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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