BT 9254 APPLICABLE MATHEMATICS FOR BIOTECHNOLOGISTS SYLLABUS | ANNA UNIVERSITY MTECH BIOTECHNOLOGY 1ST SEM SYLLABUS REGULATION 2009 2011 2012-2013 BELOW IS THE ANNA UNIVERSITY FIRST SEMESTER M.TECH BIOTECHNOLOGY DEPARTMENT SYLLABUS, TEXTBOOKS, REFERENCE BOOKS,EXAM PORTIONS,QUESTION BANK,PREVIOUS YEAR QUESTION PAPERS,MODEL QUESTION PAPERS, CLASS NOTES, IMPORTANT 2 MARKS, 8 MARKS, 16 MARKS TOPICS. IT IS APPLICABLE FOR ALL STUDENTS ADMITTED IN THE YEAR 2011 2012-2013 (ANNA UNIVERSITY CHENNAI,TRICHY,MADURAI, TIRUNELVELI,COIMBATORE), 2009 REGULATION OF ANNA UNIVERSITY CHENNAI AND STUDENTS ADMITTED IN ANNA UNIVERSITY CHENNAI DURING 2009
BT 9254 APPLICABLE MATHEMATICS FOR BIOTECHNOLOGISTS L T P C
3 0 0 3
UNIT I CALCULUS REVIEW 9
Calculus (Quick review of concepts): Review of limits, continuity, differentiability; Mean
value theorem, Taylor's Theorem, Maxima and Minima; Fundamental theorem of
Calculus; Improper integrals; Applications to area, volume; Convergence of sequences
and series; Power series; Partial Derivatives; Gradient andDirectional derivatives; Chain
rule; Maxima and Minima.
UNIT II ORDINARY DIFFERENTIAL EQUATIONS 9
First order differential equations: Exact equations, Integrating factors and Bernoulli
equations.
UNIT III SECOND AND HIGHER ORDER DIFFERENTIAL EQUATIONS 9
Linear ODE's with constant coefficients: the characteristic equations; Cauchy-Euler
equations; Linear dependence and Wronskians; Method of undetermined coefficients;
Method of variation of parameters; Laplace transforms: Inverse theorem, shifting
theorems, partial fractions.
UNIT IV LINEAR ALGEBRA 9
Basics: Vectors, matrices, determinants; Matrix addition and multiplication; Systems of
equations: Gauss elimination, Matrix rank, Linear independence, Cramer's rule; Inverse
of a matrix: Gauss-Jordan elimination; Eigenvalues and Eigenvectors: characteristic
polynomials, eigenvalues of special matrices(orthogonal, unitary, hermitian, symmetric,
skewsymmetric, normal).
UNIT V NUMERICAL METHODS 9
Solution of equations by iteration; Interpolation by polynomials;Piecewise linear and
cubic splines; Numeric integration and differentiation; Linear systems: Gauss elimination,
Gauss-Siedel, matrix inversion; LU factorization; Matrix eigenvalues; Numerical solution
of ODEs: Euler and Runge-Kutta methods, Predictor-Corrector methods; Exposure to
software packages like Matlab or Scilab.
TOTAL: 45 PERIODS
15
TEXTS/REFERENCES
1. G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, 9th Edition, ISE
Reprint, Addison-Wesley, 1998.
2. E. Kreyszig, Advanced engineering mathematics, 8th Edition, John Wiley, 1999.
3. W. E. Boyce and R. DiPrima, Elementary Differential Equations, 8th Edition, John
Wiley, 2005.
BT 9254 APPLICABLE MATHEMATICS FOR BIOTECHNOLOGISTS L T P C
3 0 0 3
UNIT I CALCULUS REVIEW 9
Calculus (Quick review of concepts): Review of limits, continuity, differentiability; Mean
value theorem, Taylor's Theorem, Maxima and Minima; Fundamental theorem of
Calculus; Improper integrals; Applications to area, volume; Convergence of sequences
and series; Power series; Partial Derivatives; Gradient andDirectional derivatives; Chain
rule; Maxima and Minima.
UNIT II ORDINARY DIFFERENTIAL EQUATIONS 9
First order differential equations: Exact equations, Integrating factors and Bernoulli
equations.
UNIT III SECOND AND HIGHER ORDER DIFFERENTIAL EQUATIONS 9
Linear ODE's with constant coefficients: the characteristic equations; Cauchy-Euler
equations; Linear dependence and Wronskians; Method of undetermined coefficients;
Method of variation of parameters; Laplace transforms: Inverse theorem, shifting
theorems, partial fractions.
UNIT IV LINEAR ALGEBRA 9
Basics: Vectors, matrices, determinants; Matrix addition and multiplication; Systems of
equations: Gauss elimination, Matrix rank, Linear independence, Cramer's rule; Inverse
of a matrix: Gauss-Jordan elimination; Eigenvalues and Eigenvectors: characteristic
polynomials, eigenvalues of special matrices(orthogonal, unitary, hermitian, symmetric,
skewsymmetric, normal).
UNIT V NUMERICAL METHODS 9
Solution of equations by iteration; Interpolation by polynomials;Piecewise linear and
cubic splines; Numeric integration and differentiation; Linear systems: Gauss elimination,
Gauss-Siedel, matrix inversion; LU factorization; Matrix eigenvalues; Numerical solution
of ODEs: Euler and Runge-Kutta methods, Predictor-Corrector methods; Exposure to
software packages like Matlab or Scilab.
TOTAL: 45 PERIODS
15
TEXTS/REFERENCES
1. G. B. Thomas and R. L. Finney, Calculus and Analytic Geometry, 9th Edition, ISE
Reprint, Addison-Wesley, 1998.
2. E. Kreyszig, Advanced engineering mathematics, 8th Edition, John Wiley, 1999.
3. W. E. Boyce and R. DiPrima, Elementary Differential Equations, 8th Edition, John
Wiley, 2005.
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