### Pre-requisite(s)

Calculus and Analytical Geometry (MTCE-1013)

### Recommended Book(s)

Differential Equations With Boundary Value Problems, Dennis. G. Zill, Michael R. Cullen, 7th Edition

### Reference Book(s)

Advanced Engineering Mathematics, Erwin Kreyszig, 8th Edition

Theory And Problems Of Laplace Transforms, Schaum’s Outline Series

## COURSE OBJECTIVES

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.

## COURSE LEARNING OUTCOMES (CLO)

CLO:1.           Understand the problems arising in field of science & technology.

CLO:2.           Apply the acquired knowledge in field of civil engineering.

## COURSE CONTENTS

### Introduction To Differential Equations

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

### First Order Differential Equations

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

### Applications Of First Order DE’s

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

### Higher Order Linear Differential Equations

• 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

### Applications Of The Second Order Differential Equations

• Spring mass problems
• Civil engineering related problems

### Partial Differential Equations

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

## MAPPING OF CLOs TO PROGRAM LEARNING OUTCOMES

 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)

## MAPPING OF CLOs TO ASSESSMENT MODULES

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