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 • • • • • • • Instructor, Tutors and Teaching Assistants Overview and Subject Classification Course Outline Course Policy Attendance Policy Some Warnings and Advise Historical Introduction & Motivation http://www.guptalab.org 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) • • • • • 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) http://www.guptalab.org 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 http://www.guptalab.org 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 http://www.guptalab.org 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) http://www.guptalab.org 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 http://www.guptalab.org SC105 Class 1 Laboratory of Natural Information Processing Holidays Fall 2015 http://www.guptalab.org 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 http://www.guptalab.org 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 http://www.guptalab.org 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 • • • • • • • • • • • • 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 http://www.guptalab.org 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 ! http://www.guptalab.org 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? • • • A device (machine) which process Information Processing -- Storing and Manipulating Representation of Information in classical computers (classical physics) Binary • 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 …. http://www.guptalab.org 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? http://www.guptalab.org 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? • • • • • • • 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 http://www.guptalab.org 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 ? http://www.guptalab.org 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 • • • • • 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 http://www.guptalab.org Laboratory of Natural Information Processing 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) • • • • • • 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 http://www.guptalab.org Laboratory of Natural Information Processing Gottfried Wilhelm Leibniz (1646-1716) Nova Methodus pro Maxima et Minimus (Published - 1684) June 28, 2012, Pedagogy Sessions in Calculus, GTU http://www.guptalab.org Laboratory of Natural Information Processing 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 http://www.guptalab.org Laboratory of Natural Information Processing 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 http://www.guptalab.org Laboratory of Natural Information Processing 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 http://www.guptalab.org 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 http://www.guptalab.org 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 http://www.guptalab.org SC105 Class 1 Laboratory of Natural Information Processing

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# SC 105 Calculus Fall 2010