multivuriable calculus 1 / 4
Topics to review:
- Functions
- Limits
- Derivatives & Differentiation
- Integration
- Matrices and Determinants
i 1insi = '=2 ✗ →
0 2 / 4
Chapter 12: Vectors and the Geometry of Space
- Vectors in 2d:
- Scalar Multiplication:
Properties of Vectors:
1) 2) 3)
4) Unit Vectors: vectors with unit magnitudes but has a
definite orientation
- Magnitude of Vectors in 3-D:
- Equation of a Sphere
- In 3-d, is a circular cylinder
- In 3-d, is a parabolic cylinder
09/07/22
- as = 5 ittut=/b-I& directions vesame as =( a , , an ) 11 cill = Taita
:
Ca ,, a) ie .
-----.......
É U , - ta = @ a , , za , ) where 7is a red number / tall -_aF+ai20,11811=0 ifta- =3 I
ñ=(79,7
az ) itÑ=( a.+ b , , aitb , ) B / AÑ /= lb , - 45th , - a.) ' +Cbs - aÑ A = Ñ= , /Ñ / = !A÷ , = ≥ a IA atlatl = aitaitai ' .sit y ' +z ' = Rt sity2 = I y =✗
2 3 / 4
17.1tlw ⑤
5+641-36
= FF = 555 ⑦ × 't y ' tz ' = 100 it36 tz ' = 100 itI = 64⑧ unit -1
(2×+4)=-4×2
+✗+ to * + 7.= ¥ ⑨( ✗ +15 + ( 2-+ E- 5 + 5 =④( oct 45 + ( y -15 + ( z - D2 = y 16 I
- / 4