Dr.-Ing. Erwin Sitompul President University Lecture 2 Multivariable Calculus President...

Dr.-Ing. Erwin SitompulPresident University

Lecture 2

Multivariable Calculus

President University Erwin Sitompul MVC 2/1

http://zitompul.wordpress.com


The Cross Product of Two Vectors in Space In space, we need a way to describe

how a plane is tilting. We accomplish this by multiplying two vectors in the plane together to get a third vector perpendicular to the plane

The direction of this third vector tells us the “inclination” of the plane.

We use cross product to multiply the vectors together.

12.4 The Cross ProductChapter 12


The Cross Product of Two Vectors in Space12.4 The Cross ProductChapter 12


The Cross Product of Two Vectors in SpaceChapter 12 12.4 The Cross Product

Example


|u v| is the Area of a ParallelogramChapter 12 12.4 The Cross Product


Distance and Spheres in Space Example

Chapter 12 12.4 The Cross Product

Example


Lines in SpaceChapter 12 12.5 Lines and Planes in Space

Suppose L is a line in space passing through a point P0(x0,y0,z0) parallel to a vector v.

Then L is the set of all points P(x,y,z) for which P0P is parallel to v.

P0P = tv, for a given value of scalar parameter t.


Lines in SpaceChapter 12 12.5 Lines and Planes in Space


Lines in SpaceChapter 12

Example

12.5 Lines and Planes in Space


Lines in Space Example

Chapter 12 12.5 Lines and Planes in Space

What if we choose Q(1,–1,4) as the base?


The Distance from a Point to a Line in SpaceChapter 12 12.5 Lines and Planes in Space


The Distance from a Point to a Line in SpaceChapter 12 12.5 Lines and Planes in Space

Example


The Distance from a Point to a PlaneChapter 12 12.5 Lines and Planes in Space


The Distance from a Point to a PlaneChapter 12 12.5 Lines and Planes in Space

Example


Chapter 13

Vector-Valued Functions and Motion in Space


Vector FunctionsChapter 13 13.1 Vector Functions



Can you see the difference?


Limits and ContinuityChapter 13 13.1 Vector Functions


Derivatives and MotionChapter 13 13.1 Vector Functions



Example


Differentiation RulesChapter 13 13.1 Vector Functions


Vector Functions of Constant LengthChapter 13 13.1 Vector Functions


Vector Functions of Constant LengthChapter 13 13.1 Vector Functions

Example


Integrals of Vector FunctionsChapter 13 13.1 Vector Functions

Example



Example


Homework 2Chapter 13

Exercise 12.4, No. 15. Exercise 12.4, No. 36. Exercise 12.5, No. 6. Exercise 12.5, No. 43. Exercise 13.1, No. 7. Exercise 13.1, No. 25.

Due: Next week, at 17.15.

13.1 Vector Functions

Dr.-Ing. Erwin Sitompul President University Lecture 2 Multivariable Calculus President...

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