# Chapter 3 (Differentiation) FSc Part 2 Math

Level: F.Sc (Pre-Engg)
Class: 2nd Year
Board: Punjab Textbook Board
Subject: Mathematics
Total Exercises: 8
Type: Notes

In this chapter we will read these topics:

• What is the differential of a function f(x) and what is the differential coefficient?
• What is the difference between delta(y) and dy?
• Use differential to find approximate value.
• Find the approximate increase in the volume of a cube of the length its each edge changes from 5 to 5.02.
• Find the approximate increase in the area of a circular disc if its diameter is increased from 44com to 44.4.
• Define integration.
• Some basic tips for integration.
• Define the indefinite integral.
• Write two theorems on anti-derivatives.
• Some basic formulae.
• Evaluate the problems.
• Write a note on integration by substitution.
• Write some important trigonometric substitutions.
• Integration by parts.
• Integration by partial fractions.
• When denominator contains non-repeated linear factors.
• When denominator contains repeated linear factors.
• When denominator contains non-repeated irreducible quadratic factors.
• Define definite integral.
• Define the fundamental theorem of integral calculus.
• Area under the curve.
• Find the area bounded by the curve.
• Find the area between the x-axis and the curve.
• Define the differential equations.
• Define the order of a differential equation.
• Define the degree of a differential equation.
• Define solution of a differential equation.
• Define general solution of a differential eqaution.
• Define particular solution of a differential equation.
• How many constants are involved in general solution of first-order differential equation.
• How many constants are involved in general solution of nth order.
• Solve the following differential equations.

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