Class notes
Mathematical Engineering 1
- Course
- Institution
- Book
Providing in depth concepts of double integral, jacobian, taylor's series, chain rule , partial differentiation and many more in detail.
[Show more]
Connected book
Book Title:
Author(s):
- Edition:
- ISBN:
- Edition:
Seller
Follow
yashgupta2
Content preview
Lecture-2Mathematics 1 (15B11MA111)
CO [C105.1]
Module: Partial differentiation
1
,Topics to be covered
Function of two variables
Neighborhood of a point
Limit
Definition
Examples
Assignment
Reference for the lecture
R.K Jain and S.R.K. Iyenger, “Advanced Engineering Mathematics” fifth
edition, Narosa publishing house, 2016.
2
,Function of two variables
Let 𝒛 = 𝒇 𝒙, 𝒚 be a function of two variables then the set of points
(𝒙, 𝒚) for which 𝒛 𝒐𝒓 𝒇(𝒙, 𝒚) be defined is called domain of 𝒛 and
the corresponding values of 𝒛 is called range of 𝒛.
For example: (i) Let 𝒛 = 𝟏 − 𝒙𝟐 − 𝒚𝟐 and 𝒛 𝒊𝒔 𝒓𝒆𝒂𝒍.
Then 𝟏 − 𝒙𝟐 − 𝒚𝟐 ≥ 𝟎, 𝒊. 𝒆 𝒙𝟐 + 𝒚𝟐 ≤ 𝟏, which is its domain and
the range is the set of all real positive numbers.
𝟏
(ii) Let 𝒛 = .
𝒙−𝒚
Here domain is the set of all points for which 𝒙 ≠ 𝒚 and the range
is R.
3
, Distance between two points
The distance between the points 𝑨 𝒙𝟎 , 𝒚𝟎 𝒂𝒏𝒅 𝑩 𝒙𝟏 , 𝒚𝟏 is given
as 𝒅 𝑨, 𝑩 = 𝒙𝟏 − 𝒙𝟎 𝟐 + 𝒚 𝟏 − 𝒚𝟎 𝟐
Neighborhood of a point:
Let 𝑷(𝒙𝟎 , 𝒚𝟎 ) be a point in 2D
Space. The (𝜹 − 𝒏𝒆𝒊𝒈𝒉𝒃𝒐𝒓𝒉𝒐𝒐𝒅) 𝒐𝒇
𝑷(𝒙𝟎 , 𝒚𝟎 ) is the set of all points which lies inside
the circle of radius 𝜹 with center at 𝑷(𝒙𝟎 , 𝒚𝟎 ).
4
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller yashgupta2. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $15.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
81531 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now