Matrices
    6.4 Matrix Multiplication
    6.5 Systems of Linear Equations. Gauss Elimination
    6.6 Determinants of Second and Third Order
    6.7 Determinants of Arbitrary Order
    6.8 Rank of a Matrix. Row Equivalence
    6.9 Systems of Linear Equations: Existence and General Properties of Solutions
    6.10 Linear Dependence and Rank. Singular Matrices
    6.11 Systems of Linear Equations: Solution by Determinants
    6.12 The Inverse of a Matrix
    6.13 BilinearQuadraticHermitianand Skew-Hermitian Forms
    6.14 EigenvaluesEigenvectors
    6.15 Eigenvalues of HermitianSkew-Hermitianand Unitary Matrices

    Chapter 7: Vector Differential Calculus. Vector Fields

    7.1 Scalar Fields and Vector Fields
    7.2 Vector Calculus
    7.3 Curves
    7.4 Arc Length
    7.5 Tangent. Curvature and Torsion
    7.6 Velocity and Acceleration
    7.7 Chain Rule and Mean Value Theorem for Functions of Several Variables
    7.8 Directional Derivative. Gradient of a Scalar Field
    7.9 Transformation of Coordinate Systems and Vector Components
    7.10 Divergence of a Vector Field
    7.11 Curl of a Vector Field

    Chapter 8: Line and Surface Integrals. Integral Theorems

    8.1 Line Integral
    8.2 Evaluation of Line Integrals
    8.3 Double Integrals
    8.4 Transformation of Double Integrals into Line Integrals,
    8.5 Surfaces
    8.6 Tangent Plane. First Fundamental Form. Area
    8.7 Surface Integrals
    8.8 Triple Integrals. Divergence Theorem of Gauss
    8.9 Consequences and Applications of the Divergence Theorem
    8.10 Stokes's Theorem
    8.11 Consequences and Applications of Stolces's Theorem
    8.12 Line Integrals Independent of Path

    Chapter 9: Fourier Series and Integrals

    9.1 Periodic Functions. Trigonometric Series
    9.2 Fourier Series. Euler Formulas
    9.3 Functions Having Arbitrary Period
    9.4 Even and Odd Functions
    9.5 Half-Range Expansions
    9.6 Determination of Fourier Coefficients Without Integration
    9.7 Forced Oscillations
    9.8 Approximation by Trigonometric Polynomials. Square Error
    9.9 The Fourier Integral

    Chapter 10: Partial Differential Equations

    10.1 Basic Concepts
    10.2 Vibrating String. One-Dimensional Wave Equation
    10.3 Separation of Variables (Product Method)
    10.4 D'AIembert's Solution of the Wave Equation
    10.5 One-Dimensional Heat Flow
    10.6 Heat Flow in an Infinite Bar
    10.7 Vibrating Membrane. Two-Dimensional Wave Equation
    10.8 Rectangular Membrane
    10.9 Laplacian in Polar Coordinates
    10.10 Circular Membrane. Bessel's Equation
    10.11 Laplace's Equation. Potential
    10.12 Laplace's Equation in Spherical Coordinates. Legendre's Equation

    Chapter 11: Complex Analytic Functions

    11.1 Complex Numbers. Triangle Inequality
    11.2 Limit. Derivative. Analytic Function
    11.3 Cauchy-Riemann Equations. Laplace's Equation,
    11.4 Rational Functions. Root
    11.5 Exponential Function
    11.6 Trigonometric and Hyperbolic Functions
    11.7 Logarithm. General Power

    Chapter 12: Conformal Mapping

    12.1 Mapping
    12.2 Conformal Mapping
    12.3 Linear Fractional Transformations
    12.4 Special Linear Fractional Transformations
    12.5 Mapping by Other Elementary Functions
    12.6 Riemann Surfaces

    Chapter 13: Complex Integrals

    13.1 Line Integral in the Complex Plane
    13.2 Basic Properties of the Complex Line Integral
    13.3 Cauchy's Integral Theorem
    13.4 Evaluation of Line Integrals by Indefinite Integration
    13.5 Cauchy's Integral Formula
    13.6 The Derivatives of an Analytic Function

    Chapter 14: Sequences and Series

    14.1 Sequences
    14.2 Series
    14.3 Tests for Convergence and Divergence of Series
    14.4 Operations on Series
    14.5 Power Series
    14.6 Functions Represented by Power Series

    Chapter 15: Taylor and Laurent Series

    15.1 Taylor Series
    15.2 Taylor Series of Elementary Functions
    15.3 Practical Methods for Obtaining Power Series
    15.4 Uniform Convergence
    15.5 Laurent Series
    15.6 Behavior of Functions at Infinity,

    Chapter 16: Integration by the Method of Residues

    16.1 Zeros and Singularities
    16.2 Residues
    16.3 The Residue Theorem
    16.4 Evaluation of Real Integrals

    Chapter 17: Complex Analytic Functions and Potential Theory

    17.1 Electrostatic Fields
    17.2 Two-Dimensional Fluid Flow
    17.3 General Properties of Harmonic Functions
    17.4 Poisson's Integral Formula

    Chapter 18: Numerical Analysis

    18.1 Errors and Mistakes. Automatic Computers
    18.2 Solution of Equations by Iteration
    18.3 Finite Differences
    18.4 Interpolation
    18.5 Numerical Integration and Differentiation. 653
    18.6 Numerical Methods for First-Order Differential Equations
    18.7 Numerical Methods for Second-Order Differential Equations
    18.8 Systems of Linear Equations. Gauss Elimination
    18.9 Systems of Linear Equations. Solution by Iteration
    18.10 Systems of Linear Equations. Ill-conditioning
    18.11 Method of Least Squares
    18.12 Inclusion of Matrix Eigenvalues
    18.13 Determination of Eigenvalues by Iteration
    18.14 Asymptotic Expansions

    Chapter 19: Probability and Statistics

    19.1 Nature and Purpose of Mathematical Statistics
    19.2 Tabular and Graphical Representation of Samples
    19.3 Sample Mean and Sample Variance
    19.4 Random ExperimentsOutcomesEvents
    19.5 Probability
    19.6 Permutations and Combinations
    19.7 Random Variables. Discrete and Continuous Distributions
    19.8 Mean and Variance of a Distribution.
    19.9 Binomial. Poissonand Hypergeometric Distributions
    19.10 Normal Distribution
    19.11 Distributions of Several Random Variables
    19.12 Random Sampling. Random Numbers
    19.13 Estimation of Parameters
    19.14 Confidence Intervals
    19.15 Testing of HypothesesDecisions
    19.16 Quality Control
    19.17 Acceptance Sampling
    19.18 Goodness of Fit. ;(;2-Test
    19.19 Nonparametric Tests
    19.20 Pairs of Measurements. Fitting Straight Lines

    Appendix 1 References
    Appendix 2 Answers to Odd-Numbered Problems
    Appendix 3 Some Formulas for Special Functions
    Appendix 4 Tables
    Index
  • Citar Libro
    • Título: Advanced Engineering Mathematics
    • Autor/es:
    • ISBN-10: 0471507296
    • ISBN-13: 9780471507291
    • Edición: 3ra Edición
    • Año de edición: 1972
    • Tema: Matemáticas
    • Subtema: Matemáticas Avanzadas
    • Tipo de Archivo: eBook
    • Idioma: eBook en Inglés

Descargar Advanced Engineering Mathematics

Tipo de Archivo
Idioma
Descargar RAR
Descargar PDF
Páginas
Tamaño
Libro
Inglés
892 pag.
61 mb

Déjanos un comentario

No hay comentarios

guest
0 Comentarios
Comentarios en línea
Ver todos los comentarios
0
Nos encantaría conocer tu opinión, comenta.x