NIELIT B0–R4: BASIC MATHEMATICS Syllabus

B0–R4: BASIC MATHEMATICS

Objective of the Course

The aim of this course is to make students aware about mathematics skills which are necessary for understanding essential topics in computer science. The course is framed in such a way that the students get exposure to basic topics in mathematics that would prepare the students to learn the advance level courses in the domain of computer science such as discrete structure, computer graphics, computer and communication networks, simulation, operations research etc.

The courses provide introduction to complex analysis, differential & integral calculus, analytic geometry, vectors and matrices.

Outline of Course

S. No.	Topic	Minimum number of hours
1.	Complex numbers	04
2.	Matrices & determinants	08
3.	Differential Calculus	12
4.	Integral Calculus	10
5.	Sequences & Series	08
6.	Differential equation	04
7.	Analytic geometry	09
8.	Vectors	05

Lectures = 60

Practical/Tutorials = 60

Total = 120

Detailed Syllabus

1. Complex Numbers 04 Hours.

Representation of complex numbers in polar form, vector form, exponential form, properties of arguments & modulus. Graphical representatives of complex numbers, De – Moiver’s theorem, roots of complex numbers, solution of complex equations.

2. Matrices & Determinants 08 Hours.

Notion of matrices, triangular, diagonal, identity matrices, transpose of a matrix, symmetric and skew - symmetric matrices, orthogonal matrices, Hermitian and skew Hermitian matrices consistent and inconsistent system of linear equations, Cramer’s rule, Gauss elimination method, rank of a matrix, inverse of a square matrix. Determinants, properties of determinants, Eigenvalues & eigenvectors of a matrix, characteristic roots and characteristic vectors of a matrix.

3. Differential Calculus 12 Hours.

Functions and their graph. Domain & ranges of functions. Real numbers, exponential & logarithmic functions.

Limits & continuity of functions. Hospital’s rule.

4. Differential Calculus

Derivative as slopes and rate of change, techniques of differentiation, chain rule, Mean Value theorem. Maxima & minima, asymptotes.

5. Integral Calculus 10 Hours.

Integration by substitution, parts, partial fractions. Definite integral. Area between two curves, volume, lengths of plane curves, area of surface of revolution.

6. Sequences & Series 08 Hours.

Limits of sequences & series. Sandwich theorem. Ratio test, comparison test, integral test. Alternating series, Taylor & Mclaurin’s series.

7. Differential Equations 04 Hours.

First order differential equations and applications. Second order linear homogeneous differential equation.

8. Analytic Geometry 09 Hours.

Polar coordinates, tangent lines and arc length for parametric and polar curves, conic sections, conic section in polar coordinates, rotation of axes: second degree equations.

9. Vectors 05 Hours.

Vectors, dot & cross product of vectors, projections parametric equations of lines, planes in 3-space.

RECOMMENDED BOOKS

MAIN READING

1. H Anton, I. Bivens, S. Davis, “Calculus”, John Wiley and Sons.

2. E. Kreysig, “Advanced Engineering Mathematics”, 8 th Edition. Wiley, 2002, McGraw Hill

3. G.B. Thomas, Jr. R.L. Finney, “Calculus and Analytic Geometry”, Pearson Education Asia, Ninth Edition, 2002

SUPPLEMENTARY READING

1. S.T.Tan, Applied “Calculus” , Kent Publishing Company.