REMEDIAL MATHEMATICS (Theory)
Partial fraction
Introduction, Polynomial, Rational fractions, Proper and Improper fractions, Partial fraction , Resolving into Partial fraction, Application of Partial Fraction in Chemical Kinetics and Pharmacokinetics
Logarithms
Introduction, Definition, Theorems/Properties of logarithms, Common
logarithms, Characteristic and Mantissa, worked examples, application of logarithm to solve pharmaceutical problems.
Function:
Real Valued function, Classification of real valued functions,
Limits and continuity :
Introduction , Limit of a function, Definition of limit of a function (๏ – ๏ค
n n definition) , lim
x ๏ญa ๏ฝ na
n๏ญ1
, lim
sin๏ฑ ๏ฝ 1,
x๏ฎa x ๏ญ a ๏ฑ๏ฎ0 ๏ฑ
Matrices and Determinant:
Introduction matrices, Types of matrices, Operation on matrices,
Transpose of a matrix, Matrix Multiplication, Determinants, Properties of
determinants , Product of determinants, Minors and co-Factors, Adjoint
or adjugate of a square matrix , Singular and non-singular matrices,
Inverse of a matrix, Solution of system of linear of equations using matrix
method, Cramerโs rule, Characteristic equation and roots of a square
matrix, CayleyโHamilton theorem,Applicationof Matrices in solving
Pharmacokinetic equations
Calculus
Differentiation : Introductions, Derivative of a function, Derivative of a
constant, Derivative of a product of a constant and a function , Derivative
of the sum or difference of two functions, Derivative of the product of two functions (product formula), Derivative of the quotient of two functions (Quotient formula) โ Without Proof, Derivative of x
n w.r.tx,where n is any rational number, Derivative of e
x ,, Derivative of loge x , Derivative of
a x ,Derivative of trigonometric functions from first principles (without
Proof), Successive Differentiation, Conditions for a function to be a
maximum or a minimum at a point. Application
Analytical Geometry
Introduction: Signs of the Coordinates, Distance formula, Straight Line : Slope or gradient of a straight line, Conditions for parallelism and perpendicularity of two lines, Slope of a line joining two points, Slope โ intercept form of a straight line
Integration:
Introduction, Definition, Standard formulae, Rules of integration , Method of substitution, Method of Partial fractions, Integration by parts, definite integrals, application
Differential Equations : Some basic definitions, Order and degree, Equations in separable form , Homogeneous equations, Linear
Differential equations, Exact equations, Application in solving
Pharmacokinetic equations
Laplace Transform : Introduction, Definition, Properties of Laplace
transform, Laplace Transforms of elementary functions, Inverse
Laplace transforms, Laplace transform of derivatives, Application to
solve Linear differential equations, Application in solving Chemical
kinetics and Pharmacokinetics equations
