Differential equation Material

Jila, 2017. dec. 24.

Tartalomjegyzék

  1. First Order
    1. Slope field- first order differential equations
    2. Euler Method with 100 points. Enter the function, the initial point and the step size. Use the spread sheet to find the numerical estimate.
    3. How does Euler method work?
    4. Slope field- first order differential equations y'=x^2-y
    5. Slope field- first order differential equations y'=-y/x
    6. Slope field- first order differential equations y'=3y^(2/3)
    7. Population Exponential Growth Slope field- first order differential equations
    8. Population Logistic Slope field- first order differential equations
    9. Exitance and Uniqueness when domain is 2e^{2x}\cos(2y)+e^y+y neq 0
    10. Euler
    11. Euler x^2/y
    12. y^(1/2) Picards iteration
    13. Picard–Lindelöf Iteration When h(x,y) and h_y(x,y) Are Bounded and Continuous Everywhere and the solution is defined everywhere.
    14. y^(2) Picards iteration
    15. Neighborhoods in R^2

1.

First Order

  • 1. Slope field- first order differential equations
  • 2. Euler Method with 100 points. Enter the function, the initial point and the step size. Use the spread sheet to find the numerical estimate.
  • 3. How does Euler method work?
  • 4. Slope field- first order differential equations y'=x^2-y
  • 5. Slope field- first order differential equations y'=-y/x
  • 6. Slope field- first order differential equations y'=3y^(2/3)
  • 7. Population Exponential Growth Slope field- first order differential equations
  • 8. Population Logistic Slope field- first order differential equations
  • 9. Exitance and Uniqueness when domain is 2e^{2x}\cos(2y)+e^y+y neq 0
  • 10. Euler
  • 11. Euler x^2/y
  • 12. y^(1/2) Picards iteration
  • 13. Picard–Lindelöf Iteration When h(x,y) and h_y(x,y) Are Bounded and Continuous Everywhere and the solution is defined everywhere.
  • 14. y^(2) Picards iteration
  • 15. Neighborhoods in R^2

1.1.

Slope field- first order differential equations

Description:
The slope field for ode [math]y'=f\left(x,y\right)[/math]. Change the function, initial value and step size.[br]You may have zoom in or out to get the entire image.
– Jila

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