COURSE SUMMARY
Course Title:
Remedial Mathematics - Theory
Course Code:
BP 106RMT
Year Taught:
2014
2015
2016
2017
2018
Semester:
1
Degree:
School:
School of Pharmacy
Campus:
Kochi

'Remedial Mathematics - Theory (30 Hours)' is a course offered in the first semester of B. Pharm program at School of Pharmacy, Health Sciences campus, Amrita Vishwa Vidyapeetham.

#### SCOPE AND OBJECTIVES

Course Duration: 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

#### SYLLABUS

Unit I (06 Hours)

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

Unit II (06 Hours)

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,Applicationof Matrices in solving Pharmacokinetic equations

Unit III (06 Hours)

Calculus

DifferentiationIntroductions, 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.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 a maximum or a minimum at a point. Application

Unit IV (05 Hours)

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 (06 Hours)

Differential Equations: Some basic definitions, Order and degree, Equations in separable form , Homogeneous equations, Linear Differential equations, Exact equations, Application in solving Pharmacokinetic equations

Plant growth and development

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

#### REFERENCE

Recommended Books (Latest Edition)

• Differential Calculus by Shanthinarayan
• Pharmaceutical Mathematics with application to Pharmacy by Panchaksharappa Gowda D.H.
• Integral Calculus by Shanthinarayan
• Higher Engineering Mathematics by Dr.B.S.Grewal