MAT1102 http:www'sci'usq'edu'aucoursesmat1102

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MAT1102 http//www.sci.usq.edu.au/courses/mat110
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• Pat Cretchley
• MAT1102 Examiner
• Undergraduate Coordinator
• D 204 A 4631-5526
• cretchle_at_usq.edu.au
• __________________________________________________
  _________________
• Consultation
• Tues 3-4 Thurs 10-11 Fri 11-1
• Other times by appointment (not Mondays)
• ________________________________________________

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• Algebra
• _________________
• Applications in Maths, Engineering,
• Computer Games, Business, Sciences
• See Appendix C and Larson Edwards
• Texts Readings
• ___________________________________
• Ch 0 Stewart Ch 9 Study Bk AppA (Grossman)
• Ch 1-3 Larson Edwards 4th or 5th Edn
• Ch 4 Study Bk Appendix B
• _____________________________________________

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Chapter 0 Vectors (Weeks 1 - 3)

• 0.1 Vectors in the Plane
• 0.2 Scalar Product Projections
• 0.3 Vectors in Space
• 0.4 Cross product of Two Vectors
• 0.5 Lines Planes in Space
• 0.6 Summary

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What use are Vectors?____________________________
______________

• Vectors are simply data stored in an ordered
  list.
• 2 and 3-dimensional vectors are used to describe
  all kinds of motion and position in a plane or
  space
• eg in Computer Games,
• Moving objects, vehicles, working parts of
  machines...
• Electro-magnetic fields forces, a
  particle...
• Maxwells Eqns for electricity magnetism
• The Universe motion of the planets, elementary
  particles...
• Matter Life itself? String Theory...
• see Elegant Universe Welcome to the 11th
  dimension
• n-dimensional vectors are used to describe a
  host of variables in many applications
• quantities that can be characterised by a
  list of numbers
• in Financial mathematics, Economics, circuits ...

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0.1 Vectors in the Plane (ie 2-D
vectors) Study Book p 9-10
plus Stewart 9.1, 9.2 and Study Bk App A
(Grossman 3.1) ___________________________________
__________________________________________________
___________________________________

• Understand
• that vectors in the plane are represented by a
  2-D ordered pair (x,y) or an arrow
• that they have 2 characteristics magnitude
  direction
• that they can be used to describe physical motion
• that they can define points or edges (ie a
  geometric shape)
• Know how to add subtract vectors
• and why you might want to.

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• Vectors in the plane are represented by ordered
  pairs, v y
• or arrows eg v (x, y) (5, 2)
  x
• Eg a 20 km/h north-easterly wind W
  E
• 20
• Vectors have magnitude direction (eg
  velocity, displacement)
• Scalars have magnitude only (eg speed,
  distance).
• The magnitude of vector v (x,y) is its length
  ? x2 y2
• written v or v .
  (by Pythagoras)
• The direction of v is the angle between 0 and
  2?
• that v makes with the positive x-axis.
• Study the Examples p 157-8 of Grossman,
  Appendix A.

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• We add vectors component-wise
• eg (2 , 3) (5 , -1) ( 2 5 , 3 - 1)
  (7 , 2)
• To find v w geometrically
• draw v or w first, then draw the other on the
  end.
• (2,3) (5,-1)
• (7,2)
• The sum is the vector forming the third side of
  the triangle
• or the diagonal of the parallelogram.
• Conclude that v w w v (ie
  any order)
• And confirm the Triangle Inequality between
  lengths of sides
• vw ? v w

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• Subtraction scalar multiplication are also
  done
• componentwise eg, (3, 5) - (1, 2) (2, 3).
• and v - w means v (-w) , ie add
  vector -w to v.
• v w -w v
  w -w
• vw v-w v
• v - w and w - v point in opposite
  directions v - w - (w - v)
• If b is a positive scalar v
  2v
• bv points in the same direction as v.
• eg 2 (3, 5) (6, 10) -3v
• If scalar b is negative , bv is in the
  opposite direction to v.
• eg -3 (3,5) (-9, -15)

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Unit vectors have length 1 eg (1 , 0) and
(1/? 2 , 1/? 2). (1,1) , (3,4) are not
unit vectors. How long are they?

• Any vector can be made into a unit vector in the
  same direction by dividing by its own length v
  v
• Eg ( 3, 4 ) has length ? 9 16 5, and
  hence
• (3/5, 4/5) is a unit vector in the same
  direction.
• We define unit vectors i (1, 0) and j
  (0, 1)
• in the
  x y-direction.
• Then any vector (a, b) can be written as
  the sum
• a i b j of its horizontal vertical
  components.
• eg (5, 3) 5
  i 3 j
• (cos t) i (sin t) j is a unit vector with
  so-called direction angle t, made with the pos
  x-axis. Draw check.

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Applications of vectors to motion and forceBe
sure you can use vectors to describe and analyse
motion and forces.

• Self-study Stewart Ch 9.2,
• Ex 22-28.

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HomeworkRead Study Book Section
0.1______________________________________________
_________________________

• Study Book Appendix A, Grossman 3.1
• Master Q 1 - 30.
• Write full solutions to 14, 20, 24, 30,
  32.
• Stewart Ch 9.2
• Master Q 1-8, 21-25.
• Write a full solution to 24.

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Objectives

• Be able to
• add, subtract take multiples of vectors,
  algebraically geometrically
• find magnitudes direction angles
• use the symbols correctly
• convert a given vector to a unit vector
• know the algebraic rules for vectors
• use vectors to describe physical motion
• use vectors to describe geometric objects like
• points and edges