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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

Fundamentals of Differential Equation2Handouts5-8
Separable Equations3Handouts9-17
Homogeneous Differential Equations4Handouts18-25
Exact Differential Equations5Handouts26-33
Integrating Factor Technique6Handouts34-43
First Order Linear Equations7Handouts44-50
Quiz 1
Bernoulli Equations and Practice ExamplesHandouts51-77
Applications of First Order Differential Equations10Handouts78-88
Radioactive Decay11Handouts89-94
Application of Non Linear Equations12Handouts95-102
Higher Order Linear Differential Equations13Handouts95-102
Solution of Higher Order Linear Differential Equations14Handouts103-126
Construction of a Second Solution15Handouts127-133
Assignment No. 1
Homogeneous Linear Equations with Constant Coefficients16Handouts134-144
Method of Undetermined Coefficients Superposition Approach17Handouts145-158
Undetermined Coefficient Annihilator Operator Approach18Handouts159-179
Undetermined Coefficient Annihilator Operator Approach19Handouts159-179
Variation of Parameters20Handouts180-189
Variation of Parameters Method for Higher-Order Equations21Handouts190-198
Applications of Second Order Differential Equation22Handouts199-209
Grand Quiz
Damped Motion23Handouts210-223
Forced Motion24Handouts210-223
Examples of Forced Motion25Handouts224-240
Differential Equations with Variable Coefficients26Handouts241-247
Cauchy-Euler Equation: Alternative Method of Solution27Handouts248-254
Power Series28Handouts255-270
Power Series29Handouts255-270
Solution about Ordinary Points30Handouts271-277
Solution about Singular Points31Handouts278-295
Solution about Singular Points32Handouts278-295
Assignment No. 2
Bessel’s Differential Equation33Handouts296-304
Legendre’s Differential Equation34Handouts305-314
Systems of Linear Differential EquationsHandouts315-332
Systems of Linear First-Order Equation37Handouts333-343
Introduction to Matrices38Handouts344-362
The Eigenvalue Problem39Handouts363-370
Matrices and Systems of Linear First-Order Equations40Handouts371-388
Quiz 2
Matrices and Systems of Linear First-Order Equations41Handouts371-388
Homogeneous Linear Systems42Handouts389-401
Real and Repeated Eigenvalues43Handouts402-413
Non-Homogeneous System44Handouts414-427
Final term Examination
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