{"id":112,"date":"2025-09-20T01:58:48","date_gmt":"2025-09-20T01:58:48","guid":{"rendered":"https:\/\/itisallmath.com\/differential-equations\/"},"modified":"2025-12-31T14:52:33","modified_gmt":"2025-12-31T14:52:33","slug":"differential-equations","status":"publish","type":"page","link":"https:\/\/itisallmath.com\/es\/mathematics\/differential-equations\/","title":{"rendered":"Differential Equations"},"content":{"rendered":"
<\/div><\/div>\n\n\n\n
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What are you going to learn?<\/h1><\/div>\n\n\n\n

Model with first-order differential equations (DE) and identify initial value problems. Solve scalar differential equations, homogeneous and non-homogeneous, using methods including separation of variables, integrating factors, eigenvalues, LaPlace transformations. Model with systems of first-order DEs and higher-order DEs. Solve systems of linear differential equations using matrices and eigenvalues.<\/p>\n\n\n\n

Content<\/h2><\/div>\n<\/div><\/div>\n\n\n\n
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Chapter 1. Introduction<\/strong><\/h3><\/div>\n\n\n\n
    \n
  • Terminology<\/li>\n\n\n\n
  • Classification of Differential Equations<\/li>\n\n\n\n
  • Initial Value Problem. Cauchy’s Theorem of y’ = f(x, y)<\/em><\/li>\n\n\n\n
  • Mathematical Models and Direction of Fields<\/li>\n<\/ul>\n<\/div>\n\n\n\n
    <\/div>\n<\/div><\/div>\n\n\n\n
    \n
    \n

    Chapter 2. First Order Ordinary Differential Equations (ODE)<\/strong><\/strong><\/h3><\/div>\n\n\n\n
      \n
    • Integrating Factors<\/li>\n\n\n\n
    • Separation of Variables<\/li>\n\n\n\n
    • Exact Equations<\/li>\n\n\n\n
    • First Order Linear Equations<\/li>\n\n\n\n
    • Equations with Homogeneous Coefficients<\/li>\n\n\n\n
    • Solution by Substitutions<\/li>\n\n\n\n
    • Bernoulli’s DE<\/li>\n\n\n\n
    • Computer Solutions<\/li>\n<\/ul>\n<\/div>\n\n\n\n
      <\/div>\n<\/div><\/div>\n\n\n\n
      \n
      \n

      Chapter 3. Second Order Ordinary Differential Equations<\/strong><\/strong><\/h3><\/div>\n\n\n\n
        \n
      • The General Second Order Linear Homogeneous Equation<\/li>\n\n\n\n
      • Linear Independence<\/li>\n\n\n\n
      • Existence and Uniqness Theorem<\/li>\n\n\n\n
      • The Wronskian<\/li>\n\n\n\n
      • General Solution of a Homogeneous Equation<\/li>\n\n\n\n
      • General Solution of a Nonhomogeneous Equation<\/li>\n\n\n\n
      • Differential Operators<\/li>\n<\/ul>\n<\/div>\n\n\n\n
        <\/div>\n<\/div><\/div>\n\n\n\n
        \n
        \n

        Chapter 4. Higher Order Constant Coefficients Linear Equations<\/strong><\/strong><\/h3><\/div>\n\n\n\n
          \n
        • Introduction<\/li>\n\n\n\n
        • Reduction of Order<\/li>\n\n\n\n
        • Homogeneous LE with Constant Coefficients<\/li>\n\n\n\n
        • Undetermined Coefficients – Superposition Approach<\/li>\n\n\n\n
        • Variation of Parameters<\/li>\n\n\n\n
        • Cauchy – Euler Equation<\/li>\n\n\n\n
        • Systems of Linear Equations<\/li>\n\n\n\n
        • Nonlinear Equations<\/li>\n<\/ul>\n<\/div>\n\n\n\n
          <\/div>\n<\/div><\/div>\n\n\n\n
          \n
          \n

          Chapter 5. Series Solutions of 2d Order LDE<\/strong><\/strong><\/h3><\/div>\n\n\n\n
            \n
          • Power Series<\/li>\n\n\n\n
          • Series Solutions Near an Ordinary Point<\/li>\n\n\n\n
          • Euler Equations, Regular Singular Points<\/li>\n\n\n\n
          • Series Solutions Near an Regular Singular Point<\/li>\n\n\n\n
          • Bessel’s Equation<\/li>\n<\/ul>\n<\/div>\n\n\n\n
            <\/div>\n<\/div><\/div>\n\n\n\n
            \n
            \n

            Chapter 6. Laplace Transform<\/strong><\/strong><\/h3><\/div>\n\n\n\n
              \n
            • Definition<\/li>\n\n\n\n
            • Solution of Initial Value Probems<\/li>\n\n\n\n
            • Step Fucntions<\/li>\n\n\n\n
            • Impulse Functions<\/li>\n\n\n\n
            • The Convolution Integral<\/li>\n<\/ul>\n<\/div>\n\n\n\n
              <\/div>\n<\/div><\/div>\n\n\n\n
              \n
              \n

              Chapter 7. Systems of First Order Differential Equations<\/strong><\/strong><\/h3><\/div>\n\n\n\n
                \n
              • Review of Matrices<\/li>\n\n\n\n
              • Systems of Linear Equations. Linear Independence<\/li>\n\n\n\n
              • Eigenvectors, Eigenvalues<\/li>\n\n\n\n
              • Basic Theory<\/li>\n\n\n\n
              • Homogeneous Linear Systems with Constant Coefficients<\/li>\n\n\n\n
              • Nonhomogeneous Linear Systems<\/li>\n<\/ul>\n<\/div>\n\n\n\n
                <\/div>\n<\/div><\/div>\n\n\n\n
                \n
                \n

                Chapter 8. Numerical Methods<\/strong><\/strong><\/h3><\/div>\n\n\n\n
                  \n
                • The Euler’s Method<\/li>\n\n\n\n
                • Runge-Kutta Method<\/li>\n\n\n\n
                • Multi Step Methods<\/li>\n\n\n\n
                • Systems of First order Equations<\/li>\n<\/ul>\n<\/div>\n\n\n\n
                  <\/div>\n<\/div><\/div>\n\n\n\n

                  Bibliography<\/h2><\/div>\n\n\n\n
                    \n
                  • Boyce, W. E., DiPrima, R. Elementary Differential Equations and Boundary Problems<\/em>.<\/strong> 8th ed., Wiley & Sons Inc., New York.<\/li>\n\n\n\n
                  • Zill, D. A First Course in Differential Equations with Modeling Applications<\/em><\/strong>. 10th ed., Brooks\/Cole, London, 1997.<\/li>\n<\/ul>\n\n\n\n

                    Webgraphy<\/h2><\/div>\n\n\n\n
                      \n
                    • <\/li>\n<\/ul>\n\n\n\n

                      <\/p>","protected":false},"excerpt":{"rendered":"

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Model with first-order differential equations (DE) and identify initial value problems. 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