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M 183 REMEDIAL MATHEMATICS (Theory), , 30 Hours, , Scope: This is an introductory course in mathematics. This subject deals with the, introduction to Partial fraction, Logarithm, matrices and Determinant, Analytical, geometry, Calculus, differential equation and Laplace transform., Objectives: Upon completion of the course the student shall be able to:1. Know the theory and their application in Pharmacy, 2. Solve the different types of problems by applying theory, 3. Appreciate the important application of mathematics in Pharmacy, Course Content:, 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, , 06Hours, ,  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 (- , sin, x n a n, nan1 , lim, 1, , definition) ,lim, xa xa, 0, , UNIT–II, 06Hours,  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, Cramer’s rule, Characteristic equation and roots of a square, matrix,, Cayley–Hamilton theorem, Application, of, Matrices, insolving Pharmacokinetic equations, , 51

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UNIT–III, 06Hours,  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 (productformula),, Derivative of the quotient of twofunctions, (Quotient formula) –Without Proof, Derivative of xn w.r.tx, where nisany, rational number,, Derivative of ex,, Derivative of loge x , Derivative of, x, a ,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, UNIT–IV, 06Hours,  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, 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, , Recommended Books (Latest Edition), , 06Hours, , 1. Differential Calculus by Shanthinarayan, 2. Pharmaceutical Mathematics with application to Pharmacy by, Panchaksharappa Gowda D.H., 3. Integral Calculus by Shanthinarayan, 4. Higher Engineering Mathematics by Dr.B.S.Grewal, 5. Advanced Engineering Mathematics by Dr. Chandrika Prasad & Dr. Reena Garg, Khanna, Publishing House, New Delhi., , 52