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Topic outline
- Mathematics-II: Calculus, Complex Variables and Linear Algebra
Mathematics-II: Calculus, Complex Variables and Linear Algebra
Welcome to Mathematics-II
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
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
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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
Class Routine
Additional Materials
WhatsApp Number: 01962199010
Semester Schedule
- Introductory Class
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
- Chapter 1
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
- Chapter 2
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
- Chapter 3
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
- Assignment 1
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).
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.
- Chapter 4
Chapter 4
Objectives:
In this chapter, we will define partial differentiation with graphical representation. We will know the properties of partial differentiation with examples and solve mathematical problems regarding this. We will also discuss homogeneous function,
Euler's theorem on homogeneous function, and solve mathematical problems using Euler's theorem.
Lecture Outcomes:
After completing this lesson, students will be able to:
- define a function of several variables
-
differentiate those functions w.r.t. different variables
- identify ordinary & partial differentiation
- denote partial derivatives & their alternative notations
- apply the concept of partial differentiation
- know Euler's theorem on homogeneous function
- solve mathematical problems using Euler's theorem
- Chapter 5
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
- Quiz 3
- Midterm Examination
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
- Chapter 6
Chapter 6
Objectives:
This chapter aims to learn about matrix & determinants, special square matrices and their differences, matrix operations (addition, subtraction, and multiplication), etc.
Lecture Outcomes:
After completing this lesson, students will be able to:
learn about the basics of matrix and determinant
classify, identify & construct different types of matrices
compute the trace of matrices
find the transpose of matrices
compute the determinant of a matrix
understand the difference between matrix and determinant
add, subtract and multiply the matrices
know symmetric and skew-symmetric matrices
construct symmetric and skew-symmetric matrices
split up a square matrix into a symmetric and skew-symmetric matrix
- Chapter 7
Chapter 7
Objectives:
The objective of this chapter is to learn about the concept of the inverse matrix, conditions for the existence of the inverse, methods for finding the inverse of a matrix, orthogonal matrix etc.
Lecture Outcomes:
After completing this lesson, students will be able to:
- find the inverse of a matrix
- check & construct orthogonal matrices
- solve mathematical problems using various types of properties of the Inverse matrix and Orthogonal Matrix
- Chapter 8
Chapter 8
Objectives:
The objective of this chapter is to learn about the elementary row operation of a matrix, row echelon form, reduced row echelon form and normal form of a matrix.
Lecture Outcomes:
After completing this chapter, students will be able to:
pick out pivots in a matrix
define & construct EMs
find the REF, RREF and NF by using ECO and ERO
find the rank of a matrix
- Chapter 9
Chapter 9
Objectives:
The objective of this chapter is to learn about solution procedure of system of linear equations, determine whether a system of linear equations is consistent or inconsistent.
Lecture Outcomes:
After completing this chapter, students will be able to:
recognize a linear equation in n variables
classify a system of linear equations
write a system of linear equations in matrix form.
know different methods of solution
determine whether a system of linear equations is consistent or inconsistent
write a given system of linear equations in the form Ax=b and use it to solve for x
find a general solution of a consistent system
- Assignment 2
Assignment 2
Please Solve the exercises of inverse matrix, rank of matrices, system of equations.
Assignment-3
Submit all your exercises and problems on Fubinis Theorem based on Multiple Integration discussed on your slides and classes.
Assignment-4
Submit exercise problems based on partial differentiation and complex variables(H.W. problems also included).
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
- Chapter 10
Chapter 10
Objectives:
The objective of this lecture is to learn about definition, properties and computation process of eigenvalues & eigenvectors of a matrix.
Lecture Outcomes:
After completing this lecture, students will be able to:
- define eigenvalue problems
- find characteristic polynomial for matrices
- solve matrix eigenvalue problems analytically using characteristic polynomial approach
- apply matrix eigenvalue theorems
- Chapter 11
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
- Chapter 12
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