100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Maths 214 Advanced Calculus notes for A1 (2024) $5.63
Add to cart
Quickly navigate to
Preview
  2.  
  3. Stellenbosch University (SUN)
  4.  
  5. Mathematics 214

Class notes

Maths 214 Advanced Calculus notes for A1 (2024)
 43 views  0 purchase
  • Course
  • Mathematics 214
  • Institution
  • Stellenbosch University (SUN)
  • Book
  • Calculus

The only document you’ll need to pass your A1. Comprehensive notes made from class, the textbook and from an amazing YouTube channel (Alexandra Niedden). This document includes a concise explanation on everything from chapters 12.6, 13.1, 13.2, 14.1, 14.2, 1.7, 14.3, 14.4 with lots of examples to...

[Show more]

Preview 3 out of 30  pages

Document information

  • March 18, 2024
  • 30
  • 2023/2024
  • Class notes
  • Dr heymann
  • All classes

Subjects

  • summary

Connected book

book image

Book Title:

Author(s):

  • Edition:
  • ISBN:
  • Edition:

More summaries for

  • Calc 3 Math2015 Chapter 14
  • Instructors solutions
  • Calculus early transcendals 8th edition
All for this textbook (6)

Written for

  • Stellenbosch University (SUN)
  • Mathematics 214
All documents for this subject (4)

Seller

avatar-seller
jessicawilliams3

Content preview

12 6
.
Cylinders & Quadric Surfaces

Cylinders : sufface that consists of all lines 1) to a


given line &
pass through a
given plane curve

(in 3 space >only two
variables)
Ex #1 :
z =
x2 Z

-


I


parabolic Cylinder
>

y




x




Ex # 2 :
y2 + z2 =
1


Y




Z




Quadric Surfaces :
graphs of 2nd degree equations in 3 variables



AX2 By 2 2z2 Dxy + Eyz + Fxz Iz J 0
+ + Gx Hy + =
+ + + +




Ex #3 :
z =
x2 + y2 zI0

Traces :




1 1 z =
0 :
0 =
x + y2
-
z =
1 : 1 =
x + y2
I
z =
4 :
4 = x +
y2

, 4
1
Intercepts Traces
:
+ + = 1


20 , =c)

#Zellises
0,


ellipsoid Co I b
, ,
0) s

c = a
,
0
. 0




· -



E E 03
=# I hyperb
2 =
+ 10, 0 , i


3 Laxis z =
#ellipse

C
a cone




A
R
O
T 4 e
(0 0 03
3
#
z = + , ,
x =




⑤ Laxis x + y2
y =
# - Parabolas
z z = #
ellipse
: =




- ⑰
elliptic
paraboloid
-




3
- = #2
4 +
hyperba e
-



Hyperboloid ellipse
O
z =
# >
-




of one


- sheet




N
, +
same as 4


>
-




is



& hyperboloid
of 2 sheets




↓ !

⑥
E
# parabaSola
z = -




2




Hyperbolick)
Paraboloid C
&I&
I
<
I
-
&

, Techniques : exercises to show how to determine general shape


4y2 x
+ 0)
Ex # (0
intercepts 0,
=
: ,




Laxis
Traces :
Y = 0 : 0 =
x +
4




=:= + elligee
N
T




D. ellistie D




L
~




Ex#5 : 462 + 4y2 + 22 +
8y -
47 = -

4



1 .
complete the square


46 + 4(y2 + 2y + 1) + z2 -
42 + 4 = -
4 + 4 + 4

4x +
4(y + 1)2 + (z- 2)2 = 4 * we want this to =1


x +
(y + 1) + (z -

2) = 1

4



intercepts : (0, 0, 2)

Co, -1
, o) all traces are ellipses

·


ellipsoid
· ·

-




·

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

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

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

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 jessicawilliams3. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy these notes for $5.63. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

52510 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy study notes for 14 years now

Start selling
$5.63
  • (0)
Add to cart
Added