Higher Engineering Mathematics

By Dr. P. N. Agrawal | IIT Roorkee

Learners enrolled: 1903

This course is a basic course offered to UG/PG students of Engineering/Science background. It consists of four main topics :
1.Discrete Mathematics: Symbolic representation of statements, Duality, Tutologies and contradictions, Quantifiers, languages and Grammers, Finite state machines, Lattices as partially ordered sets, Lattices as Algebraic systems, Sublattices, Boolean algebra and Boolean functions, Representations of Boolean functions, Application of Boolean functions to synthesis of circuits, Circuit minimizations, Karnaugh Map.
2.Graph theory: Various types of Graphs, Subgraphs, Walks, Trails, Paths, Cycles, Eularian and Hamiltonian graphs, Travelling salesman problem, Vertex and edge connectivity, Matrix representation of graphs, Incidence and adjacency matrices of graphs, Planar graphs, Kuratowski’s graphs, detection of planarity, Euler’s formula, duals of a Planar graph, Colouring of graphs, Four color theorem.
3.Linear programming problems: Graphical method, simplex method, Big-M method, two phase method, Dual Simplex method and applications.
4.Queuing theory: Basic charecteristics of Queuing modles, Distribution of arrivals and service times, M/M/1:∞/FIFO model, M/M/S:∞/FIFO model, M/M/1:N/FIFO model, M/M/S:N/FIFO model and their applications.

INTENDED AUDIENCE: UG and PG students of technical institutions/ universities/colleges

PREREQUISITES: Nil

Summary

Course Status :	Completed
Course Type :	Core
Duration :	12 weeks
Category :	Mathematics
Credit Points :	3
Level :	Postgraduate
Start Date :	29 Jul 2019
End Date :	18 Oct 2019
Exam Date :	17 Nov 2019 IST

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

Page Visits

Course layout

Week 1: Symbolic representation of statements-I, Symbolic representation of statements-II, Tautologies and Contradictions, Predicates and Quantifiers-I, Predicates and Quantifiers-II.

Week 2: Validity of Arguments, Languages and Grammers-I, Languages and Grammers-II, Languages and Grammers-III, Finite- state machines.

Week 3: Partially ordered sets-I, Partially ordered sets-II, Partially ordered sets-III, Lattices-I, Lattices-II.

Week 4: Lattices-III, Lattices-IV, Lattices-V, Boolean Algebra-I, Boolean Algebra-II.

Week 5: Boolean Algebra-III, Boolean Algebra-IV, Logic Gates, Karnaugh map-I, Karnaugh map-II.

Week 6: Various types of Graphs-I, Various types of Graphs-II, Path and Connectivity, Subgraphs and Traversable Multigraphs, Undiected and Directed Graphs.

Week 7: Eulerian and Hamiltonian Graphs, Planer Graphs, Representation of Graphs, Isomorphic and Homeomorphic Graphs, Kuratowski’s Theorem.

Week 8: Dual of Graph, Coloring of Graphs-I, Coloring of Graphs-II, Trees-I, Trees-II.

Week 9: Graphical Method-I, Graphical Method-II, General Linear Programming Problem, Simplex Method-I, Simplex Method-II.

Week 10: Big-M Method-I, Big-M Method-II, Two Phase Method-I, Two Phase Method-II, Duality-I.

Week 11: Duality-II, Dual Simplex Method, Transportation Problem-I, Transportation Problem-II, Assignment Problem-I.

Week 12: Assignment Problem-II.

Books and references

1. Liu, C. L., Elements of Discrete Mathematics, Tata McGraw Hill.

2. Kenneth, K. R., Discrete Mathematics and its Applications, 7th Ed. Tata McGraw Hill.

3. Deo, N., Graph theory with Applications to Engineering and Computer Science, Prentice Hall India.

4. Chartrand, G. and Zhang, P., Introduction to Graph Theory, Tata McGraw Hill.

5. Taha, H. A., Operations Research, PHI Private Ltd.

6. Sundarapandian V., Probability statistics and Queuing theory PHI Private Ltd.
7. Grewal B. S., “ Higher Engineering Mathematics” Khanna Publishers.

Instructor bio

Dr. P. N. Agrawal is a Professor in the Department of Mathematics, IIT Roorkee. His area of research includes approximation Theory and Complex Analysis. He delivered 13 video lectures on Engineering Mathematics in NPTEL Phase I and recently completed Pedagogy project on Engineering Mathematics jointly with Dr. Uaday Singh in the same Department. Further he has completed online certification course “Mathematical methods and its applications” jointly with Dr. S.K. Gupta and two more courses namely “Integral equations and calculus of variations and its applications” and “Numerical Linear Algebra” with Dr. D. N. Pandey of the same department. He has just completed an online certification course entitled “Advanced Engineeering Mathematics” under NPTEL. He has taught engineering mathematics to B.Tech and M.Tech students at IIT Roorkee for many years. He has supervised fourteen Ph.D. theses and has published more than 200 research papers in reputed international journals of the world. Currently, he is supervising five research students.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 17 November 2019, Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100
Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75.

If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.
Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Roorkee. It will be e-verifiable at nptel.ac.in/noc.
Only the e-certificate will be made available. Hard copies are being discontinued from July 2019 semester and will not be dispatched

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