Introduction to Differential & Integral Calculus.pptx

Introduction to Differential & Integral Calculus

1. Introduction to Calculus By Mahen Mahindaratne MBA, LLB

2. When , the rate at which changes, to a change in is . This can only be calculated with a difference in , and values. What if no such difference can be observed, or we simply need to know the rate of change at a given point in the function , and not over some range, or arc? That is where Differential Calculus becomes relevant.  

3. When ,  

4. When , And if we assume that , is negligible, we get the derivative of , as  

5. When , And if we assume that , is negligible, we get the derivative of , as  

6. , can be more formally written as , which can also be written as  

7. Just as much as the derivative of , is , and the derivative of , is , the integral of , is , and the integral of is . This can be written as , and that the  

8. Integral Calculus, is especially useful to determine the area under a curve. But we need to know the area under the curve between points , and .  

9. Thus, the derivative of the Square, , will always be , and the derivative of the Cube, , will always be . Thus, the derivative of the Exponent, , will be The derivative of a Constant, , will always be The derivative of , will always be , assuming . This can be more accurately stated that the derivative of is in fact . And the derivative of a polynomial, would simply be the sum of the derivatives of each of its terms.  

10. Thank you!