Brief introduction to Calculus Limits, its importance along with its real examples and Implementations in Sciences

1. CALCULUS PRESENTATION:THE REAL WORLD
APPLICATIONS OF LIMITS

2. Team Members
BSSE 2020
Neha Haroon
BSSE 2020
Maheen Abdul
Wahid
BSSE 2020
Tatheer Zara
BSSE 2020
.
Abdur Rehman
47 24 66 6
Roll no.
COURSE: CALCULUS SUBMITTED TO: MISS HINA SALEEM
7-July-2020

3. Outline of Calculus
Why is Calculus Important ?
What is Limit?
Why do we need Limits?
Fields using Calculus Limits
01
02
03
04
05
Demonstration
Plan

4. Outline of Calculus
Calculus is the branch of mathematics that focuses on :
Limits
Functions
Derivatives
Integrals
And Infinite Series

5. Why Is Calculus Important?
As Calculus provides a mathematical model to many such experiments that are either practically impossible (.i.e.; speed of
light) or way too dangerous and expensive(Cancer treatment)
Calculus makes us able see through the future and the past, in endless dimensions.
We use calculus to explain everything that is in some kind of motion or change(WHICH IS PRETTY MUCH ALL THAT EXISTS
! )
Climate change or
Population growth
models
01
Spread of diseases
and preprations of
medicine
MEDICENE
03
Mechanisms to resolve
conflicts or deal with
Economic or Financial crisis
BUSINESS
02
Models to approximate
risk levels and
functionality
ENGINEERING
04

6. What Is a Limit ?
Our best prediction of a point we did’nt or cannot observe due to
mathematical black holes like :
Divide by
Zero
Complex
numbers
Infinity
(in any way)
General sense
It allows us to determine what value of a function is
approaching when we use a particular input
Rather than functions output, the value getting
close to is significant

7. 01
Limits let us ask ‘What if?’ for exceptional mathematical scenarios
The limits wonders’ if you can see everything except a single value, what
do you think ?
These are the questions the problem solvers ask for real world health,
business , mechenical, and civil problems
02
For things we want an accurate estimate or predication but we cant easily
measure as we can look beyond future etc
When do we use Limits in Real World ?
LIMITS REAL
REQUIREMNTS
Why do we need Limits ?

8. Implementations of Limits from Calculus
Weather Forecasting
Systems:
Meterologist use the numerical
approximation predications of Calculus
by numerous amount of Data collected
of current states
Medicine:
By using complex estimations
(approximation ) method of Calculus
Researchers evaluate the approximate .
 Rate of disease shrink / growth
 Sizes of a tumors or clots(increasing or decreasing)
 Right timings for treatments

9. Implementations of Limits from Calculus
Complex Computations:
Limits are also used as real-life approximations
to calculating derivatives. It is very difficult to
calculate a derivative of complicated
motions in real-life situations. So, to make
calculations, engineers will approximate a
function using small differences in the a
function and then try and calculate
the derivative of the function by having
smaller and smaller spacing in the function
sample intervals.
Modern Physics and
Research:
Most of the modern physics principles
have grounds on Calculus as the
extraordinary experiments of
light and relativity are not
practically possible and
mathematical models provide a flexible
way of Research.
First real understanding of rates is
driven from limits
=> lim f(x) – f(xo)
x→xo x - xo

10. Implementations of Limits from Calculus:
Special Theory of Relativity:
Lorentz Factor relates the length contraction and
time dilation of an object to its velocity.
Anyway, the equation is :
1 = γ AND lim 1 = undefined
/1 – v² v→c / 1 - v²
√ c² √ c
∴ v ≠ c
Instantaneous Velocity:
As limits is tending certain value(s) to a veiled
or impossible value(tending= not practically, but
theoretically is achievable)
Example:
V(avg.)=dx/dt
V(inst.)=dx/dt where t → 0
here → (tending to) means velocity at an
exact certain point of time.
Some More Applications in Physics
This is also a sort of
mathematical proof that you
CANT DIVIDE BY ZERO(as you
can excede speed of light )
or the other way around.

11. Business:
Economist use the estimation methods of Calculus to all approximate all possibilities and limits to
the subtle behaviour of business by implementing bounded rationality concepts for
minimizing or maximizing the profit or loss
Limits of Calculus are also used for determining the most oppurtune times to buy or sell goods
or considering affects of price on the consumers purchase
Limits can be used when working on the concepts like Margins
Calculus can help us by providing a reasonable dependable way to record changes using
numbers and approximation
Probability and Statistics have there grounds on Calculus limits and functions
Implementations of Limits from Calculus

12. Architecture:
Architects use Limits as a means of
Analytical skills providing a reasonable
estimate of
Risk levels and Mathematical models on
grounds of the data provided . For
appropriate heights and loads which cannot
be computed in any other ways.
Implementations of Limits from Calculus
Engineers:
Almost all disciplines involve the mathematical
modeling which makes the work like for
aeronautical engineers for designing aircrafts is
completely based mathematical models and
testing using algorithms they measure the
limitations and measure the limits of the new
designs whether they can fly with load
appropriately before they practically crash them.
Model a gasoline, for a new car may be quite
complex for the designing team, as the
geometry of complex polynomials for the small
intervals called meshs. Whereas, as function
with the limits make the work quite simpler as
all the risks and approximations make the work
quite simpler.

13. THANK YOU
“Calculus is the most powerful weapon of thought yet devised by the wit of man”
~Wallace B. Smith~