Engineering Mathematics for Advanced Studies

Brief Course Summary

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Class information:

• Course begins - 5th August 2019 in Room 215 (Slot 3) 10:35am - 11:30am
  
• Date - 05-08-2019 12:35 pm
  Mutually agreed revised timing (Slot 3) (for 7 modules taken by me)
  
  • Mon 10:35 - 11:30 am
  • Tue 12:00 - 12:55 pm
  • Thu 08:30 - 09:25 am
  Classroom - 215
  Walk-in Hrs - Thu-2:00-3:00pm, SR's office near Dean R&D office. For Module #4, 7, 10 contact respective instructors.
  
• Date - 14-08-2019 18:45
  Grading policy for SR's modules (per module)-
  relative grading based on
  2 assignments (10% each) + surprise quiz (20%) + Final exam 60%
  Note- check with NMB and SV for remaining three modules

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Consolidated hyperlinks:

Linear Algebra Module

• Linear Algebra Syllabus for final exam
  
• Determinant salient properties
• Vector Space Notes
• Linear Algebra Assignment#2     LinA Assignment2 model solutions
  
• Linear Algebra Assignment#3     LinA Assignment3 model solutions
  
• Linear Algebra Assignment#4     LinA Assignment4 model solutions
  
• Linear Algebra Surprise Quiz    Surprise Quiz Solutions
  
• Linear Algebra Final Exam Question Paper     LinA Final Exam Model solutions
  

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Ordinary Differential Eqn. Module

• ODE Assignment 01 v2     ODE Assignment01 Solutions.
• ODE Assignment02     ODE Assignment 02 Solutions.
• ODE Quiz 01     Solutions ODE Quiz 01.
• ODE Surprise Quiz 01-retest     Solutions ODE Quiz 01 RETEST.
• ODE Final Exam Questions     Solutions ODE Final Exam.

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Vector Calculus Module

• Vector Calculus Syllabus
  
• Vector Calculus Assignment 02     Solutions Vector Calculus Assignment02
• Vector Calculus Assignment01     Solutions Vector Calculus Assignment01
• Vector Calculus Quiz01     Solutions Vector Calculus Quiz01
• Vector Calculus Final Exam     Solutions Vector Calculus Final Exam

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PDE Module

• PDE module syllabus
• PDE Assignment 02     PDE Assignment02 Solutions
• PDE Assignment 01     PDE Assignment01 Solutions
• PDE Surprize Quiz 01     PDE Surprise Quiz Solutions
• PDE Final Exam Questions     PDE Final Exam Solutions
• Similarity variable YouTube Video
• Great PDE book by Prof. Kersale for additional reference: Link PDE

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Numerical Methods

• Numerical Methods module syllabus (revised)
• Numerical Methods Assignment02     Assignment02 Solutions
• Numerical Methods Assignment01     Assignment01 Solutions
• Numerical Methods Quiz01     Numerical Method Quiz01 Solutions
• Numerical Methods Final Exam     Numerical Method Final Exam Solutions

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Probability & Statistics

• Probability and Statistics - Syllabus for Final exam
• Poisson distribution as a limiting case of Binomial distribution: derivation
• Probability & Statistics Assignment02     ProbStat Assignment02 Solutions
• Probability & Statistics Assignment01 ProbStatA01 Solutions - too obvious to provide here
• Probability & Statistics Quiz01     ProbStat Quiz Solutions
• Probability & Statistics Final Exam     Final Exam Solutions

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Errata in above material

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Announcement Feed:

• Date: 23-01-2020 16:37 pm
  
  • Please provide your course feedback using the survey link shared earlier
  • Some errata is posted. Note that the grading exercise was done considering this. In case of ambiguity, full credits are given to all the students (irrespective of attempt).
  • Wish you all the best!

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• Date: 26-11-2019 11:37 am
  
  • Written apology in case of misconduct to be submitted by 28th Nov. 5:30pm
  • By Monday 2nd Dec. 5:00 pm I will keep the graded answerscripts for the final exams ready. Please revert back if any queries before 5:00pm 3rd Dec.

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• Date: 21-11-2019 14:37 pm
  
  • There was a mistake in the class today while writing the normal distribution equation on the black board. Brackets of the exponent term were supposed to be for only the numerator. Wikipedia page
  • Poisson distribution as limiting case of Binomial distribution: derivation
  • Syllabus for the Prabability and Statistics module's final exam
  • Probability Final Exam:
    • Friday, 22nd Nov. 2019.
    • 5:00pm -6:30pm (Tentative) 6:00pm-7:30pm (Finalized)
    • Classroom 215
    • Calculators may be used
    • Partially open book /open notes test

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• Date: 20-11-2019 17:03 pm
  
  • Probability Assignment 02
  • Probability Final Exam:
    • Friday 22nd Nov. 2019.
    • 5:00pm -6:30pm (Tentative)
    • Classroom 215

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• Date -18-11-2019 17:03 pm
  
  • Numerical Methods Final Exam syllabus is revised. Please check.
  • Numerical Methods Final Exam time is rescheduling is requested by some students. Please be in the loop and voice if you have any concerns with the proposed common time slot in the whatsapp group discussion.
  • Prabability >> independent events >> refer to this link for clarity.

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• Date -16-11-2019 23:28 pm
  
  • Numerical Methods Final Exam
    • Wednesday 20th Nov. 2019, Room 203, Morning 8:30am-10:30am
    • Partially open book test - Exam may have a section on closed book test
    • Open book section will be based on Kreyszig. If at all any particular information needed from Numerical methods - Prof. Parviz Moin's book, graded assignments may come handy (to be returned on Exam day) or information will be provided
  • Numerical Methods Assignment01 Solutions
  • Numerical Methods Assignment01 Octave/MATLAB codes
    Cubic Spline     Padé scheme
  • Numerical Methods Assignment02 Solutions

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• Date -15-11-2019 15:25 pm
  
  • Numerical Methods Final Exam on Wednesday 20th Nov. 2019, Room 203, Morning 8:30am-10:30am
  • For Numerical methods final exam - expect clarity about open book or partially open book test by Sunday, 17th Nov. 2019.
  • Numerical Methods module syllabus
  • Numerical Methods Quiz01     Numerical Method Quiz Solutions

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• Date -12-11-2019 15:25 pm
  
  • Probability & Statistics Assignment01 due before Friday 15th Nov. 2:05pm in the class

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• Date -11-11-2019 18:25 pm
  
  • Numerical Methods Assignment02
  • Numerical Methods Final Exam on Wednesday 20th Nov. 2019, likely in the morning
  • Probability session to start from Friday 15th Nov. 2019 2:00pm
  • Probability exam to take place in final exam week - common timeslot related discussion is left to all the students enrolled in Probability module
  • In-class quiz for the numerical methods on Thursday 14th Nov. 2pm

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• Date -07-11-2019 21:50 pm
  
  • Numerical Methods Assignment01

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• Date -05-11-2019 15:45 pm
  
  • PDE Assignment01 Solutions.
  • PDE exam in Room 115 on 7th Nov. 2019 (Thursday) Morning 8:30am-10:30am.
  • PDE exam will be open book exam
  • PDE exam may need use of calculator
  • No lecture on Thursday due to exam
  • Extra lecture planned on the Friday 8th Nov. 2019 2:30pm-3:30pm in same regular room 215
  • Assurance - Zero possibility of surprize quiz on Friday, however, content covered on Friday will be included in the scope of surprize test whenever it occurs

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• Date -1-11-2019 12:45 pm
  
  • PDE module syllabus
  • Just a repeation of announcement on whatsapp group: Lecture today 1st Nov. is ON to start at 2:30pm-3:30pm in Room 215.
    ( No extra lecture on coming Friday 1st Nov. 2019 )

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• Date -30-10-2019 16:10
  
  • Few summary points from the discussion in the last class on Monday 28th Oct.:
    • PDE Final exam on Thursday 7th November (instead of earlier planned 8th Nov.)
    • We will continue with 2 assignments per module however deadlines would be given to align efforts towards the preparation for final exam
  • No extra lecture on coming Friday 1st Nov. 2019
  • PDE Assignment 02

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• Date -24-10-2019 10:10
  
  • Session on "Numerical Methods" to started today
  • For the inquisitive minds:
    • External link (GeekForGeeks) for exaplantion about IEEE 754 based floating points representation
    • Floating point as per IEEE754 - Check this floating point YouTube video for a walk-through the details of floating point representation in bytes

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• Date -22-10-2019 14:10
  
  • Session on "Numerical Methods" to start from Thursday 24th Oct.
  • Similarity variable YouTube Video
  • Please get familiar with the use of Hessian matrix for classifying PDE in higher dimensions
  • There were few mistakes in the Heat equation derivation collectively done on the blackboard on Monday 21st Oct. Please refer to the book to get correct signs and PDEs
  • A4 sized cheat sheet likely to be allowed for Vector calculus exam. You can start working on that. Only formulae and standard relations are allowed.

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• Date -21-10-2019 17:10
  
  • Vector Calculus Syllabus for final exam
    
  • PDE Assignment 01

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• Date -19-10-2019 15:10
  
  • Vector Calculus Assignment 02

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• Date -17-10-2019 12:10
  
  • Thanks to Balbheem for providing following plots for ODE-Assignment-02-Q6b that gives insight on the effect of variations of damping coeffient and the spring stiffness. X-axis is time and y-axis on displacement.
    Effect of Damping Variation
    Effect of Stiffness Variation

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• Date -12-10-2019 21:28
  
  • ODE Assignment 02 Solutions.

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• Date -11-10-2019 17:28
  
  • ODE Quiz 01.     Solutions ODE Quiz 01.
  • ODE Surprise Quiz 01-retest.     Solutions ODE Quiz 01 RETEST.

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• Date -09-10-2019 19:17
  
  • ODE Assignment01 Solutions.

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• Date -09-10-2019 13:50
  
  • No lecture on Thursday 10th October. Next lecture on Monday 10:30am as usual.

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• Date -04-10-2019 13:13
  
  • Vector Calculus Assignment01
  • Repeat post (for vecCal assignment01) - Vector Calculus book by Michael Corral. See example 1.19

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• Date -03-10-2019 10:48
  
  • Regarding the f(A)-f(B) typo error in slides that I mentioned in the class - please refer to the end of pg 147 in Vector Calculus book by Michael Corral.
  • It was great to talk to some of you after the class. It was great to receive the suggestions!
  • ODE module final exam on 14th Oct. 5:30pm-7:30pm

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• Date -01-10-2019 10:20
  
  • ODE Assignment02
  • Vector Calculus book by Michael Corral. See equation 1.23 and section 1.5

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• Date -27-09-2019 9:20
  
  • Please take a note that the Linear Algebra exam on Saturday 28th Sept. 2:30-4:30 in same room 215.
  • Repeated note - For the exam preparation on LinAlgebra, it is advised to go through all the assignments and quizes and understand the concepts. That would ensure about 50-60% preparation for the end exam is done automatically.
  • ODE Final exam on Thursday 3rd Oct. is postponed. We will identify common slot for exam in week of 7th Oct. for the same.
  • Expect 2-3 assignments in the meanwhile

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• Date -24-09-2019 17:20
  
  • Please take a note that the Linear Algebra Assignment02 Solns are revised below:
    LinA Assignment02 model solutions (revised 24th Sept.)
    
  • For the exam preparation on LinAlgebra, it is advised to go through all the assignments and quizes and understand the concepts. That would ensure about 50-60% preparation for the end exam is done automatically.

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• Date -23-09-2019 18:20
  
  • Linear Algebra Syllabus for final exam
    
  • LinA Assignment02 model solutions (revised 24th Sept.)
    

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• Date -22-09-2019 8:50
  
  • LinA Assignment03 model solutions
    

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• Date -21-09-2019 18:40
  
  • LinA Assignment04 model solutions
    
  • I just realized that I have not posted the solution for other assignments. I will start working on those asap.
  • Rescheduling exam? Because of this delay I am open in case the next Saturday (28th Sept. ) exams needs to be postponed! Suggest alternative timeslot in consultation with others. Also there is a possibility that we can schedule ODE and LinA exams back to back.

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• Date -19-09-2019 16:40
  
  • A quick note about ODE Assignment 01 v2 question 8c (the one that has zero marks!):
    You may note that Product rule of differentiation for the matrix product as given in here on the pg 267 eqn D.12 to be helpful for ^d/_dt(e^(At)e^(Bt)).
    Thanks to Heena for bringing this up.

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• Date -18-09-2019 17:10
  
  • Uploaded revised version of ODE Assignment 01 v2 with following changes:
    • Question 1.4 is modified to y'/x+x=0
    • CORRECTION - added minus sign in question 5a after "="
    • Question 6 has now cake instead of pancake :)
    • Correctly mentioned mark for each question; Anyway it is not proportionate in anyway as for most of the questions a lot of work is required. It also means start working on this assignment early
    Note that in question 5 of the ODE assignment01 there should be minus sign right after equal sign.
  • Vector Calculus module will start from Tuesday 17th Sept. 2019 class 12pm-1pm

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• Date -15-09-2019 16:10
  
  • Note that in question 5 of the ODE assignment01 there should be minus sign right after equal sign.
  • Vector Calculus module will start from Tuesday 17th Sept. 2019 class 12pm-1pm

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• Date -13-09-2019 16:10
  
  • ODE Assignment01, due 20th Sept. evening (ideally); but allowed till 23rd Sept. due to my delay in posting this!;
    ODE Assignment 01 ( Refer to revised version given above.)
    Note-
    • Marks are incorrect in current version. I will update it to reflect 1 mark per question except for question 8
    • Added more questions than normal to make it a good preparation material for Monday's "surprise" test 😁. It also means you will need more time to finish it.

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• Date -02-09-2019 16:10
  
  • Linear Algebra Assignment04; Sorry for the delay from my side in posting this online. (As a penalty I was thinking whether I should work extra to add 3-4 additional problem questions 😁.... but refrained!)
    -Linear Algebra Assignment04

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• Date -29-08-2019 10:40
  
  • Correction in derivations done on blackboard today in the class; e^(at) shown in red was absconding during the class 😁. Found later thanks to ShrutiM. - check this

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• Date -28-08-2019 18:40
  
  • To plot surface functions online: link.
  • Nice writeup on the SVD: check this out
  • Those who want to discuss Fourier matrix linear Algebra for FFT, please meet me individually. No questions on this topic in final exam.
  • Great to finish the first module - Linear Algebra today in class!
    Note -> "Mathematics is a language. The way to learn this language is to use it" (Source -Gilbert Strang, Diff. Eqns.Lin. Algebra, 4th edition pg5)
    

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• Date -27-08-2019 14:40
  
  • Again great interactive session today! Yes, y'=x*e^(x^2) is linear. Why?...It is the linearity of the Differential operator that we are talking about. More on that here.
  • Take home assignment is due today
  • Linear algebra next take home assignment will be posted here by Thursday 29th August
  • Reminder for the extra lecture on Wednesday 28th August for Linear Algebra remaining important topics
    Location : Same Room 215
    Time: 4:30-5:30pm

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• Date -25-08-2019 14:40
  
  • Surprise Quiz on Linear Algebra
    Sample solutions to in-class surprise quiz
    
  • YouTube link for Good geometrical interpretation for Eigen vectors

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• Date -20-08-2019 21:30
  Assignment#3
• Date -20-08-2019 20:30
  Determinants - Quick overview & important properties pdf
• Date -20-08-2019 14:30
  
  • Few announcement made in the class today:
    • Assignment#3(graded)to be posted today EoD. Deadline Monday 26th Aug.
    • Everyone is requested to sign the module preference sheet
    • Possible extra lecture before Monday. I plan it more like a recitation/queries for Assignment#3 on Friday. Start refreshing the concepts learned so far.
      
  • Orthogonal subspaces example from Bollywood - Angar chand and Laxmi devi family 😁
    
  • Afterthought on Least Square Method - is A^TAx=A^Tb a cheating? Whatever it is, it is a positive approach. In our life as well we find problems which are non-solvable i.e. "b" is not in the solution space. Rather than giving up, it is wise to find "p" in the feasible subspace of life that minimises the error 😇

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• Date -14-08-2019 18:30
  Few announcement made in the class today:
  • Those who are yet to submit assignments, please handover those by Friday (if those are to be graded)
  • Grading and exam policy is annouced in the class today. Please check Class Information section above
  • In case of rescheduling of lecture on 2nd/3rd Sept. please let me know in case you have consensus
  • Please ensure that you have been enrolled for appropriate course module for credit assessment; onus lies on you.
  • Leverage assignements and homework as tools to identify areas of improvement in your understanding.
  • I will upload notes on "Determinants" latest by 19th August (very likely by Friday 16th Aug.). I expect that you have gone through the proofs and in class will just discuss this topic quickly on 20th Aug.
  • Next lecture on Monday (19th Aug.) is an important one 😉

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• Date - 09-08-2019 9:00 am
  Note- Last question in Assignment#2 will need some time. You will need time to think over it.

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• Date - 08-08-2019 19:00 pm
  Assignment#2.
  

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• Date - 08-08-2019 17:00 pm
  Vector Space Notes
• Date - 08-08-2019 14:00 pm
  " Loosely speaking linear algebra is that branch of mathematics which treats common properties of algebraic systems which consist of a set, together with a reasonable notion of a "linear combination" of elements in that set....we shall define mathematical object, which experience has shown to be the most useful abstraction of this type of algebraic system"
  (source - pg28, Hoffman-Kunz Linear Algebra 2nd Ed.)
  

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• Date - 08-08-2019 11:00 am
  Lecture #3: Vector Spaces
  Great active participation today in the class! I look forward to continued involvement in the subject. I will post the vector space related rules by EoD and some assignment problems. stay tuned ...

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• Date - 05-08-2019 15:00 pm
  See what Late Girish Karnad said about Maths - Watch this clip for about 1 minute from time 8:56 to 10:06. (If you reverse it a bit, you can also find him talking about his stay in Dharwad, Subhash Road etc. 03:00 onwards)
  

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• Date - 05-08-2019 14:40 pm
  There appears to be some glitch in file access for above Assignment#1. Please solve Gaussian Elimination: Electrical Network Solved Example 2 in Kreyszig, 10th Edition, pg 275
  

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• Date - 05-08-2019 01:40 pm
  Lecture #1 - Assignment#1 Find currents i1, i2, i3 in this circuit by applying Kirchhoff's Voltage and Current laws