[vc_row el_class=”inner-body-content” css=”.vc_custom_1666601640494{padding-top: 30px !important;padding-bottom: 20px !important;}”][vc_column][vc_custom_heading text=”COURSE OBJECTIVES” use_theme_fonts=”yes” css=”.vc_custom_1666601654363{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 circuit analysis, electronics, motion, electric machines etc.
• 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

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CLO: 1. Use the knowledge of calculus to solve the ordinary differential equations by different techniques. (Level: C3)
CLO: 2. Apply the concepts of ordinary derivatives for the modeling of physical systems. (Level: C3)
CLO: 3. Understand the meaning, use and applications of the partial differential equations. (Level: C2)
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1. Introduction to Differential Equations – Four 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 – Six Lectures
   • Variables separable forms,
   • Homogenous equations,
   • Non-homogenous equations,
   • Exact equations,
   • Linear equations,
   • Solution by substitutions,
   • Exercises
3. Applications of First Order DE’s – Five Lectures
   • Modeling with the first order differential equations
   • Orthogonal trajectories
   • Population dynamics
   • Applications of linear equations
   • Applications of non-linear equations
   • Exercises
4. Higher Order Linear Differential Equations – Six 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 engineering related problems
6. Introduction to Partial Differential Equations – Six Lectures
   • Basic concepts,
   • Vibrating string,
   • Wave equation,
   • Separation of variables,
   • Heat equation solution by Fourier series.
   • Exercises

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