Linear Algebra:
Introduction - rank of matrix by elementary row operations - Echelon form. Consistency of system of linear equations - Gauss elimination method. Eigen values and Eigen vectors of a square matrix. Problems.
Numerical Methods:
Finite differences. Interpolation/extrapolation using Newton’s forward and backward difference formulae (Statements only)-problems. Solution of polynomial and transcendental equations – Newton-Raphson and Regula-Falsi methods (only formulae)- Illustrative examples. Numerical integration: Simpson’s one third rule and Weddle’s rule (without proof) Problems.
Higher order ODE’s:
Linear differential equations of second and higher order equations with constant coefficients. Homogeneous /non-homogeneous equations. Inverse differential operators.[Particular Integral restricted to R(x)=eax, sin ax/cos ax for f(D)y=R(x).]
Partial Differential Equations (PDE’s):-
Formation of PDE’s by elimination of arbitrary constants and functions. Solution of non-homogeneous PDE by direct integration. Homogeneous PDEs involving derivative with respect to one independent variable only.
Probability:
Introduction. Sample space and events. Axioms of probability. Addition & multiplication theorems. Conditional probability, Bayes’s theorem, problems.
Course Outcomes:
At the end of the course the student will be able to:
CO1: Solve systems of linear equations using matrix algebra.
CO2: Apply the knowledge of numerical methods in modelling and solving engineering problems.
CO3: Make use of analytical methods to solve higher order differential equations.
CO4: Classify partial differential equations and solve them by exact methods.
CO5: Apply elementary probability theory and solve related problems.
Question paper pattern:
• The question paper will have ten full questions carrying equal marks.
• Each full question will be for 20 marks.
• There will be two full questions (with a maximum of four sub- questions) from each module.
• Each full question will have sub- question covering all the topics under a module.
• The students will have to answer five full questions, selecting one full question from each module.
Textbook
1 Higher Engineering Mathematics B.S. Grewal Khanna Publishers 43rd Edition, 2015
Reference Books
1 Advanced Engineering Mathematics E. Kreyszig John Wiley & Sons 10th Edition, 2015
2 Engineering Mathematics N. P. Bali and Manish Goyal Laxmi Publishers 7th Edition, 2007
3 Engineering Mathematics Vol. I Rohit Khurana Cengage Learning 1st Edition, 2015