Topic outline

  • Mathematics-II: Calculus, Complex Variables and Linear Algebra

    Welcome to Mathematics-II

      

      


    • Announcements Forum

      Click here for Online Class

      Online Class 

      November 1 – December 30, 2023

      Time zone: Asia/Dhaka

      Google Meet joining info

      Video call link: https://meet.google.com/wnn-mpzr-wkz

      Or dial: ‪(US) +1 510-250-2693‬ PIN: ‪798 975 538‬#

      Online class recording link

      https://drive.google.com/drive/folders/1o3VsO8LbGJr44UOkOpnwa_IE-O82XbuF?usp=sharing


    •  Definite Integral
             Gamma & Beta Function  
                
      Multiple Integral 
      Partial Differentiation

      Complex Number
      Matrix and Determinant 
      Inverse Matrix
      Rank of Matrix

      System of Linear Equations
      Eigen Values and Eigen Vectors
      Linear Dependence & Linear Independence 
      Linear Transformation 

                    
      		 

    • Name                           : Tapan Biswas
      Designation            : Lecturer (Mathematics)
      Department            : CSE
      Office Address      : Room-745, AB-04, DSC, DIU                                  
      Contact No.             : 01632228055
      Email                            : biswas.cse0468.c@diu.edu.bd  

    • Course Information


    • Instructions/Guideline for the course:

      • All the students registered for this course have to enroll in BLC.
      • Students can find all the course materials from BLC.
      • All the students have to submit the soft copy of their "Assignment" in BLC under  assignment section created here and for this they will be graded here.
      • One discussion or feedback forum is created under each of the lecture, students have to give their feedback on this forum and marks will be given for their feedback.
      • Any announcement regarding the course will be posted on BLC. So they have to keep themselves always active on BLC.
      • All the quizzes and presentation will be held on online (BLC) and it will be announced before the class.
      • The question pattern and the syllabus for the quizzes, midterm and final exam is given here under each of the section (quizzes, midterm and final).
      • There are midterm and final exam preparation  forum under these sections where students can discuss with each other about their midterm and final exam syllabus, any problem regarding the exam etc.

    • Course Rationale

      It is offered as the most important mathematical course for CSE students throughout all universities of the world. This course provides the basic tools and techniques and includes sufficient theory to enable the methods to be used in situations not covered in the course. The course content deals with partial differentiation, multiple integral, gamma-beta function, complex number system, linear algebra etc. The material in this course is essential for further study in mathematics and statistics.


    • Course Objectives

      After completing  this course, the student should be able to: 

      • develop fluency in concepts and techniques of calculus, linear algebra and complex numbers
      • provide students with mathematical training for all further study in science/engineering and its applications.
      • become familiar with theories and principles behind calculus, complex variable and linear algebra

    • Course Outcomes (CO's)

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

      • CO1: Understand the basic concept of Matrix, operation of matrix, Gamma- Beta function and Complex Variable.
      • CO2: Demonstrate the way of finding Rank, Inverse of a matrix, modulus, argument and different form of complex number.
      • CO3: Apply different method to obtain eigen value, eigen vector of matrix, solve system of linear equations and successive differentiation.
      • CO4: Evaluate the Multiple Integrals, Application of Matrix and Integration, explain Linearity of transformation and dependency of vectors.

    • Assessment Plan


    • Syllabus


      Click here to see the detailed Course Syllabus:

      Prerequisite: 

      Mathematics-I

    • Reference Books


        1. Calculus:  Advanced Calculus, Schaum's Outlines, Howard Anton 10th Edition
          1. Complex Variable: Complex Variable, Schaum’s Outline Series
            1. Linear Algebra: Elementary Linear Algebra, Howard Anton 9th Edition

          2. Class Routine


          3. Additional Materials


            WhatsApp Number: 01962199010


          4. Semester Schedule


        2. Introductory Class


          • Objectives:

            At the very beginning of each semester, it needs to introduce myself to the students. It's also important to understand the students' abilities, performance, strengths, and weaknesses at the very beginning of the semester. As a result, it's easy to reach the students. So a nice introductory class help to buildup connection between students and teacher which make it easier to continue the whole course.
            When the students are starting a new course, they have some common questions like that,
                 1.     Why will they read this course?
                 2.     Have any real-life applications for this course?
            I think these are crucial questions and we must fulfill their demand.
            Hence, in my introductory class, I always try to buildup a clear understanding among the students and try to reach their emotions, feelings, strengths, and weaknesses. Clearly, I try to show the necessity of this course and its real-life application of this course. So, I think at the very beginning of the semester, an excellent introductory class helps to make my course easier than the other classes.

            Lecture Outcomes:

            After completing this lesson, students will be able to:

            • know the overview of this course

            • know the application of this course in real life

            • know course activity

        3. Chapter 1


          • Objectives:

            This chapter will discuss the definition and geometrical interpretation of definite integral. We will also discuss properties of definite integral with example. We will solve mathematical problems related to the definite integral.

            Lecture Outcomes:

            After completing  this lesson, students will be able to: 

            • know definition and types of integration
            • define and interpret definite integral
            • identify and distinguish different properties of definite integral with example
            • evaluate the definite integral of a function applying the rules of integration

          • Supportive Materials

                       Lecture Note

                       Reference Reading

        4. Chapter 2


          • Objectives:

            In this chapter, we will discuss the concept of gamma and beta functions with geometrical representation. We will discuss the properties of gamma and beta functions with example. We will show the relation between gamma and beta functions and solve mathematical problems.

            Lecture Outcomes:

            After completing this lesson, students will be able to:

            • identify improper integral
            • familiar with gamma and beta function
            • know the relation between gamma and beta function
            • know important properties involving gamma and beta functions
            • solve mathematical problems using properties of gamma and beta functions
            • evaluate certain integrals using gamma and beta function

          • Supportive Materials

            Lecture Note

                    Gamma Function

                     Beta Function

            Reference Reading

                       Gamma Function
                            Beta Function

        5. Chapter 3

          • Objectives:

            In this chapter we will formally define the double integral as well as giving a quick interpretation of the double integral. We will show how Fubini’s Theorem can be used to evaluate double integrals where the region of integration is a rectangle. We will start evaluating double integrals over general regions, i.e. regions that aren’t rectangles. We will define the triple integral. We will also illustrate quite a few examples of setting up the limits of integration from the three dimensional region of integration.

            Lecture Outcomes:

            After completing this lecture, students will be able to:

            • evaluate double and triple integrals of functions of several variables
            • compute double integrals using iterated integrals, reverse the order of integration
            • compute triple integrals using iterated integrals, reverse the order of integration
            • apply double and triple integration techniques in evaluating volume of a solid

          • Supportive Materials

                        Lecture Note

                        Reference Reading

        6. Assignment 1

          • Assignment 1


            Solve the problems which I have attached herewith, take photo, make a pdf, and then submit it here deadline (maximum file size 10 MB).

          • Assignment_1
            Opened: Wednesday, 27 September 2023, 11:19 AM
            Due: Saturday, 14 October 2023, 12:00 AM
          • Assignment Instructions Chat

            Good noon, my dear students.

            Please make a cover page with your name, id, course code, section and after completing assignment, take my signature. Afterwards, take photo and make pdf and submit it. Thank you.

        7. Chapter 4

        8. Chapter 5


          • Objectives:
            In this chapter, we will define complex numbers with graphical representation. We will know the different forms of a complex number and will transform from one form to another. We will also illustrate complex numbers on an Argand diagram and will find out the modulus and argument of a complex number. We will discuss the polar form of a complex number with geometrical representation, the transformation from the polar form to another form, and perform different operations in the polar form. We will also discuss the exponential form of a complex number with Euler's identity.  

            Lecture Outcomes:

            After completing this lesson, students will be able to:

            • get introduced to complex number
            • plot a complex number in an argand diagram 
            • write a complex number in  5 different forms
            • convert a complex number from one form to another
            • find the modulus and argument of a complex number
            • perform different operations in polar form
            • convert a complex number from exponential form to another form

          • Supportive Materials

        9. Quiz 3

          • Midterm Examination



             

            • Syllabus of Mid Term Exam
              Dear Students, Good Morning. Your Midterm Exam Syllabus has been stated here. Thank you all.
              • Gamma Function and Beta Function
              • Multiple Integral
              • Partial Differentiation
              • Complex Number

          • Chapter 6

          • Chapter 7


          • Chapter 8


          • Chapter 9


          • Assignment 2

            • Assignment_5
              Opened: Monday, 20 November 2023, 12:00 AM
              Due: Thursday, 23 November 2023, 11:59 PM


              Please Solve the exercises of inverse matrix, rank of matrices, system of equations.

            • Assignment_3
              Opened: Wednesday, 20 September 2023, 12:00 AM
              Due: Friday, 13 October 2023, 12:00 AM

              Assignment_3

              Assignment-3

              Submit all your exercises and problems on Fubinis Theorem based on Multiple Integration discussed on your slides and classes.


            • Assignment_4
              Opened: Wednesday, 20 September 2023, 12:00 AM
              Due: Friday, 13 October 2023, 12:00 AM

              Assignment-4


              Submit exercise problems based on partial differentiation and complex variables(H.W. problems also included).

            • Quiz_3 Assignment
              Opened: Wednesday, 22 November 2023, 9:30 PM
              Due: Wednesday, 22 November 2023, 10:20 PM

              Here I upload your question on Wednesday at 6.00 pm.

              Your Quiz Question Link

              https://drive.google.com/file/d/18S6o-zB8xt6lU5rtsMOyfkWgpGSxtmKM/view?usp=drive_link

            • Presentation Slide Assignment
              Opened: Monday, 20 November 2023, 12:00 AM
              Due: Friday, 24 November 2023, 12:00 AM

          • Chapter 10


          • Chapter 11


            • Objectives:

              The objective of this chapter is to learn about the definition, properties, and computation process of linear dependence and linear independence. We will check the linear dependency of vectors, find a linear dependence relation among the vectors, and express one vector via others.

              Lecture Outcomes:

              After completing this chapter, students will be able to:

              • understand the concept of linear dependence and linear independence
              • understand the relationship between linear independence and pivot columns / free variables.
              • determine whether a set of vectors is linearly independent or linearly dependent
              • express one vector in a linearly dependent set as a linear combination of the other vectors in the set


              1. Lecture Note 
              2. https://drive.google.com/file/d/1Pyi-ITb2rrtYTscjKfdkBoH2hu7lVcpe/view?usp=drive_link
              3. Reference Reading

          • Chapter 12


            • Objectives:

              The objective of this chapter is to learn about the definition, properties, and computation process of linear transformation. We will discuss composite linear transformation, and inverse linear transformation and will solve the related problems.


              Lecture Outcomes:

              After completing this lecture, students will be able to:

              • get introduced to transformation
              • know the classification of transformation
              • know Linear Transformation by means of the Matrix
              • know different properties of Linear Transformation Matrix with example
              • solve mathematical problems using properties of Linear Transformation Matrix
              • know composite linear transformation
              • find an inverse linear transformation
              • solve problems related to composite LT and inverse LT

          • Final Examination

            • Topic 19

              • Topic 20