"annihilator method" meaning in All languages combined

{
  "etymology_text": "From its use of an annihilator (in this case a differential operator) to render the equation more tractable.",
  "forms": [
    {
      "form": "annihilator methods",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "-",
        "2": "s"
      },
      "expansion": "annihilator method (usually uncountable, plural annihilator methods)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "langcode": "en",
          "name": "Differential equations",
          "orig": "en:Differential equations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematical analysis",
          "orig": "en:Mathematical analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1969, Tom Apostol, Calculus, Volume 2: Multi-variable calculus and linear algebra with applications to differential equations and probability, page 166:",
          "text": "Although the annihilator method is very efficient when applicable, it is limited to equations whose right members R have a constant-coefficient annihilator.",
          "type": "quote"
        },
        {
          "ref": "1997, Robert E. O'Malley, Jr, Thinking about Ordinary Differential Equations, Cambridge University Press, page 58:",
          "text": "The annihilator method is just one convenient method to select the form of solution to try when applying the method of undetermined coefficients.",
          "type": "quote"
        },
        {
          "ref": "2001, Martin Bohner, Allan Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Springer, page 116:",
          "text": "Sometimes, instead of using the variation of parameters technique, it is easier to use the so-called annihilator method (also called the method of undetermined coefficients). We now discuss this annihilator method for solving equations of the form\n(3.48) y#x7B;#x5C;Delta#x5C;Delta#x7D;#x2B;#x5C;alphay#x5C;Delta#x2B;#x5C;betay#x3D;f(t),\nwhere #x5C;alpha and #x5C;beta are constants and f is a function that can be annihilated as defined below.",
          "type": "quote"
        },
        {
          "ref": "2012, S. Graham Kelly, Mechanical Vibrations: Theory and Applications, Cengage Learning, page 206:",
          "text": "Many ways exist to solve the particular solution. These include the method of undetermined coefficients, variation of parameters, annihilator methods, Laplace transform methods, and numerical methods.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A procedure used to find a particular solution to certain types of inhomogeneous ordinary differential equations."
      ],
      "id": "en-annihilator_method-en-noun-1Fik~nxV",
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "inhomogeneous",
          "inhomogeneous"
        ],
        [
          "ordinary differential equation",
          "ordinary differential equation"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) A procedure used to find a particular solution to certain types of inhomogeneous ordinary differential equations."
      ],
      "tags": [
        "uncountable",
        "usually"
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "annihilator method"
      ]
    }
  ],
  "word": "annihilator method"
}

{
  "etymology_text": "From its use of an annihilator (in this case a differential operator) to render the equation more tractable.",
  "forms": [
    {
      "form": "annihilator methods",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "1": "-",
        "2": "s"
      },
      "expansion": "annihilator method (usually uncountable, plural annihilator methods)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "English uncountable nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Differential equations",
        "en:Mathematical analysis"
      ],
      "examples": [
        {
          "ref": "1969, Tom Apostol, Calculus, Volume 2: Multi-variable calculus and linear algebra with applications to differential equations and probability, page 166:",
          "text": "Although the annihilator method is very efficient when applicable, it is limited to equations whose right members R have a constant-coefficient annihilator.",
          "type": "quote"
        },
        {
          "ref": "1997, Robert E. O'Malley, Jr, Thinking about Ordinary Differential Equations, Cambridge University Press, page 58:",
          "text": "The annihilator method is just one convenient method to select the form of solution to try when applying the method of undetermined coefficients.",
          "type": "quote"
        },
        {
          "ref": "2001, Martin Bohner, Allan Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Springer, page 116:",
          "text": "Sometimes, instead of using the variation of parameters technique, it is easier to use the so-called annihilator method (also called the method of undetermined coefficients). We now discuss this annihilator method for solving equations of the form\n(3.48) y#x7B;#x5C;Delta#x5C;Delta#x7D;#x2B;#x5C;alphay#x5C;Delta#x2B;#x5C;betay#x3D;f(t),\nwhere #x5C;alpha and #x5C;beta are constants and f is a function that can be annihilated as defined below.",
          "type": "quote"
        },
        {
          "ref": "2012, S. Graham Kelly, Mechanical Vibrations: Theory and Applications, Cengage Learning, page 206:",
          "text": "Many ways exist to solve the particular solution. These include the method of undetermined coefficients, variation of parameters, annihilator methods, Laplace transform methods, and numerical methods.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A procedure used to find a particular solution to certain types of inhomogeneous ordinary differential equations."
      ],
      "links": [
        [
          "mathematical analysis",
          "mathematical analysis"
        ],
        [
          "inhomogeneous",
          "inhomogeneous"
        ],
        [
          "ordinary differential equation",
          "ordinary differential equation"
        ]
      ],
      "raw_glosses": [
        "(mathematical analysis) A procedure used to find a particular solution to certain types of inhomogeneous ordinary differential equations."
      ],
      "tags": [
        "uncountable",
        "usually"
      ],
      "topics": [
        "mathematical-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "annihilator method"
      ]
    }
  ],
  "word": "annihilator method"
}