Mathematics
MTH001
Elementary Mathematics
MTH100
General Mathematics
MTH101
Calculus And Analytical Geometry
MTH201
Multivariable Calculus
MTH202
Discrete Mathematics
MTH301
Calculus II
MTH302
Business Mathematics & Statistics
MTH303
Mathematical Methods
MTH401
Differential Equations
MTH501
Linear Algebra
MTH601
Operations Research
MTH603
Numerical Analysis
MTH401 - Differential Equations
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Course Category: Mathematics
Course Level: Undergraduate
Credit Hours: 3
Pre-requisites: MTH101

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 Contents

Separable Equations, Homogeneous Differential Equations, Exact Differential Equations, Integrating Factor Technique, First Order Linear Equation, Bernoulli Equations, Applications of First Order Differential Equations, Radioactive Decay, Applications of Non Linear Equations, Higher Order Linear Differential Equations, Homogeneous Linear Equations with Constant Coefficients, Method of Undetermined Coefficients ( Superposition Approach), Method of Undetermined Coefficients (Annihilator Operator Approach), Variation of Parameters for Higher-Order Equations, Applications of Second Order Differential Equations, Damped Motion, Forced Motion, Differential Equations with Variable Coefficients, Cauchy-Euler Equation: Alternative Method of Solution, Power Series, Solution about Ordinary points, Solution about Singular Points, Bessel's Differential Equation, Legendre's Differential Equation, Systems of Linear Differential Equations, System of Linear First Order Equation, Eigen value Problem, Matrices and Systems of Linear First-Order Equations, Homogeneous Linear Systems, Linear and Repeated Eigen values, Non-Homogeneous System

Course Related Links

Some basic Differential Equations Concepts
Ordinary Differential Equation
Mathematical Operators, Transforms, Differential Equations used in Engineering Mathematics
This link contains the detailed discription of partial fraction techniques with examples. It will be helpful for you in revising the method and set you at ease while solving various differential equations
For basic definitions of Differential Equations
For applications of Differential Equations
Second Order Differential Equations
This link contains the detailed description of partial fraction techniques with examples. It will be helpful for you in revising the method and set you at ease while solving various differential equations
Very simple introduction of Differential equations
Course Instructor

Dr. Junaid Zaidi, Ph.d
University of Birmingham,
England (UK)

Books

Differential Equations with Boundary Value Problems by D. G.Zill and M. R. Cullen

Differential Equations by Richard Bronson

Differential Equations with Applications by Stanly J. Farlow

An Elementary Treatise on Differential Equations and Their Applications by Henry Thomas Herbert Piaggio