مقدمة في المعادلات التفاضلية (Differential Equations)

 

• Texts: A first course in differential equations with modeling applications, by Dennis Zill 10th edition
•  Chapter one (Introduction to Differential Equations)

  1.1 DEFINITIONS AND TERMINOLOGY

  1.2 INITIAL-VALUE PROBLEMS

•  Chapter two (First-Order Differential Equations)

  2.2 SEPARABLE EQUATIONS

  2.3 LINEAR EQUATIONS

  2.4 Exact EQUATIONS

  2.5 SOLUTIONS BY SUBSTITUTIONS

  - Orthogonal trajectories.

•  

   Chapter four (Higher-Order Differential Equations)

  4.1 PRELIMINARY THEORY—LINEAR EQUATIONS

  4.2 REDUCTION OF ORDER

  4.3 HOMOGENEOUS LINEAR EQUATIONS WITH CONSTANT CO- EFFICIENTS

• 4.5 UNDETERMINED COEFFICIENTS —ANNIHILATOR APPROACH 4.6 VARIATION OF PARAMETERS
• 4.7 CAUCHY-EULER EQUATION
• 4.9 SOLVING SYSTEMS OF LINEAR DEs BY ELIMINATION

       

        Chapter six (Series Solutions of Linear Equations)

6.1 REVIEW OF POWER SERIES
6.2 SOLUTIONS ABOUT ORDINARY POINTS

 

       Chapter Seven (The Laplace Transform)
7.1 DEFINITION OF THE LAPLACE TRANSFORM
7.2 INVERSE TRANSFORMS AND TRANSFORMS OF DERIVATIVES 7.3 OPERATIONAL PROPERTIES