AUM - CH 3.1: Linear Models ( differential equations) شرح
تم عرض عينه من فيدوهات الماده علي اليوتيوب و لكن تم رفع فيديوهات الماده كامله مع نوتات الشرح علي موقع Udemy و هذا هو لينك الماده على الموقع
https://www.udemy.com/course/differen...
للتواصل واتساب مع د. ابو كارم http://wa.me/201558466735
محتوى الماده الذي تم شرحه في الفيديوهات هو
Chapter 1: Introduction
1.1: Introduction to Differential Equations (Classification, Order, Linearity)
1.2: Initial-Value Problems
Chapter 2: First-Order Differential Equations
2.1: Solution Curves Without a Solution (Direction Fields, Phase Lines)
2.2: Separable Differential Equations
2.3: Solving First-Order Linear Differential Equations (Integrating Factors)
2.4: Exact Differential Equations
2.5: Solutions by Substitutions (Bernoulli’s Equation, Homogeneous Forms)
2.6: Numerical Methods (Euler’s Method)
Chapter 3: Modeling with Differential Equations
3.1: Linear Models (Applications in Growth/Decay Models)
3.2: Nonlinear Models
Chapter 4: Higher-Order Linear Differential Equations
4.1.1: Initial-Value and Boundary-Value Problems
4.1.2: Homogeneous Linear Equations
4.1.3: Nonhomogeneous Linear Equations
4.2: Reduction of Order
4.3: Homogeneous Equations with Constant Coefficients (Characteristic Equation)
4.6: Variation of Parameters (General Solutions)
4.7: Cauchy Euler Equations
4.9: Solving Systems of Linear DEs by Elimination
Chapter 7: Laplace Transforms
7.1: Definition and Basic Properties
7.2: Inverse Transforms and Transforms of Derivatives
7.3-7.4: Operational Properties (Translation, Convolution)
7.5: The Dirac Delta Function