{"id":17760,"date":"2025-07-16T22:07:33","date_gmt":"2025-07-16T20:07:33","guid":{"rendered":"https:\/\/www2.mie.uth.gr\/?page_id=17760"},"modified":"2026-09-04T11:27:53","modified_gmt":"2026-09-04T08:27:53","slug":"%ce%b3%ce%b50103-ordinary-differential-equations-compulsory","status":"publish","type":"page","link":"https:\/\/mie.uth.gr\/?page_id=17760&lang=en","title":{"rendered":"\u0393\u03950103\u00a0Ordinary Differential Equations (Core)"},"content":{"rendered":"\t\t
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Course Information<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t
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Course Outline<\/a><\/span><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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\u03a0\u03bb\u03b7\u03c1\u03bf\u03c6\u03bf\u03c1\u03af\u03b5\u03c2 \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Course Category\u03c2<\/strong>
Course Type<\/b>
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ECTS Units<\/strong>
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Undergraduate
Core
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3rd (Winter)
5\u00a0
6

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Course Category: <\/strong>Undergraduate
Course Type: <\/strong>Core
Secretary Code: <\/strong>\u0393\u03950103
Semester: <\/strong>2\u03bf (\u0395\u03b1\u03c1\u03b9\u03bd\u03cc)
Duration: <\/strong>5 hours\/week
ECTS Units:\u00a0<\/strong>6
Instructor: Philippitzis Philippos<\/span><\/strong><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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<\/i>Aim<\/span><\/div>

This is an undergraduate course on ordinary differential equations (ODEs) and associated initial value problems. Special emphasisis placed on fundamental concepts, solution methods and applications of ODEs to problems in Mechanical Engineering and Physics more generally.\u00a0\u00a0<\/p><\/div>\n\t\t\t\t\t<\/div>

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<\/i>Syllabus<\/span><\/div>

Introduction:<\/span><\/strong> the concepts of the ordinary differential equation and of the initial value problem, applications of differential equations.<\/p>

First\u2010order equations:<\/strong><\/span> integral curves, existence and uniqueness of solutions; analytical methods for solving linear, separable, exact, homogeneous, autonomous, and Bernoulli equations; numerical methods; applications. Second\u2010order linear equations: existence and uniqueness of solutions,\u00a0 homogeneous and non\u2010homogeneous equations, equations with constant coefficients, applications to the problem of free and forced vibration.<\/p>

Third\u2010\u00a0 or higher\u2010order linear <\/strong><\/span>equations. The method of the power series:<\/strong><\/span> introduction to power series, ordinary and singular points, regular and irregular singular points, solutions about ordinary points, the Legendre equation, solutions about regular singular points, the Bessel equation.<\/p>

The Laplace transform: <\/strong><\/span>solving differential equations, step functions and applications, impulse functions and applications, the convolution theorem and applications.<\/p><\/div>\n\t\t\t\t\t<\/div>

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<\/i>Literature<\/span><\/div>

Suggested Literature:<\/strong><\/span><\/p>

  • Boyce, W.E. & DiPrima, R.C., Elementary Differential Equations and Boundary Value Problems, Wiley, 2012.<\/li>
  • \u039c\u03c5\u03bb\u03c9\u03bd\u03ac\u03c2, \u039d. & \u03a3\u03c7\u03bf\u03b9\u03bd\u03ac\u03c2, \u03a7., \u0394\u03b9\u03b1\u03c6\u03bf\u03c1\u03b9\u03ba\u03ad\u03c2 \u0395\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2, \u039c\u03b5\u03c4\u03b1\u03c3\u03c7\u03b7\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03bf\u03af \u03ba\u03b1\u03b9 \u039c\u03b9\u03b3\u03b1\u03b4\u03b9\u03ba\u03ad\u03c2 \u03a3\u03c5\u03bd\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03b9\u03c2, \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u03a4\u03b6\u03b9\u03cc\u03bb\u03b1, 2015.<\/li>
  • \u03a3\u03c4\u03b1\u03c5\u03c1\u03b1\u03ba\u03ac\u03ba\u03b7\u03c2, \u039d., \u0394\u03b9\u03b1\u03c6\u03bf\u03c1\u03b9\u03ba\u03ad\u03c2 \u0395\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2: \u03a3\u03c5\u03bd\u03ae\u03b8\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u039c\u03b5\u03c1\u03b9\u03ba\u03ad\u03c2, \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u03a3\u03c4\u03b1\u03c5\u03c1\u03b1\u03ba\u03ac\u03ba\u03b7\u03c2, 2015.<\/li>
  • \u03a4\u03c1\u03b1\u03c7\u03b1\u03bd\u03ac\u03c2, \u03a3., \u03a3\u03c5\u03bd\u03ae\u03b8\u03b5\u03b9\u03c2 \u0394\u03b9\u03b1\u03c6\u03bf\u03c1\u03b9\u03ba\u03ad\u03c2 \u0395\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2, \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03b9\u03b1\u03ba\u03ad\u03c2 \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u039a\u03c1\u03ae\u03c4\u03b7\u03c2, 2013.<\/li>
  • Cengel, Y. A. & Palm III, W. J., Differential Equations for Engineers and Scientists, McGraw\u2010Hill, 2012.<\/li>
  • \u03a3\u03bf\u03cd\u03c1\u03bb\u03b1\u03c2, \u0394., \u03a3\u03c5\u03bd\u03ae\u03b8\u03b5\u03b9\u03c2 \u0394\u03b9\u03b1\u03c6\u03bf\u03c1\u03b9\u03ba\u03ad\u03c2 \u0395\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2, \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u03a3\u03c5\u03bc\u03bc\u03b5\u03c4\u03c1\u03af\u03b1, 2010.<\/li><\/ul>

    Related Academic Journal:<\/strong><\/span><\/p>

    • Journal of Engineering Mathematics<\/li>
    • SIAM Journal on Applied Mathematics<\/li><\/ul><\/div>\n\t\t\t\t\t<\/div>
      \n\t\t\t\t\t
      <\/i>Teaching Language<\/span><\/div>

      Greek<\/p><\/div>\n\t\t\t\t\t<\/div>

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      <\/i>Teaching Method<\/span><\/div>

      Lectures<\/p><\/div>\n\t\t\t\t\t<\/div>

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      <\/i>Student Performance Evaluation<\/span><\/div>
      Midterm exams<\/strong><\/td>30%<\/td><\/tr>
      Written Final Exam<\/strong><\/td>70%<\/td><\/tr><\/tbody><\/table><\/div>\n\t\t\t\t\t<\/div>
      \n\t\t\t\t\t
      <\/i>Workload (in hours)<\/span><\/div>

      \u00a0<\/h3>
      Activity<\/strong><\/td>Semester workload<\/strong><\/td><\/tr>
      Lectures<\/td>70\u00a0<\/td><\/tr>
      Homeworks<\/td>35\u00a0<\/td><\/tr>
      Autonomous work<\/td>45\u00a0<\/td><\/tr>
      \u03a3\u03cd\u03bd\u03bf\u03bb\u03bf \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 (25 \u03ce\u03c1\u03b5\u03c2 \u03c6\u03cc\u03c1\u03c4\u03bf\u03c5 \u03b5\u03c1\u03b3\u03b1\u03c3\u03af\u03b1\u03c2 \u03b1\u03bd\u03ac \u03c0\u03b9\u03c3\u03c4\u03c9\u03c4\u03b9\u03ba\u03ae \u03bc\u03bf\u03bd\u03ac\u03b4\u03b1<\/strong>)<\/td>150<\/strong><\/td><\/tr><\/tbody><\/table>

      \u00a0<\/h3>

      \u00a0<\/h3><\/div>\n\t\t\t\t\t<\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

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