Advanced Mathematics CIVL 2306

Course description:

This course introduces definitions and concepts of the differential equations. Classifies DE.s according to the types of the derivatives: ordinary or partial. Classifies the DE.s according to the order (degree) and linearity. Introduces the first order differential equations, classifies them by type, and describes methodologies to solve them according to their types.
Classifies the second and higher order differential equations according to linearity, homogeneity and coefficients, and explains procedures to solve such higher order differential equations; Changes of a dynamic system within the limits of the infinitesimal differences are related to the mathematical derivatives of functions; Changes in a system are described by equations of differentials: the differential equations (DE.s).
Introduces a special kind of non-constant coefficient differential equations, e.g., the Cuachy-Euler type, and introduces ways to solve them.
Introduces systems of differential equations and helps learning how to solve the linear ones. 
Helps model the changes and behavior of dynamic systems by differential equations, and helps finding analytic solutions.

Course Aims:

  • Gives engineering students a mathematical background for understanding and solving problems related to changing systems. 
  • Helps students understand models and problems' solving methods.
  • Introduces some concepts of the differential equations, their applications in science and engineering, and some skills to analytically solve differential equations.

Course outcomes:

Upon completion of this course, the student should be able to:
  • Classify differential equations according to orders and the type of derivatives.
  • Find the solution of a linear and non-linear first order differential equations.
  • Find the set of solutions to second or higher order linear homogeneous differential equation.
  • Find particular solutions of non-homogeneous differential equations
  • Find the general solution of homogeneous and non-homogeneous second or higher order linear differential equation.
  • Use Laplace transform and Fourier series to find solutions of differential equations.