Course

Theory

Linear Algebra Matrices-definition, Types of matrices, Addition and subtraction of matrices, Multiplication of matrices, Properties of matrix multiplication, Determinants and properties of determinants, Minors and co-factors, 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.

Practical

Algebra Sequence and Series Sequence-definition, Arithmetic progression, Geometric Progression, Harmonic Progression, Infinite series, Sum to infinity.

Unit 1

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

Unit 2

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,

Unit 3

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.

LEARNING OBJECTIVES:   

The mathematics course deals with linear algebra, differential equations, basic calculus, statistics etc. As an area of study, it has a broad appeal in that it has many applications in different aspects of biology. 

 COURSE OUTCOMES:  

After completing the course, students shall be able to   

CO1: Apply linear algebra concepts to model, solve and analyze real world situations.  

CO2: Find rank, eigen values and eigen vectors of a matrix and understand the importance of Cayley’s Hamilton theorem.   

CO3: Demonstrate solutions to first order differential equation by various methods and solve basic applications problems related to electrical circuits, orthogonal trajectories and newton’s law cooling.  

CO4: Discriminate among the structure and procedure of solving higher order differential equations with constant and variable coefficients.  

REFERENCES:1. P. R. Vittal – Business Mathematics and Statistics, Margham Publications 2014, Chennai.2. S.C Gupta, V. K Kapoor ?Fundamentals of Mathematical statistics? Sulthan Chand and Sons 12th Edition 2020. 3. S. Lipschitz & M. Lipson ?Discrete Mathematics? 2001-TMH 4. Thomas Finney ?Calculus 9th Edition? Pearson publications 5. Seymour Lipschitz, Marc Lipson ?Schaum?s Outlines of Probability? MCGRAWHILL 2000 2nd edition.6. Bali Iyengar ?A textbook of Engineering Mathematics? Dr. B. S Grewal ?Engineering Mathematics?- 9th Edition ? 2010