[vc_row el_class=”inner-body-content” css=”.vc_custom_1666844652480{padding-top: 30px !important;padding-bottom: 20px !important;}”][vc_column][vc_custom_heading text=”Pre-requisite(s)” font_container=”tag:h3|font_size:20px|text_align:left” use_theme_fonts=”yes” css=”.vc_custom_1666844637653{margin-top: 0px !important;}”][vc_column_text]Calculus and Analytical Geometry (MTCE-1013)[/vc_column_text][vc_custom_heading text=”Recommended Book(s)” font_container=”tag:h3|font_size:20px|text_align:left” use_theme_fonts=”yes”][vc_column_text]Differential Equations With Boundary Value Problems, Dennis. G. Zill, Michael R. Cullen, 7^th Edition[/vc_column_text][vc_custom_heading text=”Reference Book(s)” font_container=”tag:h3|font_size:18px|text_align:left” use_theme_fonts=”yes”][vc_column_text]Advanced Engineering Mathematics, Erwin Kreyszig, 8^th Edition

Theory And Problems Of Laplace Transforms, Schaum’s Outline Series[/vc_column_text][vc_custom_heading text=”COURSE OBJECTIVES” use_theme_fonts=”yes”][vc_column_text]1. Model the problems arising in different areas of science and engineering in the form of differential equations.

2. Solve the linear 1st order differential equations that appear in Civil Engineering.

3. Solve second order differential equations using different techniques.

4. Apply 2nd order differential equations to the variety of theoretical problems.

5. Understand the meaning, use and applications of the partial differential equations.[/vc_column_text][vc_custom_heading text=”COURSE LEARNING OUTCOMES (CLO)” use_theme_fonts=”yes”][vc_column_text]CLO:1. Understand the problems arising in field of science & technology.

CLO:2. Apply the acquired knowledge in field of civil engineering.[/vc_column_text][vc_custom_heading text=”COURSE CONTENTS” use_theme_fonts=”yes”][vc_custom_heading text=”Introduction To Differential Equations” font_container=”tag:h3|font_size:20px|text_align:left” use_theme_fonts=”yes”][vc_column_text]

• Introduction
• Definitions and terminology
• Formulations, order, degree and the linearity of differential equation
• Initial-value problems
• De’s in mathematical models

[/vc_column_text][vc_custom_heading text=”First Order Differential Equations” font_container=”tag:h3|font_size:20px|text_align:left” use_theme_fonts=”yes”][vc_column_text]

• Variables separable forms
• Homogenous equations
• Non-homogenous equations
• Exact equations
• Linear equations
• Solution by substitutions
• Exercises

[/vc_column_text][vc_custom_heading text=”Applications Of First Order DE’s” font_container=”tag:h3|font_size:20px|text_align:left” use_theme_fonts=”yes”][vc_column_text]

• Modeling with the first order differential equations
• Orthogonal trajectories
• Population dynamics
• Applications of linear equations
• Applications of non-linear equations
• Exercises

[/vc_column_text][vc_custom_heading text=”Higher Order Linear Differential Equations” font_container=”tag:h3|font_size:20px|text_align:left” use_theme_fonts=”yes”][vc_column_text]

• 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

[/vc_column_text][vc_custom_heading text=”Applications Of The Second Order Differential Equations” font_container=”tag:h3|font_size:20px|text_align:left” use_theme_fonts=”yes”][vc_column_text]

• Spring mass problems
• Civil engineering related problems

[/vc_column_text][vc_custom_heading text=”Partial Differential Equations” font_container=”tag:h3|font_size:20px|text_align:left” use_theme_fonts=”yes”][vc_column_text]

• Basic concepts
• Vibrating string
• Wave equation
• Separation of variables
• Heat equation solution by separation of variables
• Exercises

[/vc_column_text][vc_custom_heading text=”MAPPING OF CLOs TO PROGRAM LEARNING OUTCOMES” use_theme_fonts=”yes”][vc_column_text]

CLO’s	CLO-1 (Knowledge)	CLO-2  (Application of fundamental concepts)
PLO’s
PLO-1 (Engineering Knowledge)
PLO-2 (Problem Analysis)	√	√
PLO-3 (Design/Development of Solutions)
PLO-4 (Investigation)
PLO-5 (Modern Tool Usage)
PLO-6 (The Engineer and Society)
PLO-7 (Environment and Sustainability)
PLO-8 (Ethics)
PLO-9 (Individual and Team work)
PLO-10 (Communication)
PLO-11 (Project Management)
PLO-12 (Lifelong Learning)

[/vc_column_text][vc_custom_heading text=”MAPPING OF CLOs TO ASSESSMENT MODULES” use_theme_fonts=”yes”][vc_column_text css=”.vc_custom_1669875979897{margin-bottom: 0px !important;}”]

CLOs	CLO:1	CLO:2
Assessment Modules
Assignments (20-25%)	√	√
Quizzes (15-20%)	√
Midterm Exam (20%)	√
Final Exam (40-45%)	√	√

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