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
INDUSTRY SUPPORT: None
6415 students have enrolled already!!
ABOUT THE INSTRUCTOR:
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. His research interests include Numerical Solutions of Integro-Differential Equations and numerical analysis.
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 Coefficients
SUGGESTED READING MATERIALS:
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.
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.
CERTIFICATION EXAM :
The exam is optional for a fee.
Date and Time of Exams: April 27 2019(Saturday). 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.
Final score will be calculated as : 25% assignment score + 75% final exam score
25% assignment score is calculated as 25% of average of Best 8 out of 12 assignments
E-Certificate will be given to those who register and write the exam and score greater than or equal to 40% final score. 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.