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Course Module of Discrete Structure
Course Module
of
Discrete Structure
[12 Week Course]
Course Starting from 10th
September 2022
[1 Day Demo Classes]
Days: Monday/Tuesday/Wednesday Time: 8.00PM
Discrete Structure
By Dr Sonendra Gupta | Author of 22 Books on Mathematics
Objective of Course: This course introduces the applications of discrete mathematics
in the field of computer science. It covers sets, logic, proving techniques, Combinatorics,
functions,
Relations, Graph theory and algebraic structures. These
basic concepts of sets, logic functions, and graph theory apply to Boolean algebra, logic networks while the advanced concepts of functions and algebraic
structures are applied to finite state machines and coding theory.
Ø To
introduce the idea of applying Set theory, function, and Relation in the field
of Engineering.
Ø To
introduce the fallouts of algebraic structures in the field of Computer
applications.
Ø To
develop the tool of Graph theory for learning advanced computational
mathematics.
Course
Layout
Chapter-1 Set Theory and Relation
v
Set theory
v
Countable and Uncountable sets
v
Venn Diagrams
v
Relations and Properties
v
Equivalence relation
v
Partial ordering relation
v
Function and Type of functions
v
Inverse Function
v
Job-Scheduling Problems function
v
Mathematical induction
v
Pigeonhole Principal
v MCQ Test
Chapter-2 Algebraic Structures
v
Algebraic Structures
v
Group theory
Ø
Quasi Group
Ø
Semi Group
Ø
Monoid Group
Ø
Abelian and Non-Abelian Group
v
Properties of Group
v
Subgroup
v
Cyclic Group
v
Coset, Right and Left Coset
v
Permutation Group
v
Homomorphism and isomorphism of Groups
v
Rings and Fields
v MCQ Test
Chapter-3 Algebra of Logic and Boolean algebra
v
Propositional Logic
v
logical operation, Truth Table
v
Tautologies, Contradictions
v
Algebra of Proposition
v
logical implications and Logical equivalence
v
Predicates
v
Universal and existential quantifiers
v
Boolean Algebra
v
Properties of Boolean Algebra
v MCQ Test
Chapter-4 Graph Theory
v
Introduction and basic terminology of graphs
v
Planer graphs, Multigraphs, and weighted graph
v
Paths, Cycles and connectivity
v
Eulerian paths and circuits
v
Hamiltonian paths and circuits
v
Graph coloring, chromatic number
v
Isomorphism and Homomorphism of graphs
v
Shortest path in weighted by Dijkstre’s Algorithm
v
Minimum Spanning Tree by Prism Algorithm
v
Minimum Spanning Tree by Kruskals Algorithm
v MCQ Test
Chapter-5 Relation, Poset and Lattices
v
Relations and Properties
v
Equivalence relation
v Partial ordering relation
v Partial Order Set (Poset)
v Hass Diagram of Partially ordered
set
v Well-ordered set
v Lattice
v properties of Lattices
v Bounded Lattice and complemented lattices.
v MCQ Test
Chapter-6 Combinatorics
v
Introduction of Permutation
v
Introduction of Combination
v
Binomial Theorem and Multinomial Coefficients
v MCQ Test
Chapter-7 Recurrence Relation and Generating Function
v
Discrete Numeric Function
Ø
Sum of Numeric Function
Ø
Multiplication of Numeric Function by Constant
Ø
Product of Numeric Function
Ø
Forward and Backward Numeric Function
v
Convolution of Numeric Function
v
Generating Function
Ø
Sum of GF
Ø
Multiplication of GG by Constant
Ø
Product of GF
v
Operations on Generating Function
v
Recurrence Relation
v
Homogeneous Recurrence Relation (Linear Recurrence Relation)
v
Non-Homogeneous Recurrence Relation (Non-Linear Recurrence Relation)
v
Particular Solution of Recurrence Relations
v MCQ Test
How to Enroll in the Course…
2. All the information filled correctly
3. 2-Days Demo Classes
4. Final Registration by Google Form [Link Given on Same Time]
5. 4-Hours Weekly classes
Online Platform…
Google
Meet [Download Google Meet from Google play store]
Follow
the following steps:
Study Material
Full Study Material and some
Recorded video Lectures are provided.
Fees Structure
Overall
Charges 5000/- in Indian Currency
1st
Installment 2000/- at final
Registration
2nd
Installment 3000/- after 10
Days of Final Registration
Online Payment Mode [Ask from Sir/Madam]:
1. Google Pay by QR Scan
2. Paytm by QR Scan
Online Assistant:
WhatsApp/Call: +91-9893455006
Dr. Sonendra Gupta
Dr. Sonendra Gupta, HOD (Department of Mathematics) in Oriental College of Technology, Bhopal (MP). He received Ph.D., M.Phil(Maths), M.Sc.(Computer Science) and
M.Sc.(Maths) degree. He has 20 years of teaching experience.
He is equipped with an extraordinary caliber
and appreciable academic potency. He has always been a topper throughout his
educational career. He secured the Seventeenth position in Bhopal merit, in the intermediate examination in 1995.
He ranked as a topper in the university 1997 in
B.Sc. II year. He has authored 20 popular books of Mathematics titled “Advanced Mathematics”, “Engineering
Mathematics-I”, “Engineering Mathematics-II”, Engineering Mathematics-III, Differential
equation part-II, Vector Analysis and
Geometry, Business Mathematics, Abstract
Algebra, Numerical Analysis, etc.
for numerous universities, viz. RGPV Bhopal, U.P. Technical University,
Barkatullaha University, Bhopal, and Chhattisgarh University.
Friday, 17 July 2020
Engineering Mathematics-I Course Module
Course Module
of
Engineering Mathematics-I
[12-Week Course]
Course Starting from 1st
December 2022
Days: Monday/Tuesday/Wednesday Time: 6.00PM
Engineering Mathematics - I
By Dr Sonendra Gupta | Author of 22 Books
of Mathematics
Objective of Course: The objective of this course is to familiarize prospective engineers with techniques in calculus, multivariate analysis, and
linear algebra. It aims to equip the students with standard concepts and tools
at an intermediate to advanced level that will serve them well towards tackling the more advanced level of mathematics and applications that they would find useful
in their disciplines. More precisely, the objectives are:
Ø To
introduce the idea of applying differential and integral calculus to notions of
curvature and to improper integrals. Apart from some applications, it gives a
basic introduction to Beta and Gamma functions.
Ø To
introduce the fallouts of Rolle’s Theorem that is fundamental to the application of
analysis to Engineering problems.
Ø To
develop the tool of power series and Fourier series for learning advanced
Engineering Mathematics.
Ø To
familiarize the student with functions of several variables that is essential
in most branches of engineering.
Ø
To develop the essential tool of matrices
and linear algebra in a comprehensive manner.
Course
Layout
Chapter-1 Calculus-I
v
Elementary Results of Calculus
v
Rolle’s and Lagrange’s mean value theorem
v
Maclaurin’s theorem
v
Taylor’s Series
v
Partial Differentiation and Euler’s theorem
v
Composite and Total Differentiations
v
Taylor’s Series of Two variable functions
v
Maxima and Minima of Two Variables
v
Maxima and Minima of Three Variables
v
Lagrange’s Multipliers Method
v MCQ Test
Chapter-2 Calculus-II
v
Definite integral as a limit of the sum
v
Summation of Series
v
Beta function and Properties
v
Gamma Function of Properties
v
Multiple Integral
Ø
Double integral and their applications
Ø
Triple Integral and their applications
Ø
Applications of Cylindrical and Spherical Coordinate System
v
Change the order of integral
v
Evaluate the integral for Surface and Volume Revolution
v MCQ Test
Chapter-3 Sequence and Series
v
Introduction of Sequence and Series
v
Test of Convergence of Series
Ø
Geometric Test
Ø
Leibnitz Test
Ø
p-Series Test
Ø
Comparison Test
Ø
D’Alembert’s Ratio
Test
Ø
Raabe’s Test (Higher
Ratio Test)
v
Power series and Radius of convergence
v
Convergence of Logarithmic Series
v
Convergence of Exponential Series
v
Convergence of Trigonometric Functions (Sine, Cosine)
v MCQ Test
Chapter-4 Fourier Series
v
Introduction of Periodic function, Odd Function, Even Function
v
Fourier Series and Types of Fourier Series
Ø
Full Range Fourier Series
Ø
Dirichlets Condition
Ø
Fourier Series of Discontinues Series
Ø
Fourier Series for Even Function
Ø
Fourier Series for Odd Function
v
Half Range Fourier Series
Ø
Half range Sine Series
Ø Half range Cosine Series
v
Parseval’s Identity
v MCQ Test
Chapter-5 Vector Space and Linear Transformation
v
Internal and External operations
v
Vector Space and their Properties
v
Vector Subspace
v
Linear Span, Linear Combination, Linearly independent and Linearly
dependent
v
Linear Transformation and their Properties
v
Kernel, Range, Rank,
Nullity of Linear Transformation
v MCQ Test
Chapter-6 Matrices and Linear Transformation
v
Introduction of Matrices and their properties
v
Rank of Matrix
Ø
Minor Method
Ø
Echelon Form
Ø
Normal or Canonical Form
v
PAQ Normal Form
v
Solution of Simultaneous Linear System
and Consistency of system
Ø
Non-Homogeneous system
·
Unique Solution
·
Infinite Many Solution
·
No Solution
Ø
Homogeneous System
·
Trivial Solution
·
Non-Trivial Solution
v
Eigen Value and Eigen Vectors
v
Cayley’s Hamilton Theorem
v
Diagonalization
of Matrices
v MCQ Test
Chapter-7 Appendix
v
Error and Approximation
v
Jacobian Function
v
Tangent and Normal
v
Radius of Curvature
v
Tracing of Curve
v MCQ Test
How to Enroll in the Course…
2. All the information filled in correctly
3. 3-Days Demo Classes
4. Final Registration by Google Form [Link Given on Same Time]
5. 4-Hours Weekly classes
Online Platform…
Google
Meet [Download Google Meet from Google play store]
Follow
the following steps:
Fees Structure
Overall
Charges 4000/- in
Indian Currency
1st
Installment 2000/- at final
Registration
2nd
Installment 2000/- after 10
Days of Final Registration
Online Payment Mode [Ask from Sir/Madam]:
1. Google Pay by QR Scan
2. Paytm by QR Scan
Online Assistant:
WhatsApp/Call: 9893455006
Dr. Sonendra Gupta
Dr. Sonendra Gupta, HOD (Department of Mathematics) in Oriental College of Technology, Bhopal (MP). He received Ph.D., M.Phil(Maths), M.Sc.(Computer Science) and M.Sc.(Maths) degree. He has 20 years of teaching experience.
He is equipped with an extraordinary caliber and appreciable academic potency. He has always been a topper throughout his educational career. He has secured the Seventeenth position in Bhopal merit, in intermediate examination 1995.
He ranked as a topper in the university 1997 in B.Sc. II year. He has authored 20 popular books of Mathematics titled “Advanced Mathematics”, “Engineering Mathematics-I”, “Engineering Mathematics-II”, Engineering Mathematics-III, Differential equation part-II, Vector Analysis and Geometry, Business Mathematics, Abstract Algebra, Numerical Analysis etc. for numerous universities, viz. RGPV Bhopal, U.P. Technical University, Barkatullaha University, Bhopal and Chhattisgarh University.
He has attended Mission 10x Wipro works-shop and published 8 international and 2 national research papers in various reputed journals including workshops and conferences. He has also published RGPV Paper solutions, of mathematics on its blog. He is a very successful and hardworking teacher; no doubt, he is first choice of the students. The welfare of students is reflected in his works. He never compromises with the tough presentation of the subject matter. He has high hopes to be fulfilled in the near future. As a helping hand for the mathematics community, the website is launched as https://sonendragupta.blogspot.com/ & http://www.sonendragupta.com/ and “YouTube Channel: Dr. Sonendra Gupta”
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