Applied Differential Equation (MTCE1043)

Calculus and Analytical Geometry (MTCE-1013)

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

Advanced Engineering Mathematics, Erwin Kreyszig, 8^th Edition

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

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.

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

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

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

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

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

• 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

• Spring mass problems
• Civil engineering related problems

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