Maple Tutorial
Under the terms of the GNU General Public License GPL
for the First Course, Part 1.6: ODEs with discontinuous input

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

Contents

  • Preface
    1. Introduction
      1. Getting started
      2. Case sensitivity
      3. Equal signs
      4. Complex numbers
      5. Simplify and Expand
      6. Collect
      7. Logical operators
      8. Functions
      9. Commands
      10. Solving equations
      11. Derivative
      12. Existence
      13. Uniqueness
      14. Picard iterations
      15. Adomian iterations
    2. Part I: Plotting
      1. Plotting functions
      2. Plotting solutions to ODEs
      3. Discontinuous functions
      4. Direction fields
      5. Implicit plot
      6. Parametric plots
      7. Labeling figures
      8. Figures with arrows
      9. Electric circuits
      10. Plotting with filling
      11. Polar plot
      12. Some famous curves
      13. Cycloids
      14. Miscellany
    3. Part II: First Order ODEs
      1. Solutions of ODEs
      2. Singular solutions
      3. Solving first order ODEs
      4. Plotting solutions to ODEs
      5. Phase portrait
      6. Separable equations
      7. Autonomous equations
      8. Equations reducible to the separable equations
      9. Equations with linear fractions
      10. Exact equations
      11. Integrating factors ▾
        1. Function of x
        2. Function of y
        3. Function of xy
        4. Function of x/y
        5. Function of x² + y²
        6. Common factors
        7. Homogeneous factors
        8. Special factors
        9. Approximation of integrating factors
      12. Linear equations
      13. RC circuits
      14. Bernoulli equations
      15. Riccati equations
      16. Clairaut equations
      17. Qualitative Analysis ▾
        1. Qualitative analysis
        2. Bifurcations
        3. Landau theory
        4. Validity interval
      18. Orthogonal trajectories
      19. Population models
      20. Pursuit
      21. Applications
    4. Part III: Numerical Methods and Applications
      1. Numerical solution using DSolve and NDSolve
      2. Fixed point iteration
      3. Bracketing methods
      4. Open methods
      5. Homotopy methods
      6. Comparisons
      7. Padé approximation
      8. Euler's Methods ▾
        1. Euler's methods
        2. Backward method
        3. Heun method
        4. Modified Euler method
      9. Runge-Kutta Methods ▾
        1. Runge--Kutta methods
        2. Runge--Kutta methods of order 2
        3. Runge--Kutta methods of order 3
        4. Runge--Kutta methods of order 4
      10. Polynomial approximations
      11. Error estimates
      12. Adomian Decomposition Method
      13. Finite Difference Schemes
      14. Variational iteration method
      15. Multi-step methods ▾
        1. Multistep methods
        2. Multistep methods of order 3
        3. Multistep methods of order 4
        4. Milne method
        5. Hamming method
      16. Applications
    5. Part IV: Second and Higher Order Differential Equations
      1. Differential equations of higher order
      2. Canonical forms
      3. Reduction higher order ODEs
      4. Linear operators
      5. Fundamental sets of solutions
      6. Linear ODEs
      7. Constant coefficient ODEs
      8. Complex roots
      9. Reduction of order
      10. Annihilator operators
      11. Method of undetermined coefficients
      12. Variation of parameters
      13. Factorization
      14. Euler Equations ▾
        1. Euler equations
        2. Factorization
        3. Inhomogeneous Euler equations
      15. Vibrations
    6. Part IV N: Nonlinear ODEs
      1. Numerical solutions
      2. Boundedness of solutions
      3. Spring Problems ▾
        1. Spring problems
        2. Free vibrations
        3. Damped vibrations
        4. Forced vibrations
        5. Resonance
        6. Nonlinear models
        7. Driven models
      4. Pendulum ▾
        1. Pendulum
        2. Simple pendulum
        3. Solution of pendulum equation
        4. Period of pendulum
        5. Real pendulum
        6. Driven pendulum
        7. Rocking pendulum
        8. Pumping swing
      5. Dyer model
      6. Electric circuits
      7. Adomian Decomposition Method
      8. Applications
    7. Part V: Series and Recurrences
      1. Recurrences
      2. Discrete logistic recurrence
      3. Generating functions
      4. Lagrange Inversion Theorem
      5. Series convergence
      6. Review of power series
      7. Convergence acceleration
      8. Nonlinear ODEs
      9. Picard iterations
      10. Series solutions for first order equations
      11. Series solutions for the second order equations
      12. Examples of second order ODEs
      13. Euler equations
      14. Regular Singular Points ▾
        1. Regular singular points
        2. Distinct exponents
        3. Equal exponents
        4. Integer difference
        5. Complex exponents
      16. Polynomial solutions
      17. Bessel's equations
      18. Modified Decomposition Method
      19. MDM for first order ODEs
      20. MDM for second order ODEs
      21. Applications
    8. Part VI: Laplace Transformation
      1. Definition of Laplace transform
      2. Heaviside and Dirac function
      3. Laplace transform of discontinuous functions
      4. Table of Laplace transforms
      5. Inverse Laplace transform
      6. Convolution integral
      7. Residue method
      8. Solving IVPs with Laplace transform
      9. ODEs with discontinuous input
      10. Nonconstant coefficient IVP’s
      11. Bessel functions
      12. MLDM
      13. Elzaki Transform
      14. Mechanical and electrical applications
    9. Part VII: Boundary Value Problems
      1. Boundary Value Problems
      2. Hyperbolic functions
      3. Green functions
      4. Picard iterations
      5. Finite difference schemes
      6. Shooting methods
      7. Tridiagonal linear systems
      8. Numerov method
      9. Adomian Decomposition
      10. Variational iteration method
      11. Blasius layer
      12. Falkner--Skan layer
      13. Heat transfer
      14. Singular BVPs
      15. Applications

Glossary

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