Table of contents
Remedial Mathematics Theory
UNIT I Partial fraction, Logarithms, Function
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 a limit of a function
UNIT II Matrices and Determinant
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 a 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 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 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 Analytical Geometry, Integration
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, Laplace Transform
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)
- 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
First Year B Pharm Notes, Syllabus, Books, PDF Subjectwise/Topicwise
First Year B Pharm Notes, Syllabus, Books, PDF Subjectwise/Topicwise
Calamine lotion * Pharmaceutical Analysis I Theory *
