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Advanced Engineering Mathematics Mathematica Computer Manual

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ISBN-10: 0471386693

ISBN-13: 9780471386698

Edition: 8th 2002 (Revised)

Authors: Erwin Kreyszig

List price: $48.95
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Book details

List price: $48.95
Edition: 8th
Copyright year: 2002
Publisher: John Wiley & Sons, Incorporated
Publication date: 8/21/2001
Binding: Paperback
Pages: 336
Size: 8.00" wide x 10.00" long x 0.75" tall
Weight: 1.540
Language: English

In books such as Introductory Functional Analysis with Applications and Advanced Engineering Mathematics, Erwin Kreyszig attempts to relate the changing character and content of mathematics to practical problems.

Introduction, General Commands
Ordinary Differential Equations (ODE's)
First-Order ODE's
General Solutions
Direction Fields
Mixing Problems
Integrating Factors
Bernoulli's Equation
Problems for Chapter 1
Linear ODE's of Second and Higher Order
General Solution. Initial Value Problem
Mass-Spring System. Complex Roots. Damped Oscillations
The Three Cases of Damping
The Three Cases for an Euler-Cauchy Equation
Nonhomogeneous Linear ODE's
Solution by Undetermined Coefficients
Solution by Variation of Parameters
Forced Vibrations. Resonance. Beats
Problems for Chapter 2
Systems of Differential Equations. Phase Plane, Qualitative Methods
Solving a System of ODE's by DSolve. Initial Value Problem
Use of Matrices in Solving Systems of ODE's
Critical Points. Node
Proper Node, Saddle Point, Center, Spiral Point
Pendulum Equation
Nonhomogeneous System
Method of Undetermined Coefficients
Problems for Chapter 3
Series Solutions of Differential Equations
Power Series Solutions. Plots from Them. Numerical Values
Legendre Polynomials
Legendre's Differential Equation
Orthogonality. Fourier-Legendre Series
Frobenius Method
Bessel's Equation. Bessel Functions
Problems for Chapter 4
Laplace Transform Method for Solving ODE's
Transforms and Inverse Transforms
Differential Equations
Forced Vibrations. Resonance
Unit Step Function (Heaviside Function), Dirac's Delta
Solution of Systems by Laplace Transform
Formulas on General Properties of the Laplace Transform
Problems for Chapter 5
Linear Algebra, Vector Calculus
Matrices, Vectors, Determinants. Linear Systems of Equations
Matrix Addition, Scalar Multiplication, Matrix Multiplication. Vectors
Special Matrices
Changing and Composing Matrices, Accessing Entries. Submatrices
Solution of a Linear System
Linear Systems: A Further Case
Gauss Elimination; Back Substitution
Problems for Chapter 6
Matrix Eigenvalue Problems
Eigenvalues, Eigenvectors, Accessing Spectrum
Real Matrices with Complex Eigenvalues
Orthogonal Matrices and Transformations
Complex Matrices
Similarity of Matrices. Diagonalization
Problems for Chapter 7
Vectors in R[superscript 2] and R[superscript 3]. Dot and Cross Products. Grad, Div, Curl
Vectors, Addition, Scalar Multiplication
Inner Product. Cross Product
Differentiation of Vectors. Curves and their Properties
Gradient. Directional Derivative. Potential
Divergence, Laplacian, Curl
Problems for Chapter 8
Vector Integral Calculus. Integral Theorems
Line Integrals
Independence of Path
Double Integrals. Moments of Inertia
Green's Theorem in the Plane
Surface Integrals. Flux
Divergence Theorem of Gauss
Stokes's Theorem
Problems for Chapter 9
Fourier Analysis and Partial Differential Equations
Fourier Series, Integrals, and Transforms
Functions of Period 2[pi]. Even Functions. Gibbs Phenomenon
Functions of Arbitrary Period. Odd Functions
Half-Range Expansions
Trigonometric Approximation. Minimum Square Error
Fourier Integral, Fourier Transform
Problems for Chapter 10
Partial Differential Equations (PDE's)
Wave Equation. Separation of Variables. Animation
One-Dimensional Heat Equation
Heat Equation, Laplace Equation
Rectangular Membrane. Double Fourier Series
Laplacian. Circular Membrane. Bessel Equation
Problems for Chapter 11
Complex Analysis
Complex Numbers and Functions. Conformal Mapping
Complex Numbers. Polar Form. Plotting
Equations. Roots. Sets in the Complex Plane
Cauchy-Riemann Equations. Harmonic Functions
Conformal Mapping
Exponential, Trigonometric, and Hyperbolic Functions
Complex Logarithm
Problems for Chapter 12
Complex Integration
Indefinite Integration of Analytic Functions
Integration: Use of Path. Path Dependence
Contour Integration by Cauchy's Integral Theorem and Formula
Problems for Chapter 13
Power Series, Taylor Series
Sequences and their Plots
Convergence Tests for Complex Series
Power Series. Radius of Convergence
Taylor Series
Uniform Convergence
Problems for Chapter 14
Laurent Series. Residue Integration
Laurent Series
Singularities and Zeros
Residue Integration
Real Integrals of Rational Functions of cos and sin
Improper Real Integrals of Rational Functions
Problems for Chapter 15
Complex Analysis in Potential Theory
Complex Potential. Related Plots
Use of Conformal Mapping
Fluid Flow
Series Representation of Potential
Mean Value Theorem for Analytic Functions
Problems for Chapter 16
Numerical Methods
Numerical Methods in General
Loss of Significant Digits. Quadratic Equation
Fixed-Point Iteration
Solving Equations by Newton's Method
Solving Equations by the Secant Method
Solving Equations by the Bisection Method. Module
Polynomial Interpolation
Spline Interpolation
Numerical Integration
Problems for Chapter 17
Numerical Linear Algebra
Gauss Elimination. Pivoting
Doolittle LU-Factorization
Cholesky Factorization
Gauss-Jordan Elimination. Matrix Inversion
Gauss-Seidel Iteration for Linear Systems
Vector and Matrix Norms. Condition Numbers
Fitting Data by Least Squares
Approximation of Eigenvalues: Collatz Method
Approximation of Eigenvalues: Power Method
Approximation of Eigenvalues: QR-Factorization
Problems for Chapter 18
Numerical Methods for Differential Equations
Euler Method
Improved Euler Method
Classical Runge-Kutta Method (RK). Module
Adams-Moulton Multistep Method
Classical Runge-Kutta Method for Systems (RKS)
Classical Runge-Kutta-Nystroem Method (RKN)
Laplace Equation. Boundary Value Problem
Heat Equation. Crank-Nicolson Method
Problems for Chapter 19
Optimization, Graphs
Unconstrained Optimization. Linear Programming
Method of Steepest Descent
Simplex Method of Constrained Optimization
Problems for Chapter 20
No examples, no problems
Probability and Statistics
Data Analysis. Probability Theory
Data Analysis: Mean, Variance, Standard Deviation
Data Analysis: Histograms
Discrete Probability Distributions
Normal Distribution
Problems for Chapter 22
Mathematical Statistics
Random Numbers
Confidence Interval for the Mean of the Normal Distribution With Known Variance
Confidence Interval for the Mean of the Normal Distribution With Unknown Variance. t-Distribution
Confidence Interval for the Variance of the Normal Distribution. x[superscript 2]-Distribution
Test for the Mean of the Normal Distribution
Test for the Mean: Power Function
Test for the Variance of the Normal Distribution
Comparison of Means
Comparison of Variances. F-Distribution
Chi-Square Test for Goodness of Fit
Problems for Chapter 23
Answers to Odd-Numbered Problems