## Course Detail

 Course Name Mathematics Course Code MAT 100 Program BSc. in Biotechnology, BSc. in Microbiology Semester Two Credits Four Year Taught 2019

### 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
2015 2014

### 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.

### Resources

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 ”

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