MATLAB ®

Tutorial II:

Under the terms of the GNU General Public License GPL
  the Second Course in Differential Equations, Part 2.5: Fourier transform

Email: Prof. Vladimir Dobrushkin. (Friday, September 20, 2019 11:03:36 AM)

  • Return to
    • Applied Mathematics - I
    • Applied Mathematics - II
    • Computing information for the first course APMA0330
    • Computing information for the second course APMA0340
    • Matlab tutorial page for the first course
    • Introduction to Linear Algebra with matlab
    • Glossary
  • Preface
  • Introduction +
    1. Chebop
    2. 3D plotting
    3. Tubing
    4. Existence and Uniqueness
    5. Picard iterations
    6. Adomian iterations
    7. Euler--Lagrange equations
    8. Lagrange multipliers
    9. Hamilton principle
    10. Converting to a system
    11. Scaling
    12. Probability
  • 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
  • Part II: Linear Systems of Ordinary Differential Equations +
    1. Motivation
    2. Variable coefficient systems of ODEs
    3. Floquet theory
    4. Constant coefficient systems of ODEs
    5. Planar Phase Portrait
    6. Euler systems of equations
    7. Fundamental matrices
    8. Reduction to a single equation
    9. Method of undetermined Coefficients
    10. Variation of parameters
    11. Laplace transform
    12. Stiff ODEs
    13. Second order ODEs
    14. Spring-mass systems
    15. Electric circuits
    16. Applications
  • Part III: Non-linear Systems of Ordinary Differential Equations +
    1. Numerical solutions
    2. Stability
    3. Linearization
    4. Planar autonomous systems
    5. Conservative systems
    6. Gradient systems
    7. Competing species
    8. Predator-Prey equations
    9. Harvesting species
    10. Lyapunov second method
    11. HIV models
    12. Periodic solutions
    13. Asynchronous solutions
    14. Limited Cycles
    15. van der Pol equations
    16. Neuroscience
    17. Biochemistry
    18. Miscellany
    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. 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
    7. Mechanical problems
    8. Miscellany
  • Part IV: Numerical Methods +
    1. Iterative Methods
    2. Iterations for Nonlinear Systems
    3. Numerical Solutions using ode45
    4. System conversion
    5. Power series method
    6. Modified Decomposition Method
    7. Euler's methods
    8. Runge--Kutta methods
    9. Multistep methods
    10. Finite Difference Methods
    11. Adomian Decomposition Method
    12. Variational iteration method
    13. Finite Element Method
    14. Second order ODEs
    15. Applications
  • Part V: Fourier Series +
    1. Sturm--Liouville problems
    2. Singular Sturm--Liouville problems
    3. Fourier transform
    4. Fourier series
    5. Periodic Extension
    6. Complex Fourier series
    7. Even and odd functions
    8. FFT
    9. Examples
    10. Convergence of Fourier series
    11. Modes of convergence
    12. Gibbs phenomena
    13. Cesàro summation
    14. Square wave functions
    15. Orthogonal expansions
    16. Chebyshev expansions
    17. Legendre expansion
    18. Hermite expansion
    19. Laguerre expansion
    20. Bessel expansion
    21. Motivated Examples
  • Part VI: Partial Differential Equations +
    2. First order PDEs
    3. Separation of variables
    4. Green's functions
    5. Blasius equation
    6. Fluid problems
    7. Applications
    8. Miscellany
    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
    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 domain
    6. Laplace equation in infinite stripe
    7. Laplace equation in infinite semi-stripe
    8. Numerical solutions of Laplace equation
    9. Laplace equation in polar coordinates
    10. Laplace equation in a corner
    11. Laplace equation in spherical coordinates
    12. Poisson's equation
    13. Helmholtz equation
    14. Liouville's equation
    15. Monte Carlo for Elliptic
  • 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. Recurrences
      6. Orthogonality of Bessel functions
      7. Airy functions
      8. Applications
    4. Chebyshev functions
      1. Generating functions
      2. Orthogonality
      3. Recurrences
      4. Zeroes
      5. Applications
    5. Legendre functions
      1. Generating functions
      2. Orthogonality
      3. Recurrences
      4. Spherical harmonics
      5. Applications
    6. Hermite polynomials
    7. Laguerre polynomials
    8. Lambert function
    9. Mathieu function
    10. Elliptic functions
    11. Hypergeometric functions
    12. Kummer's equation
    13. Miscellany
  • Glossary