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.
- Introduction to Differential Equations
- Definitions and terminology
- Formulations, order, degree and the linearity of differential equation
- Initial-value problems
- First Order Differential Equations
- Variables separable forms
- Homogenous equations
- Non-homogenous equations
- Exact equations
- Linear equations
- Solution by substitutions
- Applications of First Order DEs
- Modeling with the first order differential equations
- Orthogonal trajectories
- Population dynamics
- 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
- Applications of the Second Order Differential Equations
- Spring mass problems
- RLC circuits
- Simple pendulum
- Partial Differential Equations
- Basic concepts
- Vibrating string
- Wave equation
- Heat equation