Differential Equations Course Outline - University of Sargodha

Course Title: Differential Equations

Course Code: MATH-2215
Course Structure: Lectures: 3 / Labs: 0
Credit Hours: 3
Prerequisites:None

Course Objectives:

The course develops students' fundamental skills of solving ordinary differential equations, and
developing differential equations for real-world problems.

Course Syllabus:

Introduction to Differential Equations. First-Order Differential Equations. Modeling With First-
Order Differential Equations. Higher-Order Differential Equations. Undetermined Coefficients-
Superposition Approach. Undetermined Coefficients- Annihilator Approach. Variation of
Parameters. Cauchy-Euler Equation. Solving Systems of Linear Differential Equations by
Elimination. Nonlinear Differential Equations. Modeling with Higher-Order Differential
Equations: Linear Models: Initial-Value Problems, Boundary-Value Problems. Nonlinear
Models. Series Solutions of Linear Equations. Systems of Linear First-Order Differential
Equations. Homogeneous Linear Systems. Nonhomogeneous Linear Systems. Matrix
Exponential. Numerical Solutions of Ordinary Differential Equations. Euler Methods. Runge-
Kutta Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order
Boundary-Value Problems.

Course Outline:

1. Introduction to Differential Equations: Definitions and Terminology. Initial-Value
Problems. Differential Equations as Mathematical Models. [TB: Ch. 1]

2.      First-Order Differential Equations: Solution Curves without a Solution. Separable
Variables. Linear Equations. Exact Equations and Integrating Factors. Solutions by
Substitutions. A Numerical Method. [TB: Ch. 2]

3.      Modelling With First-Order Differential Equations: Linear Models. Nonlinear Models.
Modelling with Systems of First-Order Differential Equations. [TB: Ch. 3]

4.      Higher-Order Differential Equations: Preliminary Theory- Linear Equations. Reduction
of Order. Homogeneous Linear Equations with Constant Coefficients. Undetermined
Coefficients- Superposition Approach. Undetermined Coefficients- Annihilator
Approach. Variation of Parameters. Cauchy-Euler Equation. Solving Systems of Linear
Differential Equations by Elimination. Nonlinear Differential Equations. [TB: Ch. 4]

5.      Modeling with Higher-Order Differential Equations: Linear Models: Initial-Value
Problems. Linear Models: Boundary-Value Problems. Nonlinear Models. [TB: Ch. 5]

6.      Series Solutions of Linear Equations: Solutions about Ordinary Points. Solutions about
Singular Points. Special Functions. [TB: Ch. 6]

7.      Systems of Linear First-Order Differential Equations: Preliminary Theory. Homogeneous
Linear Systems. Non-homogeneous Linear Systems. Matrix Exponential.

8.      Numerical Solutions of Ordinary Differential Equations: Euler Methods. Runge-Kutta
Methods. Multistep Methods. Higher-Order Equations and Systems. Second-Order
Boundary-Value Problems. [TB: Ch. 7].

Textbook(s):

•          A First Course in Differential Equations by Dennis G. Zill, Brooks Cole; 10^th Edition
(March 15, 2012).ISBN-10: 1111827052

Reference Material:

•          Advanced Engineering Mathematics by Erwin Kreyszig, Wiley; 10^th Edition (August 16,
2011).ISBN-10: 0470458364

•          Differential Equations with Boundary-Value Problems by Dennis G. Zill, Michael R.
Cullen, Brooks Cole; 8^th Edition (March 15, 2012). ISBN-10: 1111827060

•          Elementary Differential Equations with Applications by C. H .Edwards, David E.
Penney, Pearson; 3^rd Edition (October 20, 2008). ISBN-10: 0136054250

Note: This content is obtained from official documents of University of Sargodha and applied on BS Computer Science for Main Campus, Sub Campuses, and Affiliated Colleges.