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PHYS16 – Lecture 3. Math Review Ch. 3 Vectors. http://www.onlinemathtutor.org/help/wp-content/uploads/math-cartoon-20112009.jpg. Register clickers. Can you correctly answer A to this question? Yes No. http://kookaburra.com.au. Class Logistics. Get Text book + Access card

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phys16 lecture 3

PHYS16 – Lecture 3

Math Review

Ch. 3 Vectors

http://www.onlinemathtutor.org/help/wp-content/uploads/math-cartoon-20112009.jpg

register clickers
Register clickers
  • Can you correctly answer A to this question?
  • Yes
  • No

http://kookaburra.com.au

class logistics
Class Logistics
  • Get Text book + Access card
    • Purchase them from book store
    • Purchase them online – Lifetime Edition vs. Single term
  • Homework for next week – Due Wednesday at 11:00 am
    • Online homework is on WebAssign
    • Written homework is on course website
  • Get clickers, need them by next Wednesday
math review
Math Review
  • Ch. 1 Physics and Measurement
    • Unit Analysis
    • Order-of-Magnitude
    • Significant Digits
  • Scientific Notation
  • Ch. 3 Vectors
    • Trigonometry
    • Vectors
  • Calculus
significant digits calculations
Significant Digits - Calculations
  • Multiply or Divide
    • Same number as number with least significant digits
  • Add or Subtract
    • Same number as number with least precision
    • Same number as number that has the highest rightmost digit
  • Examples
    • 45+0.0000005 = 45
    • 24.5+14.23+1.567 = 40.3
    • 0.00002+0.0001 = 0.0001
    • 45.6*9 = 400

Counted Numbers – Infinite Sig Figs!

1 apple is 1 apple, infinite precision

scientific notation
Scientific Notation
  • A way of representing a number so that you can clearly see the significant digits and the order of magnitude
    • 110 would be 1.1E2 or 1.1x102
  • Examples
    • 1.001 (1.001E0)
    • 234 (2.34E2)
    • 900 (9.00E2 or 9.0E2 or 9E2)
    • 0.005 (5E-3)
    • 3.4 (3.4E0)
    • 45.6 (4.56E1)
    • 10 (1.0E1 or 1E1)
trigonometry
Trigonometry
  • 2π radians = 360 degrees
  • Right triangle – soh, cah, toa
  • Isosceles triangle

h

sin θ = o/h

cosθ = a/h

tan θ = o/a

o2 + a2 = h2

o

θ

a

Φ=2θ

Φ

θ

s s

vectors definition
Vectors - Definition
  • Scalar – a single value with units, no direction
    • 4 apples
    • 5.5 kg
    • 4 s
  • Vector – a value and a direction
    • 26 m/s, east (velocity)
    • 4 N downward (force)
    • 5 m at 5 degrees south of west (displacement)

Can a scalar be negative?

Yes, -5 degrees F.

vectors definition1
Vectors - Definition
  • Ways to write Vectors
    • 3 mph to the right or 3 mph to the east
    • 5 mph at 45 degrees from x axis
    • (3,2) or or
  • Magnitude, Direction, Components
vectors algebraically
Vectors - Algebraically
  • Adding Vectors
    • Break into components and add the components
  • Subtracting Vectors – Add the negative vector
vectors graphically
Vectors - Graphically
  • Adding Vectors
  • Subtracting Vectors – Add the negative vector

V2

V3

V3 = V1 + V2

V1

V3 = V1 – V2

V1

-V2

V3

calculus
Calculus
  • Derivatives
    • Polynomials, xn -> nxn-1
    • Trig functions, sin(x) -> cos(x), cos(x) -> -sin(x)
    • Exponentials, ex -> ex
  • Integrals
    • Polynomials , xn -> xn+1/(n+1)
    • Trig functions, sin(x) -> -cos(x), cos(x) -> sin(x)
    • Exponentials, ex -> ex
  • Partial Derivative
conclusion math topics to know
Conclusion – Math Topics to Know
  • Unit analysis
  • Order-of-Magnitude
  • Significant Digits
  • Scientific Notation
  • Trigonometry
  • Vectors
  • Calculus
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