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