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INTRO TO DIFFERENTIAL CALCULUS NOTES
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  • Course
  • MAT135 (MAT135)
  • Institution
  • University Of Toronto (U Of T )

Elevate your understanding of calculus and secure a top grade at the University of Toronto with this comprehensive package of introductory differential calculus course notes! Designed specifically for U of T students, these notes cover essential topics such as limits, continuity, and differentiatio...

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  • March 24, 2024
  • March 24, 2024
  • 1
  • 2023/2024
  • Class notes
  • Afiny akdemir
  • All classes

Subjects

  • limits
  • continuity
  • differentiation
  • derivatives
  • rules of differentiation
  • power rule
  • quotient rule
  • chain rule
  • implicit differentiation
  • related rates
  • linear approximation
  • optimization
  • curve sketching
  • conc

Written for

  • University of Toronto (U of T )
  • Computer Science And Mathematics
  • MAT135 (MAT135)
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WEEK 10 STUDY NOTES
Textbook Section 4.4: Families of Functions and Modelling
1. Defining variables in a word problem
h = the function itself, height in meters
t = the variable, time in seconds
k = the parameter, the balls initial height in meters

2. Explaining figure 4.67 (a value)
As a increases, the function moves further to the right.

3. Explaining figure 4.67 (b value)
As b increases, the function alternates between forming a cusp and the left side of
the cusp alternatively becomes concave down.

Textbook Section 4.6: Rates and Related Rates
1. Defining which units determine the rate of change
The angular velocity of the spinning wheely would determine how fast the wheel is
spinning. Meaning the units which measure how fast the wheel is spinning is radians
per second.

2. Determining what derivatives represent
𝑑𝐻
- 𝑑𝐿 : the rate of change of the temperature with respect to the length of the shadow
𝑑𝐿
- 𝑑𝑎
: the rate of change of the length of the shadow with respect to the angle the sun
makes with the the base of the cabin
𝑑𝑎
- 𝑑𝑡
: the rate of change of the angle the sun makes with the base of the cabin with
respect to time

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