## Details

COURSE NAME: Mathematics
COURSE CODE: MAT 100
PROGRAM: B.Sc. Biotechnology and B.Sc. Microbiology
SEMESTER: Two
CREDITS: Four

## Syllabus

Linear Algebra:

Matrices-definition, Types of matrices, Addition and subtraction of matrices, Multiplication of matrices, Properties of matrix multiplication, Transpose of a matrix, Symmetric and Skew-symmetric matrix, Orthogonal matrix, Adjoint of a matrix, Singular and Non-Singular matrix, Inverse of a matrix, Rank of a matrix, Cramer’s rule, Eigen Values and Eigen Vectors, Cayley Hamilton Theorem,

Sequence and Series Sequence-definition, Arithmetic progression, Geometric Progression, Harmonic Progression, Infinite series, Sum to infinity, Matrices, Determinants and properties of determinants, Minors and co-factors,

Basic calculus:

Functions, Limits-definition problems Continuity-definition, properties, Continuity on an interval and continuity of polynomials, continuity of rational functions Differentiation- Slopes and Rate of change Product rule, Quotient rule Derivative of rational powers of x, Implicit differentiation Indeterminate forms and L Hospital rule Integration – Indefinite integral Integration from the view point of differential equations, Integration by  substitution,  Area as a limit of  a sum, The definite integral,

Differential Equation:

Differential Equations Definition, Initial and boundary value problems, Classification of First order differential equations, Linear equations, Bernoulli’s equation, Exact equations  Separable equations, Homogeneous equations,

Statistics:

Statistics, Collection, Classification and Tabulation of data, Bar diagrams and Pie diagrams, Histogram, Frequency curve and frequency polygon, Ogives Mean, median,mode, Standard deviation.

Lecture by lecture details

Lecture number

Topics

Objectives

Remarks

1

Matrices-definition, Types of matrices, Addition and subtraction of matrices

2

Multiplication of matrices, Properties of matrix multiplication

3

Determinants and properties of determinants, Minors and co-factors

Transpose of a matrix, Symmetric and Skew- symmetric matrix, Orthogonal matrix

5

Adjoint of a matrix, Singular and Non-Singular matrix, Inverse of a matrix

6

Cramer’s rule

Use vectors and matrices to solve linear systems of algebraic euqations.

7 – 8

Rank of a matrix

9

Eigen Values and Eigen Vectors

Find the eigenvalues and eigenvectors of a matrix.

10

Cayley Hamilton Theorem

11 – 13

Arithmetic progression, Geometric Progression, Harmonic Progression

14

Functions, Limits-definition problems Continuity-definition, properties

Basic Concepts

15-16

Continuity on an interval and continuity of polynomials, continuity of rational functions

17-18

Differentiation- Slopes and Rate of change, Product rule Quotient rule

19-20

Derivative of rational powers of x, Implicit differentiation Indeterminate forms and L Hospital rule

21-22

Integration – Indefinite integral Integration from the view point of differential equations

23 – 24

Integration by  substitution Area as a limit of  a sum The definite integral,

25- 27

Differential Equations Definition, Initial and boundary value problems

Know what is meant by a "differential equation." Determine if a given function is a solution to a particular differential equation.

Understand how the terms linear, non-linear, order, ordinary and partial are used to classify differential equations. Find all solutions of a separable differential equation. Find the general solution to a linear first order differential equation. Find the general solution for a first order, linear, constant coefficient, homogeneous system of differential equations.

28

Classification of First order differential equations, Linear equations

29-30

Bernoulli’s equation

31 – 32

Exact equations  Separable equations

33 -35

Homogeneous equations

36 – 38

Statistics, Collection, Classification and tabulation of data

39 -40

Bar diagrams and Pie diagrams,

40 – 42

Histogram, Frequency curve and frequency polygon, Ogives

43

Measures in central tendency Measures of dispersion

44-45

Problem solving

## Text Books

1. Anton-Bivens-Davis   “ 7th Edition Calculas ”  WSE  WILEY
2. S.C Gupta , V. K Kapoor “Fundamentals of Mathematical statistics ” Sulthan Chand and Sons.

## REFERENCE BOOKS

1. S.Lipschutz&M.Lipson        “Discrete Mathematics” 2001-TMH
2. Thomas, Finney “Calculus    9th edition” Pearson publications
3. Seymour Lipschutz, Marc Lipson   “Schaum’s Outlines Of Probability” MCGRAWHILL    2000 2nd
4. Bali  Iyengar “ A text book of Engineering Mathematics ”   Dr. B . S  Grewal “ Engineering Mathematics ”