[vc_row el_class=”inner-body-content” css=”.vc_custom_1666784133967{padding-top: 30px !important;padding-bottom: 20px !important;}”][vc_column][vc_custom_heading text=”COURSE OBJECTIVES” use_theme_fonts=”yes” css=”.vc_custom_1666784018427{margin-top: 0px !important;}”][vc_column_text]This course provides an introduction to the theory, solution, and application of ordinary differential equations. Topics discussed in the course include methods of solving first-order differential equations, existence and uniqueness theorems, second-order linear equations, power series solutions, higher-order linear equations, and their applications.[/vc_column_text][vc_custom_heading text=”COURSE LEARNING OUTCOMES (CLO)” use_theme_fonts=”yes”][vc_column_text]
CLO-1: Use their knowledge of calculus to solve the 1st order ordinary differential equations.
CLO-2: Use various techniques to solve higher order ordinary differential.
CLO-3: Model the problems arising in different areas of science and engineering in the form of ordinary differential equations.
CLO-3: Understand the meaning, use and applications of the partial differential equations[/vc_column_text][vc_custom_heading text=”COURSE CONTENTS” use_theme_fonts=”yes”][vc_column_text css=”.vc_custom_1666784101895{margin-bottom: 0px !important;}”]

1. Introduction to Differential Equations – Five Lectures                

• Introduction,
• Definitions and terminology
• Formulations
• Order
• Degree and the linearity of differential equation
• Initial-Value problems
• DE’s in Mathematical Models

2. First Order Differential Equations – Five Lectures                                

• Variables Separable Forms
• Homogenous Equations
• Non-homogenous equations
• Exact Equations
• Linear Equations
• Solution by Substitutions

3. Applications of First Order DE’s – Six Lectures                          

• Modeling with the First Order Differential Equations
• Orthogonal Trajectories
• Population Dynamics
• Applications of Linear Equations
• Applications of Non-linear Equations

4. Higher Order Linear Differential Equations – Five Lectures                              

• Introduction and Preliminary Theory
• Initial-value and Boundary-value Problems
• 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 – Five Lectures                                  

• Spring Mass Problems
• Electrical Circuit Problem

6. Partial Differential Equations – Six Lectures                                                                             

• Basic Concepts
• Vibrating String
• Wave Equation
• Separation of Variables
• Heat Equation Solution by Separation of variables

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