Syllabus
UNIT-I
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 ( Î – d definition)
UNIT-II
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 of adjugate of a square matrix, Singular and non-singular matrices, Inverse of a matrix,
Solution of system of linear equations using matrix method, Cramer's rule, Characteristic equation and roots
of a square matrix, Cayley-Hamilton theorem, Applications of Matrices in solving Pharmacokinetic equations.
UNIT-III
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 fucntions (Quotient formula) – Without Proof,
Derivative of xn w.r.tx, where n is any rational number, Derivative of ex
,. Derivative of loge x, Derivative of ax.
Derivative of trigonometric functions from first principles (Without Proof) Successive Differentiation, Conditions
for a function to be maximum or a minimum at a point. Application
UNIT-IV
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 – intercept form a straight line
Integration: Introduction, Definition, Standard formulae, Rules of integration, Method of substitution, Method
of Partial fractions, Integration by parts, definite integrals, application.
UNIT-V
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, Definitions, 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.
