COURSE OBJECTIVES

The successful completion of this course would help students in achieving the following objectives:
• Model the problems arising in different areas of science and engineering in the form of differential equations.
• Solve the linear 1st order differential equations that appear in Civil Engineering.
• Solve second order differential equations using different techniques.
• Apply 2nd order differential equations to the variety of theoretical problems.
• Understand the meaning, use and applications of the partial differential equations.

COURSE LEARNING OUTCOMES (CLO)


CLO: 1. to use the knowledge of calculus to solve the ordinary differential equations by different techniques. (C2)
CLO: 2. to apply the concepts of ordinary derivatives for the modeling of physical systems. (C3)
CLO: 3. to understand the meaning, use and applications of the partial differential equations. (C3)
CLO: 4. to clarify his/her analysis of civil engineering problems performed by applying differential equation. (A2)

COURSE CONTENTS

  1. Introduction to Differential Equations
    • Introduction
    • Definitions and terminology
    • Formulations, order, degree and the linearity of differential equation
    • Initial-value problems
  2. First Order Differential Equations
    • Variables separable forms
    • Homogenous equations
    • Non-homogenous equations
    • Exact equations
    • Linear equations
    • Solution by substitutions
  3. Applications of First Order DEs
    • Modeling with the first order differential equations
    • Orthogonal trajectories
    • Population dynamics
  4. Higher Order Linear Differential Equations
    • Introduction and preliminary theory
    • Initial-value and boundary-value problems
    • Introduction to Complex numbers
    • Homogenous and non-homogenous equations
    • Method of undetermined coefficients
    • Method of variation of parameters
    • Power series solution
  5. Applications of the Second Order Differential Equations
    • Spring mass problems
    • RLC circuits
    • Simple pendulum
  6. Partial Differential Equations
    • Basic concepts
    • Vibrating string
    • Wave equation
    • Heat equation