Welcome to Math 102 Section 107 Krishanu Sankar MWF 8:00 - 8:50 - - PowerPoint PPT Presentation

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Welcome to Math 102 Section 107 Krishanu Sankar MWF 8:00 - 8:50 - - PowerPoint PPT Presentation

Jun 07, 2023 152 likes •594 views

Welcome to Math 102 Section 107 Krishanu Sankar MWF 8:00 - 8:50 AM, LSK 200 Math 102: Announcements Instructor: Krishanu Sankar Email: ksankar@math.ubc.ca Course website: https://wiki.math.ubc.ca Today: Course information

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SLIDE 1

Welcome to Math 102 Section 107

Krishanu Sankar MWF 8:00 - 8:50 AM, LSK 200

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SLIDE 2

Math 102: Announcements

◮ Instructor: Krishanu Sankar ◮ Email: ksankar@math.ubc.ca ◮ Course website: https://wiki.math.ubc.ca ◮ Today:

◮ Course information ◮ Cell size and power functions

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SLIDE 3

Assignments and Grading

◮ Homework

◮ WeBWorK (online, 3x/week) - 10% (5% points

dropped)

◮ Old-School Homework (written, 6 total) - 10%

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SLIDE 4

Assignments and Grading

◮ Homework

◮ WeBWorK (online, 3x/week) - 10% (5% points

dropped)

◮ Old-School Homework (written, 6 total) - 10%

◮ Quizzes (3 total) - 15%

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SLIDE 5

Assignments and Grading

◮ Homework

◮ WeBWorK (online, 3x/week) - 10% (5% points

dropped)

◮ Old-School Homework (written, 6 total) - 10%

◮ Quizzes (3 total) - 15% ◮ Midterm (October 26) - 15%

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SLIDE 6

Assignments and Grading

◮ Homework

◮ WeBWorK (online, 3x/week) - 10% (5% points

dropped)

◮ Old-School Homework (written, 6 total) - 10%

◮ Quizzes (3 total) - 15% ◮ Midterm (October 26) - 15% ◮ Final exam (Date TBD) - 50% (44% rule)

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SLIDE 7

Typical Math 102 Week

◮ Monday:

◮ 7 am: Pre-lecture WeBWorK due ◮ 8-8:50 am: Lecture

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SLIDE 8

Typical Math 102 Week

◮ Monday:

◮ 7 am: Pre-lecture WeBWorK due ◮ 8-8:50 am: Lecture

◮ Wednesday:

◮ 7 am: Pre-lecture WeBWorK due ◮ 8-8:50 am: Lecture

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SLIDE 9

Typical Math 102 Week

◮ Monday:

◮ 7 am: Pre-lecture WeBWorK due ◮ 8-8:50 am: Lecture

◮ Wednesday:

◮ 7 am: Pre-lecture WeBWorK due ◮ 8-8:50 am: Lecture

◮ Thursday:

◮ 7 am: WeBWorK due

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SLIDE 10

Typical Math 102 Week

◮ Monday:

◮ 7 am: Pre-lecture WeBWorK due ◮ 8-8:50 am: Lecture

◮ Wednesday:

◮ 7 am: Pre-lecture WeBWorK due ◮ 8-8:50 am: Lecture

◮ Thursday:

◮ 7 am: WeBWorK due

◮ Friday:

◮ 8-8:50 am: Lecture & OSH or Quiz

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SLIDE 11

What resources are available?

◮ Fellow students - study groups

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SLIDE 12

What resources are available?

◮ Fellow students - study groups ◮ Me - questions after class ◮ My office hours: Fill Doodle Poll on section

website! (Provisionally MF9-10 and Th1-2, in LSK300B, starting this Friday)

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SLIDE 13

What resources are available?

◮ Fellow students - study groups ◮ Me - questions after class ◮ My office hours: Fill Doodle Poll on section

website! (Provisionally MF9-10 and Th1-2, in LSK300B, starting this Friday)

◮ Math Learning Centre (LSK 301 & 302) ◮ Piazza

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SLIDE 14

What resources are available?

◮ Fellow students - study groups ◮ Me - questions after class ◮ My office hours: Fill Doodle Poll on section

website! (Provisionally MF9-10 and Th1-2, in LSK300B, starting this Friday)

◮ Math Learning Centre (LSK 301 & 302) ◮ Piazza ◮ Free course notes (pdf) and supplemental

videos

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SLIDE 15

What resources are available?

◮ Fellow students - study groups ◮ Me - questions after class ◮ My office hours: Fill Doodle Poll on section

website! (Provisionally MF9-10 and Th1-2, in LSK300B, starting this Friday)

◮ Math Learning Centre (LSK 301 & 302) ◮ Piazza ◮ Free course notes (pdf) and supplemental

videos

◮ Lecture slides/scans posted after class

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SLIDE 16

Other Admin

◮ All questions regarding registration or

sectioning should be directed to Mark MacLean

  • r Margaret Ness.
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SLIDE 17

Other Admin

◮ All questions regarding registration or

sectioning should be directed to Mark MacLean

  • r Margaret Ness.

◮ Lectures will be interactive with prompts and

clicker questions. (register your iClicker on Connect)

◮ I’d like to thank Eric Cytrynbaum, Leah

Edelstein-Keshet, and Cole Zmurchok, whose slides were the basis for these lectures.

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SLIDE 18

Why are cells so small?

https://en.wikipedia.org/wiki/White_blood_cell/media/File:SEM_blood_cells.jpg

◮ WBCs are 12-15 microns in diameter.

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SLIDE 19

◮ Cells absorb nutrients through their surface,

and use the nutrients in their interior. Must have nutrient absorption rate ≥ consumption rate, or the cell dies!

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SLIDE 20

◮ Cells absorb nutrients through their surface,

and use the nutrients in their interior. Must have nutrient absorption rate ≥ consumption rate, or the cell dies!

◮ Mathematical model: assume the cell is

spherical, and

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SLIDE 21

◮ Cells absorb nutrients through their surface,

and use the nutrients in their interior. Must have nutrient absorption rate ≥ consumption rate, or the cell dies!

◮ Mathematical model: assume the cell is

spherical, and

  • 1. Absorption rate is proportional to surface area.
  • 2. Consumption rate is proportional to volume.
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SLIDE 22

A mathematical model

r

  • 1. Nutrient absorption

rate is proportional to surface area

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SLIDE 23

A mathematical model

r

  • 1. Nutrient absorption

rate is proportional to surface area A = k1S

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SLIDE 24

A mathematical model

r

  • 1. Nutrient absorption

rate is proportional to surface area A = k1S = k14πr2

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SLIDE 25

A mathematical model

r

  • 1. Nutrient absorption

rate is proportional to surface area A = k1S = k14πr2

  • 2. Consumption rate is

proportional to volume

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SLIDE 26

A mathematical model

r

  • 1. Nutrient absorption

rate is proportional to surface area A = k1S = k14πr2

  • 2. Consumption rate is

proportional to volume C = k2V

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SLIDE 27

A mathematical model

r

  • 1. Nutrient absorption

rate is proportional to surface area A = k1S = k14πr2

  • 2. Consumption rate is

proportional to volume C = k2V = k2 4 3πr3 where k1 and k2 are positive constants.

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SLIDE 28

Cell shape

A(r) = 4πk1r2 C(r) = 4 3πk2r3

  • Q1. Which of the following is true?
  • A. Absorption is greater than consumption for

sufficiently large cells and vice versa for small cells.

  • B. Consumption is greater than absorption for

sufficiently large cells and vice versa for small cells.

  • C. Both A and B are possible, depending on k1

and k2.

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SLIDE 29

Cell shape

A(r) = 4πk1r2 C(r) = 4 3πk2r3

  • Q1. Which of the following is true?
  • A. Absorption is greater than consumption for

sufficiently large cells and vice versa for small cells.

  • B. Consumption is greater than absorption for

sufficiently large cells and vice versa for small cells.

  • C. Both A and B are possible, depending on k1

and k2.

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SLIDE 30

Power functions

◮ A function of the form f(x) = axn (where a is

a constant and n is an integer) is called a power function.

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SLIDE 31

Power functions

◮ A function of the form f(x) = axn (where a is

a constant and n is an integer) is called a power function.

◮ The integer n is called the degree, and a is

called the coefficient.

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SLIDE 32

Power functions

◮ A function of the form f(x) = axn (where a is

a constant and n is an integer) is called a power function.

◮ The integer n is called the degree, and a is

called the coefficient.

Example

A(r) = (4πk1)r2 and C(r) = 4 3πk2

  • r3

are power functions with independent variable r.

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SLIDE 33

Power functions

  • Q2. Match!
  • A. Red: x3, blue: x2,

purple: x5, yellow: x4.

  • B. Red: x5, blue: x4,

purple: x3, yellow: x2.

  • C. Red: x3, blue: x4,

purple: x5, yellow: x2.

  • D. Don’t know, please

explain.

  • 0.5

0.5 1 1.5

x

0.5 1 1.5 2

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SLIDE 34

Power functions

  • Q2. Match!
  • A. Red: x3, blue: x2,

purple: x5, yellow: x4.

  • B. Red: x5, blue: x4,

purple: x3, yellow: x2.

  • C. Red: x3, blue: x4,

purple: x5, yellow: x2.

  • D. Don’t know, please

explain.

  • 0.5

0.5 1 1.5

x

0.5 1 1.5 2

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SLIDE 35

Cell size

A(r) = 4πk1r2 C(r) = 4 3πk2r3 Consumption is greater than absorption for sufficiently large cells and vice versa for small cells.

0.5 1

x

0.5 1 A(r) C(r)

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SLIDE 36

Limit on cell size

◮ When is the absorption rate greater the

consumption rate?

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SLIDE 37

Limit on cell size

◮ When is the absorption rate greater the

consumption rate?

◮ i.e., for which values of r is the absorption

rate A(r) bigger than the C(r)?

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SLIDE 38

Limit on cell size

◮ When is the absorption rate greater the

consumption rate?

◮ i.e., for which values of r is the absorption

rate A(r) bigger than the C(r)? A(r) = 4πk1r2 > 4 3k2πr3 = C(r) r < 3k1 k2 Does this make sense with the plot above?

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SLIDE 39

Limit on cell size

  • Q3. Which of the following cells can survive?
  • A. r < 3k1

k2

  • B. r = 3k1

k2

  • C. r > 3k1

k2

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SLIDE 40

Limit on cell size

  • Q3. Which of the following cells can survive?
  • A. r < 3k1

k2

  • B. r = 3k1

k2

  • C. r > 3k1

k2

What about bigger cells, such as neurons, Caulerpa prolifera, or eggs?

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SLIDE 41

Today...

◮ Course info

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SLIDE 42

Today...

◮ Course info ◮ Cell size and mathematical models

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SLIDE 43

Today...

◮ Course info ◮ Cell size and mathematical models ◮ Power functions: f(x) = ax2 versus

g(x) = bx3. Which is bigger? For which x?