Advanced Engineering Mathematics 1st edition by Larry Turyn ISBN 9781439834480 1439834482

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Product details:

ISBN 10: 1439834482
ISBN 13: 9781439834480
Author:  Larry Turyn 

Table of contents:

1. Linear Algebra Equations, Matrices, and Eigenvalues

   1. Systems and Row Echelon Forms
   2. Matrix Addition, Multiplication, and Transpose
   3. Homogeneous Systems, Spanning Set, and Basic Solutions
   4. Solutions of Nonhomogeneous Systems
   5. Inverse Matrix
   6. Determinant, Adjugate Matrix, and Cramer’s Rule
   7. Linear Independence, Basis and Dimension

2. Matrix Theory

   1. Eigenvalues and Eigenvectors
   2. Basis of Eigenvectors and Diagonalization
   3. Inner Product and Orthogonal Sets of Vectors
   4. Orthonormal Bases and Orthogonal Matrices
   5. Least Squares Solutions
   6. Symmetric Matrices, Definite Matrices, and Applications
   7. Factorizations: QR and SVD
   8. Factorizations: LU and Cholesky
   9. Rayleigh Quotient
   10. Short Take: Inner Product and Hilbert Spaces

3. Scalar ODEs I: Homogeneous Problems

   1. Linear First-Order ODEs
   2. Separable and Exact ODEs
   3. Second-Order Linear Homogeneous ODEs
   4. Higher-Order Linear ODEs
   5. Cauchy–Euler ODEs

4. Scalar ODEs II: Nonhomogeneous Problems

   1. Nonhomogeneous ODEs
   2. Forced Oscillations
   3. Variation of Parameters
   4. Laplace Transforms: Basic Techniques
   5. Laplace Transforms: Unit Step and Other Techniques
   6. Scalar Difference Equations
   7. Short Take: z-Transforms

5. Linear Systems of ODEs

   1. Systems of ODEs
   2. Solving Linear Homogeneous Systems of ODEs
   3. Complex or Deficient Eigenvalues
   4. Nonhomogeneous Linear Systems
   5. Nonresonant Nonhomogeneous Systems
   6. Linear Control Theory: Complete Controllability
   7. Linear Systems of Difference Equations
   8. Short Take: Periodic Linear Differential Equations

6. Geometry, Calculus, and Other Tools

   1. Dot Product, Cross Product, Lines, and Planes
   2. Trigonometry, Polar, Cylindrical, and Spherical Coordinates
   3. Curves and Surfaces
   4. Partial Derivatives
   5. Tangent Plane and Normal Vector
   6. Area, Volume, and Linear Transformations
   7. Differential Operators and Curvilinear Coordinates
   8. Rotating Coordinate Frames

7. Integral Theorems, Multiple Integrals, and Applications

   1. Integrals for a Function of a Single Variable
   2. Line Integrals
   3. Double Integrals, Green’s Theorem, and Applications
   4. Triple Integrals and Applications
   5. Surface Integrals and Applications
   6. Integral Theorems: Divergence, Stokes, and Applications
   7. Probability Distributions

8. Numerical Methods I

   1. Solving a Scalar Equation
   2. Solving a System of Equations
   3. Approximation of Integrals
   4. Numerical Solution of Ax = b
   5. Linear Algebraic Eigenvalue Problems
   6. Approximations of Derivatives
   7. Approximate Solutions of ODE-IVPs
   8. Approximate Solutions of Two Point BVPs
   9. Splines

9. Fourier Series

   1. Orthogonality and Fourier Coefficients
   2. Fourier Cosine and Sine Series
   3. Generalized Fourier Series
   4. Complex Fourier Series and Fourier Transform
   5. Discrete Fourier and Fast Fourier Transforms
   6. Sturm–Liouville Problems
   7. Rayleigh Quotient
   8. Parseval’s Theorems and Applications

10. Partial Differential Equations Models

    1. Integral and Partial Differential Equations
    2. Heat Equations
    3. Potential Equations
    4. Wave Equations
    5. D’Alembert Wave Solutions
    6. Short Take: Conservation of Energy in a Finite String

11. Separation of Variables for PDEs

    1. Heat Equation in One Space Dimension
    2. Wave Equation in One Space Dimension
    3. Laplace Equation in a Rectangle
    4. Eigenvalues of the Laplacian and Applications
    5. PDEs in Polar Coordinates
    6. PDEs in Cylindrical and Spherical Coordinates

12. Numerical Methods II

    1. Finite Difference Methods for Heat Equations
    2. Numerical Stability
    3. Finite Difference Methods for Potential Equations
    4. Finite Difference Methods for the Wave Equation
    5. Short Take: Galerkin Method

13. Optimization

    1. Functions of a Single Variable
    2. Functions of Several Variables
    3. Linear Programming Problems
    4. Simplex Procedure
    5. Nonlinear Programming
    6. Rayleigh–Ritz Method

14. Calculus of Variations

    1. Minimization Problems
    2. Necessary Conditions
    3. Problems with Constraints
    4. Eigenvalue Problems
    5. Short Take: Finite Element Methods

15. Functions of a Complex Variable

    1. Complex Numbers, Roots, and Functions
    2. Analyticity, Harmonic Function, and Harmonic Conjugate
    3. Elementary Functions
    4. Trigonometric Functions
    5. Taylor and Laurent Series
    6. Zeros and Poles
    7. Complex Integration and Cauchy’s Integral Theorem
    8. Cauchy’s Integral Formulas and Residues
    9. Real Integrals by Complex Integration Methods

16. Conformal Mapping

    1. Conformal Mappings and the Laplace Equation
    2. Möbius Transformations
    3. Solving Laplace’s Equation Using Conformal Maps

17. Integral Transform Methods

    1. Applications to Partial Differential Equations
    2. Inverse Laplace Transform
    3. Hankel Transforms

18. Nonlinear Ordinary Differential Equations

    1. Phase Line and Phase Plane
    2. Stability of an Equilibrium Point
    3. Variation of Parameters Using Linearization
    4. Liapunov Functions
    5. Short Take: LaSalle Invariance Principle
    6. Limit Cycles
    7. Existence, Uniqueness, and Continuous Dependence
    8. Short Take: Horseshoe Map and Chaos
    9. Short Take: Delay Equations

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