Mathematics Second Semester Syllabus for BSc Biotechnology and BSc Microbiology
Details
COURSE NAME: Mathematics
COURSE CODE: MAT 100
PROGRAM: B.Sc. Biotechnology and B.Sc. Microbiology
SEMESTER: Two
CREDITS: Four
Syllabus
Linear Algebra:
Matricesdefinition, Types of matrices, Addition and subtraction of matrices, Multiplication of matrices, Properties of matrix multiplication, Transpose of a matrix, Symmetric and Skewsymmetric matrix, Orthogonal matrix, Adjoint of a matrix, Singular and NonSingular matrix, Inverse of a matrix, Rank of a matrix, Cramer’s rule, Eigen Values and Eigen Vectors, Cayley Hamilton Theorem,
Sequence and Series Sequencedefinition, Arithmetic progression, Geometric Progression, Harmonic Progression, Infinite series, Sum to infinity, Matrices, Determinants and properties of determinants, Minors and cofactors,
Basic calculus:
Functions, Limitsdefinition problems Continuitydefinition, 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 
Matricesdefinition, Types of matrices, Addition and subtraction of matrices 


2 
Multiplication of matrices, Properties of matrix multiplication 


3 
Determinants and properties of determinants, Minors and cofactors 


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



5 
Adjoint of a matrix, Singular and NonSingular 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, Limitsdefinition problems Continuitydefinition, properties 
Basic Concepts 

1516 
Continuity on an interval and continuity of polynomials, continuity of rational functions 


1718 
Differentiation Slopes and Rate of change, Product rule Quotient rule 


1920 
Derivative of rational powers of x, Implicit differentiation Indeterminate forms and L Hospital rule 


2122 
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, nonlinear, 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 


2930 
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 


4445 
Problem solving 


Text Books
 AntonBivensDavis “ 7^{th} Edition Calculas ” WSE WILEY
 S.C Gupta , V. K Kapoor “Fundamentals of Mathematical statistics ” Sulthan Chand and Sons.
REFERENCE BOOKS
 S.Lipschutz&M.Lipson “Discrete Mathematics” 2001TMH
 Thomas, Finney “Calculus 9th edition” Pearson publications
 Seymour Lipschutz, Marc Lipson “Schaum’s Outlines Of Probability” MCGRAWHILL 2000 2^{nd}
 Bali Iyengar “ A text book of Engineering Mathematics ” Dr. B . S Grewal “ Engineering Mathematics ”
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