ADDITIONAL MATHEMATICS – II(18MATDIP41)

ADDITIONAL MATHEMATICS – II

Course Code:18MATDIP41
CIE Marks:40
SEE Marks :60
Teaching Hours/Week (L:T:P) :(2:1:0)
Credits :0
Exam Hours :03

Course Learning Objectives:

• To provide essential concepts of linear algebra, second & higher order differential equations
along with methods to solve them.
• To provide an insight into elementary probability theory and numerical methods.

Module-1

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.

Module-2

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.

Module-3

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)=e ax ax
ax sin, cos/ for ( )yDf = (xR ).]

Module-4

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.

Module-5

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:

7. The question paper will have ten full questions carrying equal marks.
8. 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 a sub-question covering all the topics under a module.
• The students will have to answer five full questions, selecting one full question from each

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

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ADDITIONAL MATHEMATICS – II(18MATDIP41)