[vc_row el_class=”inner-body-content” css=”.vc_custom_1666598374752{padding-top: 30px !important;padding-bottom: 20px !important;}”][vc_column][vc_custom_heading text=”COURSE OBJECTIVES” use_theme_fonts=”yes” css=”.vc_custom_1666598368191{margin-top: 0px !important;}”][vc_column_text]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.[/vc_column_text][vc_custom_heading text=”COURSE LEARNING OUTCOMES (CLO)” font_container=”tag:h3|text_align:left” use_theme_fonts=”yes”][vc_column_text]

**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.

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**Introduction to Differential Equations**- Introduction
- 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

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