# Virtual University of Pakistan

## Featured Courses

Home > Courses > Mathematics > MTH401

## MTH401 : Differential Equations

### Course Overview

#### Course Synopsis

This course contains more than 90 interactive differential equations tools and covers the entire differential equations course, First-Order Differential Equations, Second Order Differential Equations, Linear and Nonlinear Applications, Series Solutions, and Boundary Value Problems.

#### Course Learning Outcomes

At the end of the course, you should be able to:

• Apply the concept of Fist Order Differential Equations.
• Deduce the applications of first order differential equations.
• Conclude differential equations of orders with methods of their solutions and homogenous and non-homogenous equations are explained and solved.
• Construct the applications of second order differential equations and different vibration models.
• Evaluate the differential equations of higher orders with variable coefficients and methods of their solutions, including solution in series. Also Bessel"s equation and Legendre"s equation are introduced and solved.
• Compute the concept of systems of linear differential equations and different methods of solutions is provided.

#### Course Calendar

 Topic Lecture Resource Page Introduction 1 Handouts 3-4 Fundamentals of Differential Equation 2 Handouts 5-8 Separable Equations 3 Handouts 9-17 Homogeneous Differential Equations 4 Handouts 18-25 Exact Differential Equations 5 Handouts 26-33 Integrating Factor Technique 6 Handouts 34-43 First Order Linear Equations 7 Handouts 44-50 Quiz 1 Bernoulli Equations and Practice Examples Handouts 51-77 Applications of First Order Differential Equations 10 Handouts 78-88 Radioactive Decay 11 Handouts 89-94 Application of Non Linear Equations 12 Handouts 95-102 Higher Order Linear Differential Equations 13 Handouts 95-102 Solution of Higher Order Linear Differential Equations 14 Handouts 103-126 Construction of a Second Solution 15 Handouts 127-133 Assignment No. 1 Homogeneous Linear Equations with Constant Coefficients 16 Handouts 134-144 Method of Undetermined Coefficients Superposition Approach 17 Handouts 145-158 Undetermined Coefficient Annihilator Operator Approach 18 Handouts 159-179 Undetermined Coefficient Annihilator Operator Approach 19 Handouts 159-179 Variation of Parameters 20 Handouts 180-189 Variation of Parameters Method for Higher-Order Equations 21 Handouts 190-198 Applications of Second Order Differential Equation 22 Handouts 199-209 Mid term Examination Damped Motion 23 Handouts 210-223 Forced Motion 24 Handouts 210-223 Examples of Forced Motion 25 Handouts 224-240 Differential Equations with Variable Coefficients 26 Handouts 241-247 Cauchy-Euler Equation: Alternative Method of Solution 27 Handouts 248-254 Power Series 28 Handouts 255-270 Power Series 29 Handouts 255-270 Solution about Ordinary Points 30 Handouts 271-277 Solution about Singular Points 31 Handouts 278-295 Solution about Singular Points 32 Handouts 278-295 Assignment No. 2 Bessel’s Differential Equation 33 Handouts 296-304 Legendre’s Differential Equation 34 Handouts 305-314 Systems of Linear Differential Equations Handouts 315-332 Systems of Linear First-Order Equation 37 Handouts 333-343 Introduction to Matrices 38 Handouts 344-362 The Eigenvalue Problem 39 Handouts 363-370 Matrices and Systems of Linear First-Order Equations 40 Handouts 371-388 Matrices and Systems of Linear First-Order Equations 41 Handouts 371-388 Homogeneous Linear Systems 42 Handouts 389-401 Quiz 2 Real and Repeated Eigenvalues 43 Handouts 402-413 Non-Homogeneous System 44 Handouts 414-427 Final term Examination