Introduction to Partial Fraction, Logarithms & Limits
Unit 1 lays the groundwork for pharmaceutical calculations. It starts with ‘Partial Fractions’, essential for simplifying integration problems. ‘Logarithms’ are the key to understanding pH, pKa, and First-Order Kinetics. Finally, ‘Functions and Limits’ introduce the concepts of continuity, preparing you for Calculus in Unit 3.
Syllabus & Topics
- 1Partial fraction: Introduction, Polynomial, Rational fractions, Proper and Improper fractions
- 2Resolving into Partial fraction: Linear non-repeated, linear repeated, and quadratic factors
- 3Application of Partial Fraction in Chemical Kinetics and Pharmacokinetics
- 4Logarithms: Introduction, Definition, Theorems/Properties
- 5Common logarithms, Characteristic and Mantissa
- 6Application of logarithm to solve pharmaceutical problems
- 7Function: Real Valued function, Classification
- 8Limits and continuity: Definition (ε – δ), Standard limits (x → a) (xⁿ – aⁿ) / (x – a) = n aⁿ⁻¹, lim (θ → 0) (sinθ / θ) = 1
Learning Objectives
Frequently Asked Questions (FAQs)
Q1. What is a Proper Fraction?
A proper fraction is one in which the degree of the numerator is less than the degree of the denominator (e.g.,𝑥/(𝑥2+1)x/(x2+1)). If the degree of the numerator is equal to or greater than that of the denominator, it is called an improper fraction.
Q2. How are Partial Fractions used in Pharmacy?
Partial fractions are used to simplify complex equations in chemical kinetics and pharmacokinetics. This simplification makes integration easier, helping to calculate drug concentration over time.
Q3. What is a Logarithm?
A logarithm answers the question: “To what power must a base be raised to obtain a given number?”
For example, log₁₀(100) = 2, because 10 2 = 100 10 2 =100.
Q4. What is a Real Valued Function?
A real-valued function assigns a real number to each value in its domain. In pharmacy, drug concentration C(t) is a real-valued function of time (t).
Q5. Define Limit of a function.
The limit of a function as x approaches a value a is the value that f(x) gets closer and closer to as x approaches a. It is a fundamental concept in calculus.