# Engineering Mathematics - I

By Prof. Jitendra Kumar   |   IIT Kharagpur
Learners enrolled: 2818
This course is about the basic mathematics that is fundamental and essential component in all streams of undergraduate studies in sciences and engineering. The course consists of topics in differential calculus,integral calculus, linear algebra and differential equations with applications to various engineering problems. This course will cover the following main topics: Mean Value Theorems; Indeterminate Forms; Taylor's and Maclaurin's Theorems. Partial Derivatives; Differentiability; Taylor's Expansion of Functions of Several Variables. Maxima and Minima. Improper Integrals. Differentiation under Integral Sign (Leibnitz rule).Multiple Integrals and their Properties. Applications of Multiple Integrals. System of Linear Equations. Vector Spaces; Basis and Dimension of a Vector Space. Rank of a Matrix and its Properties. Linear Transformation. Eigenvalues and Eigen vectors. Diagonalization . First Order Differential Equations. Higher Order Differential Equations with Constant Coefficients. Cauchy-Euler Equations.

INTENDED AUDIENCE  : All branches of science and engineering

Summary
 Course Status : Upcoming Course Type : Core Duration : 12 weeks Start Date : 26 Jul 2021 End Date : 15 Oct 2021 Exam Date : 23 Oct 2021 IST Enrollment Ends : 09 Aug 2021 Category : Mathematics Credit Points : 3 Level : Undergraduate

### Course layout

Week 1  :  Differential Calculus - Functions of One Variable
Week 2  :  Partial Derivatives
Week 3  :  Total Differential and Differentiability
Week 4  :  Taylor's Expansion of Functions. Maxima and Minima
Week 5  :  Improper Integrals
Week 6  :  Double Integrals
Week 7  :  Multiple Integrals & their Applications
Week 8  :  System of Linear Equations - Gauss Elimination. Vector Spaces
Week 9  :  Linear Transformations
Week 10 :  Eigenvalues and Eigenvectors, Diagonalization
Week 11 :  First Order Differential Equations
Week 12 :  Higher Order Differential Equations with Constant Coefficientss

### Books and references

• Piskunov, N., Differential and Integral Calculus, Vol 1 & 2, 2nd edition.Mir Publishers, 1974.
• Kreyszig, E., Advanced Engineering Mathematics, 10th edition. John Wiley & Sons, 2010.
• Thomas Jr, George B., Weir, Maurice D. and Hass, Joel R., Thomas’ Calculus, 12th edition. Pearson 2014.
• O’Neil, Peter V., Advanced Engineering Mathematics, 7th edition. Cengage learning, 2011.
• Strang, G., Linear Algebra and its Applications, Fourth Edition, 2009.
• Thomas, G.B. and Finney, R.L., Calculus and Analytic Geometry, 9th Edition, Pearson, Reprint, 2002.

### Prof. Jitendra Kumar

IIT Kharagpur
Jitendra Kumar is an Associate Professor at the Department of Mathematics, IIT Kharagpur. He completed his M.Sc. in Industrial Mathematics from IIT Roorkee and Technical University of Kaiserslautern, Germany in 2001 and 2003, respectively. He received his PhD degree in 2006 from Otto-von-Guericke University Magdeburg, Germany. He was Research Associate at the Institute for Analysis and Numerical Mathematics, Otto-von-Guericke University Magdeburg, Germany from 2006 to 2009. Dr. Kumar is the recipient of several recognized awards and fellowships, including Alexander von Humboldt fellowship, DAAD & DGF scholarships. His research interests include Numerical solutions of integro-differential equations, numerical analysis and modelling and simulations of problem in particulate systems.

### 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: 23 October 2021 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 Kharagpur .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team