http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
SC 105 Calculus and Complex Variables
Lecture 1: Admin Details & Background Building
Prof. Manish K. Gupta
Laboratory of Natural Information Processing
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
Outline of Presentation
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Instructor, Tutors and Teaching Assistants
Overview and Subject Classification
Course Outline
Course Policy
Attendance Policy
Some Warnings and Advise
Historical Introduction & Motivation
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SC105 Class 1
Laboratory of Natural Information Processing
Your Courses Autumn 2015-16
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
SC 105 Instructor
• Manish K Gupta (www.mankg.com)
• Office: Room 2209 Faculty Block 2
• Office Hours: Friday 5:00 to 6:00 pm
every week
• Email: [email protected]
• Phone: 91-79-30510549
• Course Page:
http://courses.daiict.ac.in//course/view.php?id=343
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
SC 105 Tutors
• Krishna Gopal,
Room Lab 202 , Phone: 522
Email: [email protected]
• Dixita Limbachiya,
Room Lab 202, Phone: 522
Email: [email protected]
SC 105 Teaching Assistants
• TA1: Kamal Captain
• TA2: KARAVADRA RAJU DUDA
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
SC 105 Timings
Lectures (Slot-9)
Tuesday 12:00 Noon (LT-3) Wednesday 10:00 am (LT-3) and
Friday 10:00 am (LT-3)
Tutorials (1:00 pm all 5 days)
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Monday (Group 3, Room CEP 203)
Tuesday (Group 4, Room CEP 203)
Wednesday (Group 5, Room CEP 203)
Thursday (Group 1, Room CEP 203)
Friday (Group 2, Room CEP 203)
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SC105 Class 1
Laboratory of Natural Information Processing
SC 105 Overview and Subject Classification
This exciting course is foundation
to your ICT degree.
• Basic calculus of real variables
• Basic calculus of complex
variables
• Differential Equations
(Ordinary and partial differential
equations with a few
applications)
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
SC 105 Course Outline-1
Week
1 (Aug 3)
Tentative Topics
2 (Aug 10)
Fundamental theorem of integral
calculus, definite integrals,
trapezoidal and Simpson's rules
3 (Aug 17)
Functions of several variablesPartial derivatives, chain rule,
chain differentiation, implicit
functions and Jacobians
4 (Aug 24)
Revision Summary (Aug 26)
and Test 1 (Aug 27to Aug 29)
5 (Aug 31)
Taylor's theorem for functions of
several variables, maxima, minima
and saddle points
6 (Sep 7)
Multiple integrals
Introduction, functions of single
variable-Mean value theorems and
Taylor's theorem
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SC105 Class 1
Laboratory of Natural Information Processing
SC 105 Course Outline-2
Week
Tentative Topics
7 (Sep 14)
Complex Variables-Introduction,
8 (Sep 21)
Complex Variables-Differentiability and
analyticity
9 (Sep 28)
Complex Variables-definite integrals
(contour integrals-line integrals)
10 (Oct 5)
Test 2 (Oct 5 to Oct 7)
11 (Oct 12)
Cauchy integral theorem and formula,
Taylor and Laurent series, zeroes,
singularities and residues
12 (Oct 19)
Ordinary differential equations-ODE of
first order, linear ODE of second and
higher order with constant and nonconstant coefficients
Continuity
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SC105 Class 1
Laboratory of Natural Information Processing
SC 105 Course Outline-3
Week
Tentative Topics
13 (Oct 26)
Non-homogeneous equations, power series
solutions to ODEs
14 (Nov 2)
Partial differential equations-Classification of
PDEs Diffusion equation: separation of
variables
15 (Nov 7) Holiday Week
16 (Nov 16) Course Evaluation
Week
Wave equation, separation of variables,
vibrating string and d'Alembert's solution
Laplace Transforms & Fourier Transforms
17 (Nov 23)
Test 3 (Nov 22 to Nov 27)
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SC105 Class 1
Laboratory of Natural Information Processing
Semester Break: Deepawali Week 15 (Nov 9)
Nov 7 to Nov 15 (Holiday Week)
SC 105 Application Home Assignment Time
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SC105 Class 1
Laboratory of Natural Information Processing
Holidays Fall 2015
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SC105 Class 1
Laboratory of Natural Information Processing
Marks Distribution (Tentative) /
Grading Policy
Test 1
20%
Test 2
20%
Test 3
30%
Quiz/Tutorials/Class
20%
Take Home
10%
• Take-home Policy: Each of you need
to work alone on an application and
upload one application in latex and
pdf files at Moodle.
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
Tutorials Policy
• One Tutorial per week with some additional bonus
problems for you to enjoy in the evening tea time !
• You need not to submit your Tutorial but
attendance is mandatory as any time surprize quiz
may occur and discussions will be useful !
Labs: None
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SC105 Class 1
Laboratory of Natural Information Processing
Attendance Policy
• Each of you must attend each lecture as I
usually give a few questions (called type-2
questions) that you need to solve by that
week itself and clear your doubts about it.
Note that I usually ask them in the exams or
quizzes. There could be a surprise quiz at
any time in Lectures or Tutorials and
sometime I may change the % of quiz for
final grade to quite a lot.
• If for some reason beyond your control (for
example you are sick) you are about to miss
a lecture please fill the leave application
form available at Moodle that you will not be
able to attend the lecture that day.
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
Lecture Notes
• Notes are available in the lecture
folder and it is advisable that you
read them before coming to class.
This will help you to clear your
doubts.
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
Text Book
• Thomas Calculus (Must have !)
• Advanced Engineering Mathematics,
Jain, RK and SRK Iyengar, 3rd edition,
Narosa, 2007 ISBN 978-81-7319-7307, New Delhi, India (Reference Book)
• Occasionally there will be reading
advice in every week or lectures for
some additional material
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SC105 Class 1
Laboratory of Natural Information Processing
Course Web Page
• Course Web Page:
http://courses.daiict.ac.in//course/vie
w.php?id=343
• Create your login with your daiict
email address as and when you get it
at http://courses.daiict.ac.in
• Register for the course SC 105 at
Moodle
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
Advice on Problem Solving
• Please attend (and participate…) each lecture and tutorial:
Once done that you will get at least a grade of 8 or 9.
• Mark your doubts and clear them that week itself
• Step 0: Think about it for 15 minutes
• Step 1: Ask your peers
• Step 2: Ask your seniors
• Step 3: Ask the TAs
• Step 4: Ask the Tutors
• Step 5: Finally ask the Instructor (me) on Friday every
week between 5:00 and 6:00 pm at Room 2209, Faculty
Block 2
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
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Common Mistakes Students Make !
Do not go to the class as first year is rest year
Study only from exam point of view
Study towards the exam date
Calculus I know from my 10+2 so there is no need to learn
Receive advice from bad seniors
(Listen to some good seniors who have achieved something)
Thinking that CPI is not important
Not having a study plan
Sometime it is good to study in groups
Not reading the text book
Only studying few courses and not paying attention to all
courses
Playing games on computers or just wasting time in gossip
I could not get admission in computer science so I will not
study this ICT
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
A Good Plan for your BTech (ICT)
• First year (particularly 1st semester) just focus on
study (you will not get time for extra activities)
• Once you are in good shape CPI wise and you
have a better understanding of the system you will
observe that you are getting extra time for many
other activities
• Learn programming languages by taking a big
project in Summer or Winter breaks (at least 15K
lines program): C, C++, Java, Python etc…
• You require strong mathematical/
algorithmic/problem solving/analytical skills
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SC105 Class 1
Laboratory of Natural Information Processing
Focus on Foundations in first 2 years
• Explore Everything……Read Read Read in Y1 & Y2
• On Weekends (may be till Sunday afternoon) go to Library
and read periodicals and some general reading
• Have proper sleep of at least 7-8 hours every day
• Try to explore your interest : What do you like most and
what you want to do after 5-10 years …
• Discover your interest and then look for the heroes in that
field
• Make a plan and then execute it in Y3 & Y4. You will get
success for sure !
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SC105 Class 1
Laboratory of Natural Information Processing
Pick up the topics according to your interest
in the last 2 years
After BTech (ICT)
• People expect a good CPI from you
• Strong fundamentals
• Strong programming skills
• Strong in one specialization
What path you will choose will depend upon what
you do in these 4 years….
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
Outline of Story
Science is the catalyst,
Technology is the application,
Business is the opportunity ……
»ICT is everywhere!
» Philosophy of Information
Processing
Do you know what is ICT?
Manish K Gupta, PhD
http://www.guptalab.org
Laboratory of Natural Information Processing
ICT-Information & Communication
Technology
• IT-Information Technology --Applications
(Mathematical Root- Computer Science –Turing
Machine)
• CT-Communication Technology -- Applications
(Mathematical Root-Theory of CommunicationInformation and Coding Theory)
• Realization via Logic Gates and Circuits(Computation by Circuits)-Hardware, Software,
Electronics and VLSI-Semiconductor Technology
Do you know what is ICT?
Manish K Gupta, PhD
http://www.guptalab.org
Laboratory of Natural Information Processing
What is a Computer?
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A device (machine) which process Information
Processing -- Storing and Manipulating
Representation of Information in classical computers (classical physics) Binary
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Representation of Information in quantum computers (quantum physics) Qubits
IT468
Class
11
SC105
Class
http://www.guptalab.org
Laboratory of Natural Information Processing
What is the purpose of Computing?
“The purpose of computing is insight, not
numbers. The purpose of computing numbers is
not yet in sight” Richard W. Hamming
RW Hamming (1971). Introduction to Applied Numerical Analysis. McGraw Hill.
IT468
Class
11
SC105
Class
http://www.guptalab.org
Laboratory of Natural Information Processing
What is a Communication?
• Sending /Receiving Information from here to there
• This will require Information Processing -- Storing and
Manipulating (So you require a computer !)
• Storing- Sending Information from now to then
• Retrieving - Receiving Information from then to now
IT468
Class
11
SC105
Class
http://www.guptalab.org
Laboratory of Natural Information Processing
What is Information?
Representation of Information is different in different information
processing process /machine
Digital Information Processing
Quantum Information Processing
Chemical Information Processing
Biological Information Processing
Structural Information Processing
Social Information Processing
Natural Information Processing
IT468
Class
11
SC105
Class
http://www.guptalab.org
Laboratory of Natural Information Processing
Computer Science
Electrical Engineering
Communications
Coding and Information Theory
Information Processing in Nature
Mathematics
Biology
Chemistry
Physics
Nanotechnology
Medicine
Interdisciplinary
(Goldmine for Science, Technology and Business) !
How systems of all kinds -- computers, atoms, brains, cells,
societies, and the universe as a whole -- process information ?
-- S. Lloyd, MIT
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
What is Computational Science (CS) ?
Computational Science and Engineering
Communications --ICT-- Computer Science
Two sides of the same coin
Computational-ICT
Information Processing VIEW
of the World around you
Modeling/
Simulations
DATA
Try to decipher rules of Information Processing
SOME Applications:
Computational Advertisement, Computational Finance, Computational Networks,
Computational Physics, Computational Social Media, Computational Biology,
Computational Bla Bla ….
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SC105 Class 1
Laboratory of Natural Information Processing
ICT vs ICT(CS) ?
CS
ICT
http://addapinch.com/cooking/cherry-cheesecake-ice-cream-recipe/
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
What is Computational Science (CS) ?
Communications --ICT-- Computer Science
Two sides of the same coin
Computational-ICT
http://www.shodor.org/os411/courses/411e/module01/unit01/page01.html
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
ICT vs Computer Science vs ECE vs ICT(CS) ?
• Which degree is best?
• Please understand that your degree has an advantage over other
traditional degrees in a sense that it prepares you for areas which
require interdisciplinary skills
• ICT is the degree of the 21st century…
• Do you know that ICT engineers are preferred over holders of other
degrees as long as they are good…
• ICT degree prepares you for the future Technologies…
• Do you know that after BTech in ICT you can join
MD-PhD program without doing MBBS at many good universities?
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SC105 Class 1
Laboratory of Natural Information Processing
What you will get after BTech depends on
what you do in these 4 years: Case Studies
• Case1: Muskan Kukereja (2004 batch student) just after
BTech got admission in Arizona Biodesign PhD Program in
2008 with scholarship values US$60,000 per annum /
Shalin Shah (2011 batch) got direct admission to Duke
University PhD program in 2015 with scholarship value
US$84,000 per annum
• Case2: Many have joined Google, Microsoft,…
• Case3: Many have joined PhD and MS abroad
• Case4: Many have joined IIMs for MBA
• Case5: Many have joined normal company job
• Case6: Many have started their own company
• Case7: Many are confused…as they have not done their
proper home work or studies…still discovering
themselves… NO PROBLEM…THEY WILL CATCH
LATER
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
Destiny?
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Thought
Feeling
Action
Habit
Attitude
Personality
Destiny
A man is but the product of his thoughts.
What he thinks, he becomes.
https://en.wikipedia.org/wiki/Mahatma_Gandhi#/media/File:Portrait_Gandhi.jpg
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SC105 Class 1
Laboratory of Natural Information Processing
Objectives: SC105
• Developing a thinking process for solving difficult
problems in other words developing mathematical
(problem solving) skills
• Understanding limit, continuity, differentiability
and integration for real and complex variables
• Solving Ordinary and Partial Differential
Equations
• Some applications using Laplace and Fourier
transforms
• Later on in other courses you will see how these
skills are applied in understanding and solving the
real world engineering problems
http://www.guptalab.org
SC105 Class 1
Laboratory of Natural Information Processing
In science if you know what you are doing you
should not be doing it.
In engineering if you do not know what you are
doing you should not be doing it
Richard W. Hamming
Any Questions ?
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SC105 Class 1
Laboratory of Natural Information Processing
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
Calculus, Where are you?
Imagehttp://www.eringrieger.com/wp-content/uploads/2012/05/calculus2.png
Credit: Nick Papadakis, Copyright P.W.K.R. and N.P.
http://www.dna.caltech.edu/~pwkr/
Manish K. Gupta
Laboratory of Natural Information Processing
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
Outline of Story
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Historical Introduction & Motivation
Building Blocks
Applications
Tools: Visual Calculus, Matlab, Maple and Mathematica
Intellectual Challenges
What is Calculus?
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
Motivation and Historical Introduction
As the births of living creatures, at first,
are ill-shapen: so are all Innovations, which are
the births of time. . . .
Francis Bacon (1561-1626)
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
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Around 600 Years Ago…
Kerala school
of astronomy
and mathematics
1400
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
First Text Book of Calculus (1530)
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Infinite Series Expansion
Power Series, Taylor Series
Trigonometric Series
Test of Convergence
∏ ~ 3.14159265359 (11 decimal)
Fundamentals of Calculus:
1. Differentiation
2. Term by term Integration
3. Iterative methods for solutions
of non-linear equations
4. The theory that the area
under a curve is its integral etc.
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
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Gottfried Wilhelm Leibniz (1646-1716)
Nova Methodus pro
Maxima et Minimus
(Published - 1684)
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
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Sir Isaac Newton (1642-1727)
http://upload.wikimedia.org/wikipedia/commons/4/41/NewtonsPrincipia.jpg
1686
http://upload.wikimedia.org/wikipedia/commons/3/39/GodfreyKneller-IsaacNewton-1689.jpg
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
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Calculus Timeline (1600-1800)
http://www.uiowa.edu/~c22m025c/timeline.html
Joseph Louis Lagrange (1736-1813)
Johann Carl Friedrich Gauss (1777-1885)
Jean Baptiste Joseph Fourier (1768-1830)
Pierre-Simon Laplace (1749-1827)
Johann Peter Gustav Lejeune Dirchlet (1805-1859)
Lord Kelvin (1824-1907)
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
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http://www.foodandtechconnect.com/site/wp-content/uploads/2011/01/building-blocks.jpg
Building Blocks of Calculus
“In science if you know what you are doing you should
not be doing it.
In engineering if you do not know what you are
doing you should not be doing it.”
Richard W. Hamming
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
Applications
“The purpose of computing is insight,
not numbers. The purpose of computing
numbers is not yet in sight”
Richard W. Hamming
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
Maximize Profit
http://www.axiomint.com/images/mst/jan08/cadmanager.gif
http://ottawawebsites.files.wordpress.com/2012/02/maximizing-profits.jpg
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
Cooking a Potato
http://morethymethandough.com/wp-content/uploads/2012/04/IMG_7824.jpg
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
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Laboratory of Natural Information Processing
Love Affairs
Vikas
Seema
http://healthandpharmainsight.tumblr.com/post/17606658530/epharma-love-affairs
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
Mathematics of Marriage
Book by the MIT Press
2003
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
Visual Calculus
“The purpose of computing is insight,
not numbers. The purpose of computing
numbers is not yet in sight”
Richard W. Hamming
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
Outline of Story
Science is the catalyst,
Technology is the application,
Business is the opportunity ……
» Calculus is everywhere!
» Philosophy of Calculating the
change
Do you know what is ICT?
Manish K Gupta, PhD
http://www.guptalab.org
Laboratory of Natural Information Processing
Intellectual Challenges: Pathological Examples
“Logic sometimes makes monsters. For half a century we have
seen a mass of bizarre functions which appear to be forced to
resemble as little as possible honest functions which serve some
purpose. More of continuity, or less of continuity, more
derivatives, and so forth…
Henri Poincare (1854-1912)
…In former times when one invented a new
function it was for a practical purpose;
today one invents them purposely to show up
defects in the reasoning of our fathers and
one will deduce from them only that….
http://upload.wikimedia.org/wikipedia/commons/a/af/JH_Poincare.jpg
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
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Laboratory of Natural Information Processing
Pathological Example: 1
Give an example of a real-valued continuous function which is no-where
differentiable on the real line.
June 28, 2012, Pedagogy
Sessions
in Calculus, GTU
Laboratory of Natural Information Processing
http://upload.wikimedia.org/wikipedia/commons/thumb/6/60/WeierstrassFunction.svg/1000px-WeierstrassFunction.svg.png
http://www.guptalab.org
Pathological Example: 2
Give an example of a real-valued function which is discontinuous everywhere
on the real line.
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
Pathological Example: 3
Give an example of a real-valued function which is continuous only at one
point on the real line.
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
Pathological Example: 4
Give an example of a real-valued function which is differentiable only at
one point on the real line.
Exercise ! Try to construct one example !
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
Pathological Example: 5
Give an example of a real-valued function which is differentiable any
number of times but for which no Maclaurin Series exist.
June 28, 2012, Pedagogy
Sessions in Calculus, GTU
http://www.guptalab.org
Laboratory of Natural Information Processing
Reading Work Class 1
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SC105 Class 1
Laboratory of Natural Information Processing
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SC 105 Calculus Fall 2010