Remedial Mathematics in B.Pharm 1st semester: Complete unit-wise notes covering Algebra, Trigonometry, Calculus, Analytical Geometry, Statistics & Probability. Simple, clear, and exam-oriented study material for pharmacy students.
UNIT– I
Theory of Indices
- Laws of exponents (multiplication, division, powers, fractional and negative indices).
- Application: Calculation of drug concentrations and dilutions.
Logarithms
- Definition of logarithm.
- Laws of logarithms:
- log(ab) = log a + log b
- log(a/b) = log a – log b
- log(a^n) = n log a
- Application: Used in pH calculations, exponential growth/decay, and pharmacokinetics.
Partial Fractions
- Breaking down rational functions into simpler fractions.
- Useful in solving complex equations in biostatistics and kinetics.
Determinants & Matrices
Cramer’s rule for solving linear equations.
Determinant of a 2×2 and 3×3 matrix.
Link ↓
UNIT–II
Measurement of Angles
- Degree and radian system.
- Conversion between degrees and radians.
Trigonometric Ratios
- Sine, cosine, tangent, cotangent, secant, cosecant.
- Relations between them.
Relations between Sides and Angles of a Triangle
Law of sines, law of cosines, law of tangents.
Link ↓
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),
Functions and Limits
- Concept of functions, types of functions (polynomial, exponential, logarithmic).
- Definition of limit, left-hand limit and right-hand limit.
Differentiation and its Rules
- Derivatives of algebraic, exponential, and logarithmic functions.
- Rules: sum rule, product rule, quotient rule, chain rule.
- Application: Rate of change in drug concentration.
Maxima and Minima
Application: Optimization of dosage forms, stability studies.
Finding maximum and minimum values of functions.
Link ↓
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
Link ↓
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
Link ↓