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

## 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