Calculus II - 13
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Calculus II - 13

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Stewart Calculus Section 9.2

Stewart Calculus Section 9.2

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Calculus II - 13 Calculus II - 13 Presentation Transcript

  • 9.2 Direction Fields and Euler’s Method Most differential equation cannot be solved explicitly. We can study the solution through a graphical approach (direction fields) or a numerical approach (Euler’s method).
  • Direction fields. = +
  • Direction fields. = +
  • Direction fields. = + , ( )=
  • Direction fields. = + , ( )=
  • Direction fields. = + , ( )=
  • Direction fields. = + , ( )=
  • Direction fields. = + , ( )=
  • Direction fields. = + , ( )=
  • Direction fields. = + , ( )=
  • Direction fields. = +
  • Direction fields. = +
  • Direction fields. = + , ( )= , , , ,
  • Direction fields. = + , ( )= , , , ,
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  • Direction fields. = + , ( )= , , , ,
  • Euler’s method = ( , ), ( )=
  • Euler’s method = ( , ), ( )= Let be a small step size.
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  • Euler’s method = ( , ), ( )= Let be a small step size. = + = + = + ······ = + · ( , ) = + · ( , ) = + · ( , ) ······
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  • Euler’s method = + , ( )= Let be a small step size. = . = + = + = . = + = + = . = + = + = . ······ ······ = + · ( , ) = + ·( + )= . = + · ( , ) = + ·( + )= . = + · ( , ) = + ·( + )= . ······ ······
  • Euler’s method = + , ( )=
  • Euler’s method = + , ( )=
  • Euler’s method = + , ( )= =
  • Euler’s method = + , ( )= = .
  • Euler’s method = + , ( )= = .
  • Euler’s method = + , ( )= = .