# Calculus

By Dr. Mansoor P   |   MES College of Engineering, Kuttippuram, Kerala
Learners enrolled: 894
The fundamental idea of calculus is to study change by studying “instantaneous” change, by which we mean changes over tiny intervals of time. It turns out that such changes tend to be lots simpler than changes over finite intervals of time. This means they are lots easier to model. Calculus is the broad area of mathematics dealing with such topics as instantaneous rates of change, areas under curves, and sequences and series. It has two basic applications: differential calculus and integral calculus. The simplest introduction to differential calculus involves an explicit series of numbers. Differential calculus essentially lets one calculate the rate of change. So say variable ‘y’; is a function of variable ‘x’. Integrals, together with derivatives, are the fundamental objects of calculus. The process of computing an integral is called integration. Among the disciplines that utilize calculus include physics, engineering, economics, statistics, and medicine. It is used to create
Summary
 Course Status : Upcoming Course Type : Core Duration : 15 weeks Category : Mathematics Credit Points : 4 Level : Undergraduate Start Date : 08 Jan 2024 End Date : 28 Apr 2024 Enrollment Ends : 29 Feb 2024 Exam Date : 18 May 2024 IST Exam Shift : Shift 2

Note: This exam date is subjected to change based on seat availability. You can check final exam date on your hall ticket.

### Course layout

Weeks Weekly Lecture Topics (Module Titles)
1 Day 1 Module 1 : Transcendental functions- Inverse trigonometric function and logarithmic function
Day 2 Module 2 : The exponential functions
Day 3 Module 3 : Hyperbolic functions and inverse hyperbolicfunctions
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.

2 Day 1 Module 4 : Successive differentiation- n th derivatives
Day 2 Module 5 : Taylor series and Maclaurin series expansions
Day 3 Module 6 : Concavity, points of inflexion and multiple points
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.

3 Day 1 Module 7 : Curvature and evolutes
Day 2 Module 8 : Asymptotes
Day 3 Module 9 : Tracing of curves
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.

4 Day 1 Module 10 : Partial differentiation
Day 2 Module 11 : Young’s theorem and Schwarz’s theorem
Day 3 Module 12 : Partial differentiation of implicit, homogeneous and composite functions
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.

5 Day 1 Module 13 : Integration by successive reduction
Day 2 Module 14 : Definite integrals and their evaluation
Day 3 Module 15 : Application of integration- rectification and quadrature
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.

6 Day 1 Module 16 : Application of integration- Volume of solids ofrevolution
Day 2 Module 17 : Infinite series
Day 3 Module 18 : Series of arbitrary terms
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.

7 Day 1 Module 19 : Tests for positive term series
Day 2 Module 20 : Fourier series representation of a periodicfunction
Day 3 Module 21 : Fourier series of a function having period 2C
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.

8 Day 1 Module 22 : Fourier series representation of even and oddfunctions
Day 2 Module 23: Half range Fourier series expansion offunctions
Day 3 Module 24 : Differential equations- Introductions
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.

9 Day 1 Module 25 : Variable separable and homogeneousdifferential equations
Day 2 Module 26 : Linear and exact differential equationsObjectives
Day 3 Module 27: Equations reducible to exact differentialequations
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.

10 Day 1 Module 28 : Application of differential equations- orthogonal trajectories
Day 2 Module 29 : Differential equation of the first order but not of the first degree
Day 3 Module 30 : Higher order differential equations
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.

11 Day 1 Module 31 : Second order differential equations with variable coefficients
Day 2 Module 32 : Method of undetermined coefficients, method of variation of parameters and normal form
Day 3 Module 33: Cauchy’s differential equation and particular integrals
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.

12 Day 1 Module 34 : Partial differential equations- introduction
Day 2 Module 35 : Non-linear partial differential equations of first order
Day 3 Module 36 : Charpit’s method
Day 4 Interaction based on the three Modules covered.
Day 5 Deadline for submitting assignments.

13 Day 1 Module 37 : Linear partial differential equations of higher order with constant coefficients
Day 2 Module 38 : separation of variables.
Day 3 Module 39 : Application of partial differential equations- Vibrations of a stretched string
Day 4 Module 40 : Application of partial differential equations- One dimensional heat flow
Day 5 Interaction based on the three Modules covered.

14 Day 1 Module 41 : Two dimensional heat equation and wave equation
Day 2 Module 42 : Laplace transform and inverse Laplace transform
Day 3 Module 43 : Laplace transform- some special results
Day 4 Module 44 : Application of Laplace transforms andLaplace transforms of some useful functions
Day 5 Deadline for submitting assignments.

### Books and references

• George B. Thomas, Ross L. Finney, Calculus, 9th Edition, Pearson Education, New Delhi(2002).
• Theory and Problems of Advanced Calculus, Schaums outline series, Schaum publishing company, New York.
• Erwin Kreyszig, Advnced Engineering Mathematics, John Wiley and sons, New York,1999.
• Ordinary and Partial Differential Equations by M.D. Raisinghania, S.Chand, New Delhi (2010).
• Differential Equations and Their Applications, 2nd  ed. by Zafar Ahsan, Prentice-Hall, New Delhi (2006).

### Dr. Mansoor P

MES College of Engineering, Kuttippuram, Kerala
Dr. MANSOOR P, Assistant Professor, Department of Mathematics, MES College of Engineering Kuttippuram, Trikkanapuram P.O., Malappuram D.T., Kerala, India

PhD in Mathematics from Bharathiar University, M.Phil from Annamalai University, MSc. Mathematics from University of Calicut.

Served as Course Coordinator for offering a Massive Open Online Course (MOOC) on Numerical Methods under SWAYAM MOOC platform (Jan 2023 section) (https://onlinecourses.swayam2.ac.in/cec23_ma05/preview)

Worked as Translator for translating the book titled "Linear algebra and calculus for CSE Branches" under AICTE.

Working as Translator for translating various courses offered by IIT's under NPTEL from 2019 onwards.

Subject expert for preparing Mathematics questions under AICTE Students Learning Assessment Program (ASLAP) 2019.

Served as Course Coordinator for offering a Massive Open Online Course (MOOC) on Mathematical Analysis under SWAYAM MOOC platform of MHRD of India during 2019-20.      (https://onlinecourses.swayam2.ac.in/cec21_ma05/preview)

Served as Principal Investigator (PI) for offering a Massive Open Online Course (MOOC) on Calculus under SWAYAM MOOC platform of MHRD of India.

Served as Subject Expert for the development of e- content modules in various topics of Mathematics for the Consortium for Educational Communication (CEC), an Inter University Centre set up by the University Grants Commission of India during 2011-2014.

Presented a number of e- content modules at EMMRC, University of Calicut in Mathematics for CEC, an Inter University Centre set up by the University Grants Commission of India during 2011-2014.

Served as Resource Person to deliver a number of lectures at EMMRC, University of Calicut for the DTH Swayam Prabha channel (a group of 32 DTH channels devoted to telecasting of high-quality educational programmes on 24X7 basis using the GSAT-15 satellite) of MHRD India during 2017-18

### Course certificate

30% weightage internal assessment and 70% weightage main examination