Topic outline

• Welcome to MAT211 and
  

  Welcome to MAT211 and

  

  My dear Students, 
  You are cordially welcome to my course which is so easy and more important in your life due to its necessity in the real life and also help you to proceed in your further academic career.

  
  

  

  
  
  
  

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    Books	Authors
    1. Differential Equations	Dr. B. D. Sharma
    2. Fourier Analysis with application to boundary value problems	Murray R Spiegel
    3. Advance Engineering Mathematics	John Bird

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    Semester Schedule for Spring 23

    
    

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• Group Study
  

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  •  Complex Variable Book 

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• Lecture 1
  

  Lecture 1

  
  

  Introduction:
  

  In this class, an Ordinary differential equation will be discussed. In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.

  Objectives and Outcomes

  • know about differential equation
  • use equations to solve a real-life problem
  • order and degree of ordinary differential equation
    

  Lesson Plan:

  • Discussion from lecture slide
    
  • Problem-solving
    
  • Group Work
    
  • Question and Answering
  • Home Work

  
  

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• Lecture 2 : Chapt. 01 : Oder, Degree and Formation of ODE
  

  Lecture 2 : Chapt. 01 : Oder, Degree and Formation of ODE

  Oder, Degree and Formation of ODE

  Introduction:

  In this class, the Oder, Degree and Formation of a differential equation will be discussed.

  Objectives and Outcomes:

  • find the order and degree of ordinary differential equation
  • solve 1st order ODE by using variable separation method
  • know about some real-life problem solving by this method
  • know about how to solve 1st order differential equation by the reducible separation method

  Lesson Plan:

  • Discussion from lecture slide
    
  • Problem-solving
    
  • Group Work
    
  • Question and Answering
  • Home Work

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  • Formation URL

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• Lecture 3 , Chapter 2 : Separation of variable
  

  Lecture 3 , Chapter 2 : Separation of variable

  variable separable

  Introduction:

  In this class, the variable separable of a differential equation will be discussed.

  There is no need to use two constants in the integration of a separable equation because difference of constants can be replaced by a single constant that is solution of first order and first degree equation contain only one arbitrary constant.

  Objectives and Outcomes:

  • find the order and degree of ordinary differential equation
  • solve 1st order ODE by using variable separation method
  • know about some real-life problem solving by this method
  • know about how to solve 1st order differential equation by the reducible separation method

  Lesson Plan:

  • Discussion from lecture slide
    
  • Problem-solving
    
  • Group Work
    
  • Question and Answering
  • Home Work

  
  

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• Lecture 4
  

  Lecture 4

  Reduced variable separable

  Introduction:

  In this class, the variable separable of a differential equation will be discussed.

  There is no need to use two constants in the integration of a *Reducible separable* equation because difference of constants can be replaced by a single constant that is solution of first order and first degree equation contain only one arbitrary constant.
  

  Objectives and Outcomes:

  • find the order and degree of ordinary differential equation
  • solve 1st order ODE by using  reduced variable separation method
  • know about how to solve 1st order differential equation by the reducible separation method

  Lesson Plan:

  • Discussion from lecture slide
    
  • Problem-solving
    
  • Group Work
    
  • Question and Answering
  • Home Work

  
  

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• Lecture 5
  

  Lecture 5

  Homogeneous Differential Equation
  

  Introduction:

  In this class, a Homogeneous differential equation will be discussed. An equation of the form  in which  and  are homogeneous functions of x and y of the same degree.

  Objectives and outcomes:

  • know about homogeneous equation
  • solving method of homogeneous equations
  • application of homogeneous equation

  Lesson Plan:

  • Discussion from lecture slide
    
  • Problem-solving
    
  • Group Work
    
  • Question and Answering
  • Home Work

  
  

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• Lecture 6
  

  Lecture 6

  Equation reducible to Homogeneous Differential Equation

  Introduction:

  In this class, a  reducible Homogeneous differential equation will be discussed. 

  Objectives and Outcomes:

  • know about  reducible homogeneous equation
  • solving method of reducible  homogeneous equations

  Lesson Plan:

  • Discussion from lecture slide
    
  • Problem-solving
    
  • Group Work
    
  • Question and Answering
  • Home Work

  
  

  • Non Homogeneous Page

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• Lecture 7
  

  Lecture 7

  1st order differential equation and integrating factor

  Introduction:

  In this class, the first order and integrating factor of differential equations will be discussed. 

  Objectives and Outcomes:

  • to generalize the integrating factor method from linear scalar differential equations to linear system of differential equations
    
  • to solve first-order linear differential equation
  • to make an exact differential equation
  • solving the real-life problem by IF method

  Lesson Plan:

  • Discussion from lecture slide
  • Problem-solving
  • Group Work
  • Question and Answering
  • Home Work

  
  

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• Lecture 8
  

  Lecture 8

  Bernoulli differential equation:

  Introduction:

  In this class, the Bernoulli differential equation will be discussed. 

  Objectives and Outcomes:

  • know about first-order non-linear differential equation
  • transforming non-linear to a linear equation

  Lesson Plan

  • Discussion from lecture slide
    
  • Problem-solving
    
  • Group Work
    
  • Question and Answering
  • Home Work

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• Lecture 10
  

  Lecture 10

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• Lecture 11
  

  Lecture 11

  linear differential equation with constant coefficients
  

  Introduction:

  In this class, a linear differential equation with constant coefficients will be discussed. 

  If the constant term is the zero function, then the differential equation is said to be homogeneous, as it is a homogeneous polynomial in the unknown function and its derivatives. ... A differential equation has constant coefficients if only constant functions appear as coefficients in the associated homogeneous equation.

  Objectives and Outcomes:

  • Solve the homogeneous linear differential equations with constant coefficients.
  • solve systems of linear differential equations.
  • determine the type of linear differential equation systems
  • Use the operator method to solve linear systems with constant coefficients.
  • Solve the linear systems in normal form.

  Lesson Plan

  • Discussion from lecture slide
    
  • Problem-solving
    
  • Group Work
    
  • Question and Answering
  • Home Work

  
  

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• Lecture 12
  

  Lecture 12

  Non Homogeneous differential equation with constant coefficients

  Introduction:

  In this class, a linear non Homogeneous differential equation with constant coefficients will be discussed. 

  Objectives and Outcomes:
  

  • Apply the method to solve the non-homogeneous linear differential equations with constant coefficients.
  • solve systems of linear differential equations.
  • determine the type of linear differential equation systems
  • Use the operator method to solve linear systems with constant coefficients.
  • Solve the linear systems in normal form.

  Lesson Plan:

  • Discussion from lecture slide
  • Problem-solving
  • Group Work
    
  • Question and Answering
  • Home Work

  
  

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• Lecture 13
  

  Lecture 13

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• Lecture 14
  

  Lecture 14

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• Lecture 15-16
  

  Lecture 15-16

  Laplace transformations

  Introduction:
  

  In this class, the Laplace transformation will be discussed.

  Objectives:

  • derive the Laplace transform of expression by using an integral definition
  • obtain Laplace transformation with the help of a table of Laplace transformations
  • derive the Laplace transform of the derivative of an expression
  • derive further Laplace transforms from known transforms
  • solve linear, first-order constant coefficients inhomogeneous differential equations using Laplace transform
  • construct transfer functional model
  • understand the properties of Laplace transform
  • apply Laplace transform for analyzing linear time-invariant systems
    
  • perform  operation of Laplace transform

  Lesson Plan:
  

  • Discussion from lecture slide
    
  • Problem-solving
    
  • Group Work
    
  • Question and Answering
  • Home Work

  • Assignment on Laplace Fourier Transform

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  • Laplace Transform 1st Part

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• Lecture 17 - 19
  

  Lecture 17 - 19

  Inverse Laplace Transform:

  Introduction:

  In this class, the inverse Laplace transform will be discussed. 

  Objectives:

  • derive the inverse Laplace transform of expression by using an integral definition
  • obtain  inverse Laplace transformation with the help of a table of Laplace transformations
  • derive the inverse Laplace transform of the derivative of an expression
  • derive further inverse Laplace transforms from known transforms
  • solve linear, first-order constant coefficients inhomogeneous differential equations using inverse Laplace transform
  • construct transfer functional model
  • understand the properties of  inverse Laplace transform
  • perform  operation of Laplace transform

  Lesson Plan:
  

  • Discussion from lecture slide
    
  • Problem-solving
    
  • Group Work
    
  • Question and Answering
  • Home Work

  • Inverse Laplace Transform 1st Part

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  • Inverse Laplace Transform 1st Part

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  • Application of LT

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• Lecture 20-22
  

  Lecture 20-22

  Fourier transformations and application

  Introduction:
  

  In this class, the Fourier transform will be discussed.
  

  Objectives:
  

  • Due to the properties of sine and cosine, it is possible to recover the amplitude of each wave in a Fourier series using an integral.
    

  • apply Fourier analysis to periodic and aperiodic signals:  compute the Fourier series representation of a periodic ct signal; determine the Fourier transform (ft) of a CT signal; represent a periodic DT signal  through Fourier series; find the Fourier transform (ft) of a DT signal; use and relate the properties of DT/CT Fourier series and transforms.

  Lesson Plan:
  

  • Discussion from lecture slide
    
  • Problem-solving
    
  • Group Work
    
  • Question and Answering
  • Home Work

  • Assign. on Fourier seri. first part Assignment

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• Quizzez
  

  Quizzez

  

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    Syllabus of 1st Quiz :

    
    

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• Quiz 2
  

  Quiz 2

  
  
• Quiz 3
  

  Quiz 3

  
  

  Syllabus of 3rd Quiz :

  
  

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• Assignment & Presentation
  

  Assignment & Presentation

  

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• Presentation
  

  Presentation

  
  

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• Mid Term Exam
  

  Mid Term Exam

  
  

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• Week 14 (Final Exam)
  

  Week 14 (Final Exam)