(MA05367) MATHEMATICS FOR BIOTECHNOLOGISTS

UNIT I: Differential Calculus
Introduction to Sets, Relations, Functions.
Concepts of limit, continuity, differentiation, product rule, quotient rule. Differentiation
of trigonometric, logarithmic, exponential functions. Applications of differentiation –
problems on tangent, sub tangent normal, sub normal. Introduction to partial
differentiation, Euler’s theorem.
Unit II: Integral Calculus
Introduction, Integration of different functions, methods of Integration, Integration
by parts. Concept of definite integrals. Applications of definite integrals – problems
on areas.
Unit III: Matrices
Types of matrices, determinants, Inverse of a square matrix, Solving of simultaneous
equations by Cramer’s method Matrix inversion method and Gauss Jordan methods.
Rank of a matrix, Echelon form. Solutions for linear equations. Eigen values and
Eigen vectors.
Unit IV: Ordinary Differential equations
Forming of differential equation by eliminating arbitrary constants, first order and
first degree – variables and separables, exact, homogeneous, linear and Bernoulli’s
equations.
UNIT-V : Bernoulli’s equations
Non-homogeneous Linear Differential Equations of Second and higher order with
constant coefficients with RHS term of the type -eax sinax cosax Polynomials in x,
eax V(x), xV(x) Applications to first order differential equations to growth and decay
problems
UNIT VI: Numerical Methods
Iterative Methods: Bisection, Newton Raphson, Successive approximation, Guass
Jordan and Guass siedel methods.
UNIT-VII:
Interpolation, Lagrange interpolation, Newton’s forward difference, backward
difference and central difference interpolation methods. Numerical Integration by
Trapezoidal and Simpson’s rules, numerical solution to differential equations, Euler,
Ranga kutta methods.
Unit – VIII
Laplace Transforms
Laplace transforms of some standard functions, linear property, shifting theorems,
change of scale property, multiplication by powers of t, division by t.
Inverse Laplace Transforms - Shifting property, finding inverse laplace by partial
fractions, multiplication by powers of s, division by s.
Applications of laplace transforms for solving ordinary differential equations.
Mathematical Modelling in Biotechnology.
TEXT BOOKS:
1. A Text Book of Engineering Mathematics Volume-II, 2005 T,K.V.Iyengar,
B.Krishna Gandhi and others, S. Chand and Company.
2. Engineering Mathematics, B.V.Ramana, Tata McGraw-Hill 2003.
REFERENCES:
1. Engineering Mathematics-II, 2002, P.Nageswara Rao, Y.Narsimhulu,
Prabhakara Rao.
2. Engineering Mathematics, S.K.V.S. Sri Rama Chary, M.Bhujanga Rao, Shankar,
B.S.Publications 2000.
3. Advanced Engineering Mathematics (eighth edition), Erwin Kreyszig, John
Wiley & Sons (ASIA) Pvt. Ltd.2001.
4. Advanced Engineering Peter V.O’Neil Thomson Brooks/Cole.
5. Advanced Engineering Mathematics, Merle C.Potter, J.L.Goldberg, E.F.
Arbufadel, /oxford University Press. Third Edition 2005.
6. Numerical Methods: V N Vedamurthy, Iyengar N Ch N Vikas Pub. Reprint
2005.
7. Numerical Methods: S.Arumugam & others. Scitech Pub.
8. Elementary Numerical Analysis: An Algorithmic Approach: S.D.Conte and
Carl.D.E.Boor, Tata Mac-Graw Hill
9. Introductory Methods of Numerical Analysis: S.S.Sastry, Prentice Hall of India,
Pvt Ltd.,