Topic outline

  • Introduction

    Title:  Mathematics – II : Linear algebra & coordinate geometry

    Code:  MAT 121                                                                                                                       Credit:   03.00

    Instructions/Guidelines for this course: 

    1. All students registered for this course have to enroll in Moodle
    2. Students can find all the course materials from Moodle.
    3. All of the students have to submit the soft copy of their "Assignment" in Moodle under assignment section created here.


    The course will be  conducted by:  

        

                                         Faculty:  Mohammad  Salek  Parvez

    Designation:  Assistant Professor

    Department:  GED

    Faculty:  FSIT

    Off. address: R#307, DT-5, MC

    Mobile No:  01552327706

    Email:sparvez@diu.edu.bd ; sparvez@daffodilvarsity.edu.bd

    ·



    Welcome Note : Plz, listen :  

     To know further about the importance of this course,  I  refer you to the following links:


      

    Objectives:            

    It is offered as the most important mathematical course for CSE students throughout all universities of the world.  It helps them to become expert at (i) making programming languages, (ii) networking, (iii) robotics, (iv)web-developing, (v) computer graphics and (vi) many other discourses.

    Outcomes :  

    After a successful completion of this course, students will be able to :

    1.   Evaluate so easily a good number of improper integrals useful in different engineering courses ;

    2.   Compute area, volume and similar things using the concept of multiple integration ;

    3.   To clarify behavior, regarding extreme values, of natural phenomena with the help of knowledge of max/min/inflex etc ;

    4.   Work with c-numbers in 5 different ways ;

    5.   Use matrices & vectors to depict physical phenomena ;

    6.   Understand what happens to objects when a dimensional shipment occurs ;

    7.   Define a pre-planned change in structures in case of a dimensional shipment.   

    Syllabus:

    Complex Variables : Complex numbers & functions, Complex differentiation, Line integral.  

    Calculus : Extrema & Inflexes, Partial Differentiation, Beta & Gamma functions, Multiple integration. 

    Linear Algebra :Matrix ----Introduction, Classification, Special types, Operations & EO, Inverse, Rank- RREM-NF ;  SLE --- Introduction, Classification, Solution ; Vector space --- Introduction& Linear Combination of vectors  ; Linear Transformation--- Basics, Composition, Inversion, Special Linear Operators ; Eigenvalues & Eigenvectors----Basics, Evaluation.

     Course Requirements  :

    ·*       Completion of  Higher Algebra  at  Intermediate level. Or, Completion of   A-level  mathematics.

    ·*       Completion of   Mathematics-I   at  DIU under FSIT/ FE..

    ·*      A textbook on this course.

    · *     Regular attendance.


    Course Assessment Plan

     Methods to assess a student’s performance in this course will consist of the following steps.

    A)    On-going Assessment :

    Assessment Methods

    Weighting

    Description of Assessment Tasks

    Class Attendance

    7%

    Discussions ( in class & online ) will  ensure, encourage & reward students’ activeness in learning and engagement with others.

     

    Assignments

     

    5%

    Assignments will                                                                                   : enhance students’ ability to solve problems without teacher’s help ;  : help students’ group study or interaction with other students.

     

    Presentations

     

    8%

    Verbal presentation by individual students  will                                       : test the students’ ability to present what they understand throughout the course ;                                                                                : find out their lacks in expressing a known thing ;                                : make them accustomed to face an audience ;                                      : give them an excellent preparation and skills for future professional meeting/conference .

    Total

    20%

     

     

    B).  Overall Assesment :

    Assessment Methods

    Weighting

    Description of Assessment Tasks

     

    Quiz: (1st +2nd +3rd )/3

     

    15%

    Quizzes will  consolidate                                      : their learning ;                                                    :  test their basic concepts ;                                :  reward students’ ability to solve problems

    Midterm Examination

    25%

    The midterm examination will justify students’ progress of subject based knowledge.

    Final Examination

    40%

    The final examination will test the students’ overall performance throughout the course. 

    Total

    80%

     

     

    Adding all weights a grade will be conferred to the student. The grading policy is the same  as suggested by the UGC, Bangladesh.

    Recommended Books and Materials:

    Subject

    Text Book

    Reference Book

    Coordinate Geometry

    Titas Series

    Calculus

    By

    Weir, Maurice, et al., Thomas’

    Addison-Wesley, 2010

    12th  edition


    Linear Algebra

    Linear Algebra

    A first Course

    ( 4th  edition )

    By

    Mohammad Salek Parvez

    Linear Algebra

    By

    Seymour Lipschutz

    Schaum’s Outline Series

    Online text materials may be included.

    Wolfram Alpha ( a software from internet ) is being referred.

     

     



    • Google Class-room :


      class  code meet-link
      sec-A
      eu23o3t
      		https://meet.google.com/lookup/ajiqinsjh5


      N.B.  Online recordings of classes are available in google class-rooms.

  • Lecture -1: Matrix -1

     Introduction :

    ·        

     

    Objectives  :

    ·         To know about how to make a matrix

    ·         To become familiar  with different parts of a matrix

    ·         To demarcate a matrix from a determinant.

               To classify matrices.

     

    Lesson Plan: 

    ·         Lecture ( classroom/Online ) ;

    ·          Group –discussion ;

    ·         Problem based teaching ;

    ·         Solving exercises.

     

    Lecture Notes :

    ·         PPT ( link) : see at the bottom. The file explains the ins and outs about the basics of matrices. The 

             materials will require 1 more class. If  you can master it , the rest of matrices will become easy to 

              you. So go over this portion once and again until all become clear to you like crystal.  

    ·         Page 4-8 (text book)

     

     

    Activities

    ·         Quiz ( offline/online)

    ·         Discussion-forum

    ·         Assignment ( SQ : #1- # 40, page-9, text book)      

     

     




    ·         


  • Lecture-2, 3 : Matrix -1 (continued)

    Introduction :

    ·         

     

     Objectives :

    ·         To know about how to classify  matrix

    ·         To identify & construct different types of matrices

    ·         To compute trace of matices

     

    Lesson Plan: 

    ·         Lecture ( classroom/Online ) ;

    ·          Group –discussion ;

    ·         Problem based teaching ;

    ·         Solving exercises.

     

    Lecture Notes :

    ·         PPT ( link): see below

    ·         Page 14-25 (text book)

     

     

    Activities

    ·         Quiz ( offline/online)

    ·         Discussion-forum

    ·         Assignment ( SQ : #1- # 10, page-18 ; SQ : #1- # 10, p-24 ; SQ : #1- # ,p-26, text book  )

     


     



  • Lec-4: Matrix -2: Operations

    Introduction :

    ·         

     

     

    Objectives :

    ·         To know about scalar multiplication

    ·         To  add/subtract  matrices

    ·         To multiply matrices

     

    Lesson Plan: 

    ·         Lecture ( classroom/Online ) ;

    ·          Group –discussion ;

    ·         Problem based teaching ;

    ·         Solving exercises.

     

    Lecture Notes :

    ·         PPT ( link): see below. 

    ·         Page 8-14 (text book)

     

     

    Activities

    ·         Quiz ( offline/online)

    ·         Discussion-forum

    ·         Assignment ( #1-#9, Exercise-2, text book)

     



  • Lec-5 : Matrix -3: Symmetric & skew-symmetric matrices

     Introduction :

    ·         

     Objectives  :

    ·         To construct symmetric matrix of any order

    ·         To construct skew- symmetric matrix of any order

    ·         To split a matrix into 2 parts : symmetric matrix & skew-symmetric

     

    Lesson Plan: 

    ·         Lecture ( classroom/Online ) ;

    ·          Group –discussion ;

    ·         Problem based teaching ;

    ·         Solving exercises.

     Lecture Notes :

    ·         PPT ( link)

    ·         Page 21-23 (text book)

     Activities : 

    ·         Quiz ( offline/online)

    ·         Discussion-forum

    ·         Assignment ( #65, Exercise-2, text book)

     External resources:

    https://en.wikipedia.org/wiki/Symmetric_matrix


     



  • Lec-6 : Matrix -4: Inverse matrices

    Introduction :

    ·         

      Objectives  :

    ·         To understand the meaning of inverse matrices

    ·         To calculate inverse matrix order 2x2

    ·         To calculate inverse matrix order 3x3  and higher

    ·         To  understand especial properties of inverse matrices 

     Lesson Plan: 

    ·         Lecture ( classroom/Online ) ;

    ·          Group –discussion ;

    ·         Problem based teaching ;

    ·         Solving exercises.

     Lecture Notes :

    ·         PPP : see below at the resource section. Try to understand every word of it. Insha-Allah, you will  

             become expert in computing the inverse of matrices . 

    ·         Page 30-34 (text book)

    Activities:

    ·         Quiz ( offline/online)

    ·         Discussion-forum

    ·         Assignment ( #21- #25, Exercise-2, text book)

     External resources :

    https://www.mathsisfun.com/algebra/matrix-inverse-minors-cofactors-adjugate.html


  • Lec-7 : Matrix -5: Orthogonal matrices

     Introduction :

    ·        

    Objectives  :

    ·         To become familiar with orthogonal  matrices  of any order

    ·         To construct orthogonal  matrices  of any order

    ·         To understand special properties & importance  of  orthogonal  matrices

     

    Lesson Plan: 

    ·         Lecture ( classroom/Online ) ;

    ·          Group –discussion ;

    ·         Problem based teaching ;

    ·         Solving exercises.

     

    Lecture Notes :

    ·         PPT ( link)

    ·         Page 35-37 (text book)

     

     

    Activities

    ·         Quiz ( offline/online)

    ·         Discussion-forum

    ·         Assignment ( #73, 75, 77,  Exercise-2, text book)

     


    External resources :

    https://medium.com/jun-devpblog/linear-algebra-9-properties-of-orthogonal-matrices-840b1d28ac20

     


  • Lec- 8, 9: Matrix -6: Pivot, EM, RREM, ERO, ECO

    Introduction :

    ·         

     Objectives  :

    ·         To pick out pivots in a matrix

    ·         To define & construct EMs

    ·         To define RREMs

    ·         To operate EOs in a matrix

    ·         To construct equivalent matrices

     Lesson Plan: 

    ·         Lecture ( classroom/Online ) ;

    ·          Group –discussion ;

    ·         Problem based teaching ;

    ·         Solving exercises.

    Lecture Notes :

    ·         PPP : Added below as a file under resource subsection. It will clarify the objectives to you so that you can achieve the required outcomes.   

                Page  7,9,41-42 (text book)

     Activities

    ·         Quiz ( offline/online)  

               Discussion-forum        


  • Lec-10, 11: Matrix -8: Rank, RREF, NF

    Introduction :

    ·         Give an audio of yourself/or, add 2-3 line statement

     

     

    Objectives  :

    ·         To signify the rank of  a matrix

    ·         To convert a matrix into its RREF 

    ·         To  convert a matrix into its NF 

    ·         To operate EOs in a matrix

     

    Lesson Plan: 

    ·         Lecture ( classroom/Online ) ;

    ·          Group –discussion ;

    ·         Problem based teaching ;

    ·         Solving exercises.

     

    Lecture Notes :

    ·         PPT ( link)

    ·         Page ,43-47 (text book)

     

     

    Activities

    ·         Quiz ( offline/online)

    ·         Discussion-forum

    ·         Assignment ( #43, Exercise-2, text book)

     

    ·         External resources :

                https://en.wikipedia.org/wiki/Rank_(linear_algebra)

               


  • Lec-12,13 : Systems of Linear Equations

    Introduction :

    ·         Give an audio of yourself/or, add 2-3 line statement

     Objectives  :

    ·         To define & classify a  SLE

    ·         To solve a SLE

    ·         To write the GS, and then some PSs  of a redundant system

    ·         To apply SLE 

     

    Lesson Plan: 

    ·         Lecture ( classroom/Online ) ;

    ·          Group –discussion ;

    ·         Problem based teaching ;

    ·         Solving exercises.

     

    Lecture Notes :

    ·         PPP : Added below as a file under resource subsection. 

    ·         Chapter -3 (text book)


    Activities

    ·         Quiz ( offline/online)

    ·         Discussion-forum

    ·         Assignment ( #1- #31, Exercise-3, text book)

     

    ·        External resources :

          https://en.wikipedia.org/wiki/System_of_linear_equations

         https://www.youtube.com/watch?v=hagIIYC1JiM&ab_channel=ENGINEER%27SACADEMY 

    • SLE File

      Read it minutely, before you read anything else on this topics.

  • Lec-14: Linear Combination of vectors

    Introduction :

    ·         

     Objectives  :

    ·         To know about vectors

    ·         To identify Vectors’ Linear combination 

    ·         To  identify  linear dependence  and independence of vectors 

    ·         To  express 1 vector in terms of others

    Lesson Plan: 

    ·         Lecture ( classroom/Online ) ;

    ·          Group –discussion ;

    ·         Problem based teaching ;

    ·         Solving exercises.

     Lecture Notes :

    ·         PPT ( link)

    ·         Page  133-136, 142-144 (text book)

     Activities

    ·         Quiz ( offline/online)

    ·         Discussion-forum

    ·         Assignment ( #1 #10, Exercise-6, text book)

    ·External resources :

            https://onlinemschool.com/math/library/vector/linear-independence/

         


    • Lec-15, 16, 17: Linear Transformation

      Introduction :

      ·        

       

       

       Objectives  :

      ·         To conceptualize vector space

      ·         To understand transformation  

      ·         To identify LTs

      ·         To formulate LT  from matrices

      ·          To formulate LT  from matrices

      ·         To composite  LTs

      ·         To find inverse LT

       Lesson Plan: 

      ·         Lecture ( classroom/Online ) ;

      ·          Group –discussion ;

      ·         Problem based teaching ;

      ·         Solving exercises.

       

      Lecture Notes :

      ·         PPP : attached under "activity" section as LT by name. Go thorough it once & again until you've no complexity.

      ·         Page  110,184, 209-210, 215, 220-221 (text book)

       

      Activities

      ·         Quiz ( offline/online)

      ·         Discussion-forum

      ·         Assignment ( #1,2,9, Exercise-9, text book)

       ·         External resources :


      • LT File

        Read it first ; then any other book on this topics. 

      • Practice File

        Try to answer questions of this file.

    • Lec-18, 19 : Common Linear Operators

      Introduction :

      ·         Give an audio of yourself/or, add 2-3 line statement

      Objectives  :

               To identify such operators 

      ·         To find the effect of them 

      ·         To composite them

       

      Lesson Plan: 

      ·         Lecture ( classroom/Online ) ;

      ·          Group –discussion ;

      ·         Problem based teaching ;

      ·         Solving exercises.

       

      Lecture Notes :

      ·         PPT ( link)

      ·         Page 228-237 (text book)

       

      Activities

      ·         Quiz ( offline/online)

      ·         Discussion-forum

      ·         Assignment ( #1-#5, Exercise-10, text book)

       

      ·         External resources :


      • Lec-20 : Eigenvalues

        Introduction  :

        ·         

        Objectives  :

        • To evaluate eigenvalues of a matrix
        • To compute evs of powers of  a matrix
        • To establish the relationship between evs, trace & determinant of a matrix

        Lesson Plan: 

        ·         Lecture ( classroom/Online ) ;

        ·          Group –discussion ;

        ·         Problem based teaching ;

        ·         Solving exercises.

         Lecture Notes :

        ·         Follow the PPP  enlisted as a resource activity. 

        ·         Page ,244-251 (text book)

         Activities

        ·         Quiz ( offline/online)

        ·         Discussion-forum

        ·         Assignment ( #1-#4, Exercise-10, text book)

         External resources :

        ·     https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors

             


        • Eigenvalues File

          1. A smooth introduction to eigenvalues.
          2. An almost complete treatise on eigenvalues. 

        • EvProb File

          Practise problems given in this file.

      • Lec-21 : Eigenvectors

        Introduction  :

        ·         Give an audio of yourself/or, add 2-3 line statement

         

        Objectives  :

        • To compute eigenvectors
        • To diagonalise a matrix
        • To give physical interpretation to all these

        Lesson Plan: 

         Lecture ( classroom/Online ) ;

        ·Group –discussion ;

        · Problem based teaching ;

        · Solving exercises.

         

        Lecture Notes :

        ·         PPT ( link)

        ·         Page ,259-271 (text book)

         

        Activities

        ·         Quiz ( offline/online)

        ·         Discussion-forum

        ·         Assignment ( #1-#4, Exercise-10, text book)

        External resources :

        https://www.mathsisfun.com/algebra/eigenvalue.html


        • lec 25 : Q & A forum

        • Works & Evaluation

          This page informs about quizzes & assignments.

        • Final Evaluation

        • Lec-22, 23, 24 : Coordinate Geometry

          • Coordinate Geometry File

            This file deals with: 

            1. Basics of coordinates
            2. 2nd degree general equation in 2 variables in details
            3. Coordinate systems in 3D