BP106RMT. REMEDIAL MATHEMATICS (Theory)30 Hours

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 (∈ – δ definition),

Unit-II (06 Hours)

Matrices and Determinant:

• Introduction to 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.

Unit-III (06 Hours)

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 w.r.t , where is any rational number.
• Derivative of , Derivative of , Derivative of .
• 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.
• Applications.

Unit-IV (06 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, applications.

Unit-V (06 Hours)

Differential Equations:

• Some basic definitions, Order and degree, Equations in separable form, Homogeneous equations, Linear Differential equations, Exact equations.
• Applications in solving Pharmacokinetic equations.

Laplace Transform:

• Introduction, Definition, Properties of Laplace transform.
• Laplace Transforms of elementary functions, Inverse Laplace transforms, Laplace transform of derivatives.
• Applications to solve Linear differential equations.
• Applications in solving chemical kinetics and Pharmacokinetics equations.