BPH-208: PHARMACEUTICAL MATHEMATICS
THEORY
Max. Marks: 80 Total Hours: 75 (3hrs/week)Note: Examiner to set eight questions and the candidates are required to attempt any five.
- Algebra: Solution of linear equation up to two variables only, solution of quadratic equation. Determinants and their six important properties, solutions of simultaneous equations by Cramar’s rule. Definition of various matrices up to upper triangular matrices, arithmetic operations on matrices, transpose, adjoint reciprocal and inverse of a matrix, solution of simultaneous equations using matrix methods. Partial fractions and resolution of linear and quadratic (non-repeated) partial functions. (20)
- Trigonometry: revision on angle measurement and T-ratios, addition, subtraction and transformation formulae. T- ratio of multiple, sub multiple and allied angles, solution of simple trigonometric identities based on above concepts. Pharmaceutical application of logarithms. (5)
- Analytical plane geometry: Cartesian co-ordinates, distance between two points, area of triangle, locus of a point, straight line, slope and intercept form, general equation of first degree. (4)
- Calculus:
- Differential: Limits and functions, differential coefficient, differentiation of standard functions, including function of a function (chain rule), differentiation of implicit functions, logarithmic differentiation, parametric differentiation, elements of successive differentiation. (6)
- Intergral: Integration as inverse of differentiation, indefinite integrals of standard forms, integration by parts, by partial fractions and by substitution, formal evaluation of definite integrals. (5)
- Differential equations: definition and formation of ordinary differential equations, equations of first order and first degree, variable separable, homogeneous equations, linear equations (Liebnitz form) and differential equations reducible to these types. Linear differential equations of order greater than one with constant coefficients, complementary function and paricular integrals of ex, xm, sin (ax + b) or cos (ax + b) types of functions, solution of simple simultaneous linear differential equations. Pharmaceutical transforms. (8)
- Lapalace transforms: definition, properties of linearity and shifting, transforms of elementary function (without proof) and inverse laplace transforms not involving Euler’s theorem, transforms of derivatives, solutions of ordinary and simultaneous differential equations. (6)
- Collection of primary and secondary data through experiments or surveys sampling and complete enumeration survey, merits and limitations of various random and non-random sampling methods, data organization including frequency distributions and tabulation, diagrammatic representation of data, simple, multiple, sub-divided and floating bar diagrams, pie diagrams. 2-D and 3-D pictographic representation, graphs of frequency distributions. (6)
- Measures of central tendency, ideal characteristics, mean, median, mode, GM, HM and weighted arithmetic mean from discrete and continuous frequency distributions, quartiles, measures of dispersion, range, quartile deviation, mean deviation, standard deviation, calculation of standard deviation from discrete and continuous frequency distributions, standard error of means, coefficient of variation. (4)
- Probability and events, Bayes theorem, probability theorems, probability distributions, elements of binomial and Poisson distributions, normal distribution, normal distribution curve, and properties, calculation of areas under normal curve and standard normal curve (Z statistic), confidence limits, deviations from normality, Kurtosis and skewness, elements of central limit theorem. (5)
- Linear correlation and regression analysis, scatter plots, method of least squares, Pearsonian coefficients of correlation and determination, definitions, of amount of explained variance, standard error of estimate and significance of regression(F). (3)
- Statistical inference, type I and II errors, t-test (paired and unpaired). (3)
- S. Grewal, Higher Engineering Mathematics, Khanna Publishers, New Delhi (Latest Edition).
- Schaum, Differeptial Equations, McGraw-Hill, Singapore, 1982.