Remedial Mathematics

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 ( – definition), = , = 1 (Chapters - 1, 2 , 3)
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 or 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, Application of Matrices in solving Pharmacokinetic equations. (Chapters - 4, 5)
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 functions (Quotient formula) - Without Proof, Derivative of xn w.r.t x, 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 a maximum or a minimum at a point. Application. (Chapter - 6)
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 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. (Chapters - 7, 8)
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, 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. (Chapters - 9, 10, 11)