Maple Tutorial
Under the terms of the GNU General Public License GPL
for the Second Coursee. Part V: Orthogonal expansions

Email: Vladimir Dobrushkin | (Monday, September 30, 2019 11:34:18 AM)

 

  2. Moiseev, S., Orthogonal Series Expansions package for Maple, 2009.

Contents

  • Preface
    1. Introduction
      1. 3D plotting
      2. Tubing
      3. Existence and Uniqueness
      4. Picard iterations
      5. Adomian iterations
      6. Euler--Lagrange equations
      7. Lagrange multipliers
      8. Hamilton principle
      9. Converting to a system
    2. Part I: Matrix Algebra
      1. How to define vectors
      2. How to define matrices
      3. Basic operations with matrices
      4. Linear systems of equations
      5. Determinants and inverses
      6. Special matrices
      7. Eigenvalues and Eigenvectors
      8. Diagonalization procedure
      9. Sylvester formula
      10. The resolvent method
      11. Polynomial interpolation
      12. Positive matrices
      13. Roots
      14. Miscellany
    3. Part II: Linear Systems of Ordinary Differential Equations
      1. Variable coefficient systems of ODEs
      2. Floquet theory
      3. Constant coefficient systems of ODEs
      4. Planar Phase Portrait
      5. Euler systems of equations
      6. Fundamental matrices
      7. Reduction to a single equation
      8. Method of undetermined coefficients
      9. Variation of parameters
      10. Laplace transform
      11. Second order ODEs
      12. Spring-mass systems
      13. Electric circuits
      14. Applications
    4. Part III: Non-linear Systems of Ordinary Differential Equations
      1. Planar autonomous systems
      2. Numerical solutions
      3. Stability
      4. Linearization
      5. Spring-mass systems ▾
        1. Anharmonic motion
        2. Forced anharmonic motion
        3. Duffing equations
        4. Forced Duffing equation
        5. Driven hard spring
        6. Driven soft spring
        7. Coulomb damping
        8. Quadratic damping
      6. Conservative systems
      7. Gradient systems
      8. Competing species
      9. Predator-Prey equations
      10. Harvesting species
      11. Lyapunov second method
      12. HIV models
      13. Periodic solutions
      14. Asynchronous solutions
      15. Limited Cycles
      16. van der Pol equations
      17. Neuroscience
      18. Biochemistry
      19. Miscellany
      5. Part III C: Chaos
      1. Lorenz equations
      2. Rössler attractor
      3. Electric circuits
      4. Chua circuits
      5. Pendulum ▾
        1. Phase Portrait
        2. Moving pivot
        3. Numerical simulation
        4. Sprung pendulum
        5. Elastic pendulum
        6. Double pendulum
        7. Escapement
        8. Inverted pendulum
        9. ADM approximation
        10. Fourier series
      6. Mechanical problems
      7. Miscellany
    5. Part IV: Numerical Methods
      1. Iterative methods
      2. Iterations for nonlinear systems
      3. Numerical solutions using NDSolve
      4. System conversion
      5. Power series method
      6. Modified Decomposition Method
      7. Euler's methods
      8. Runge--Kutta methods
      9. Finite Difference Methods
      10. Adomian Decomposition Method
      11. Variational iteration method
      12. Finite Element Method
      13. Second order ODEs
      14. Applications
    6. Part V: Fourier Series
      1. Sturm--Liouville problems
      2. Fourier transform
      3. Fourier series
      4. Periodic extension
      5. Complex Fourier series
      6. Even and odd functions
      7. Examples
      8. Modes of convergence
      9. Gibbs phenomenon
      10. Convergence of Fourier series
      11. Cesàro summation
      12. Square wave functions
      13. Orthogonal expansions
      14. Bessel expansion
      15. Chebyshev expansions
      16. Legendre expansion
      17. Hermite expansion
      18. Laguerre expansion
      19. Motivated examples
    7. Part VI: Partial Differential Equations
      1. First order PDEs
      2. Separation of variables
      3. Green's functions
      4. Blasius equation
      5. Fluid problems
      6. Applications
      7. Miscellany
      8. Part VI P: Parabolic Equations
      1. Heat conduction problems
      2. Boundary Value Problems for heat equation
      3. Other heat transfer problems
      4. Fourier transform
      5. Fokas method
      6. Resolvent method
      7. Fokker--Planck equation
      8. Numerical solutions of heat equation
      9. Black Scholes model
      10. Monte Carlo for Parabolic

      Part VI H: Hyperbolic equations
      1. Wave equations
      2. IBVPs
      3. 2D wave equations
      4. Forced wave equations
      5. Transverse vibrations of beams
      6. Numerical solutions of wave equation
      7. Klein–Gordon equation
      8. 3D wave equations
      9. Cagniard method

      Part VI E: Elliptic equations
      1. Laplace equation
      2. Dirichlet problem
      3. Neumann problems for Laplace equation
      4. Mixed problems for Laplace equation
      5. Laplace equation in infinite stripe
      6. Laplace equation in infinite semi-stripe
      7. Numerical solutions of Laplace equation
      8. Laplace equation in polar coordinates
      9. Laplace equation in a corner
      10. Laplace equation in spherical coordinates
      11. Poisson's equation
      12. Helmholtz equation
      13. Liouville's equation
      14. Monte Carlo for Elliptic
    8. Part VII: Special Functions
      1. Orthogonal polynomials
      2. Gamma function
      3. Bessel functions ▾
        1. Generating functions
        2. Modified Bessel functions
        3. Hunkel functions
        4. Kelvin functions
        5. Recurences
        6. Orthogonality of Bessel functions
        7. Airy functions
        8. Applications
      4. Chebyshev functions ▾
        1. Generating functions
        2. Orthogonality
        3. Recurences
        4. Zeroes
        5. Applications
      5. Legendre functions ▾
        1. Generating functions
        2. Orthogonality
        3. Recurences
        4. Zeroes
        5. Applications
      6. Lambert function
      7. Mathieu function
      8. Elliptic functions
      9. Hypergeometric functions
      10. Kummer's equation
      11. Miscellany

Glossary

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  • • Second course APMA0340
  • • Maple tutorial APMA0330
  • • Main page for APMA0340
  • • Main page for APMA0330