calculus i

Schedule for Help Sessions. During most lab sessions I will be able to provide some homework help (for those who aren't in that lab).

week 01

Class 01 (September 12, 2022): Logistics, Introductions, Idea of a Function, Linear Functions

In-class content

• Topics: Introductions, Course Overview, What is a Function?
• Linear Exercises

Lab 01 (September 12, 2022): Exponential Functions, Field Guide to Functions

In-class content

• Topics: Exponential Functions, Initial thoughts on Field Guide to Functions
• Handout

Class 02 (September 15, 2022): Exponential Functions, New Functions from Old

Pre-class:

• none

In-class content

• Handout: Exponential Functions
• Handout: New Functions from Old

After-class:

• Video of exponential function example. Likely useful for week two homework.

Homework 01 (due September 16, 2022)

• Homework 01, due Friday, September 16

week 02

Class 03 (September 19, 2022): More Exponential Functions, Power Functions, Inverse Functions

Pre-class:

• none

In-class content

• Handout: More Exponential Functions
• Handout: Power Functions
• Handout: More Power Functions
• Handout: Inverse Functions

After-class:

• None

Lab 02 (September 19, 2022): Exponential Functions, Field Guide to Functions

In-class content

• Topics: Some graphing puzzles, work on field guide
• Handout

Class 04 (September 22, 2022): More with Inverses. Logarithms

Pre-class:

• none

In-class content

• Handout: More Inverse Functions
• Handout: Logarithms
• Handout: More Logarithms
• Video of Class

After class

• Video:Properties of Logarithms
• Video:Applications of Logarithms

Homework 02 (Due September 23, 2022)

• Homework 02, Due 23 September 2022

week 03

Class 05 (September 26, 2022): "Natural" Logarithms, Trig Functions

Pre-class:

• none

In-class content

• Handout: More Logarithms
• Handout: Trig Functions
• Video of Class

Lab 03 (September 26, 2022): Circle exercise, Some Graphing Puzzles, Field Guide to Functions

In-class content

• Topics: Some graphing puzzles, circle exercise, work on field guide
• Handout

Class 06 (September 29, 2022): Polynomials, Rational Functions, Measuring Average Speed

Pre-class:

• none

In-class content

• Handout: Polynomials
• Handout: Average speed of a cat
• Handout: More average cat speeds
• Video of Class (from 2014)

Homework 03 (Due September 30, 2022)

• Homework 03, Due 30 September 2022

week 04

Class 07 (October 3, 2022): The Derivative at a Point

In-class content

• Handout: More average speed
• Handout: Derivative at a Point
• Handout: More derivative at a Point
• Video of class

After-class:

• Limits

Lab 04 (October 3, 2022): Rational Funcions, Average and Instantaneous Speeds, Field Guide to Functions

In-class content

• Topics: Rational Functions, Graphical views of Average and Instantaneous Speeds, More work on Field Guides
• Handouts: [Parts I and III]   [Part II]

Class 08 (October 6, 2022): The Derivative Function, Interpretations of the Derivative

In-class content

• Video of class coming soon
• Handout: Graphing the Derivative Function
• Handout: Derivative Interpretations
• Video of Class

After-class:

• The paradox of the derivative, a video by Grant Sanderson (3Blue1Brown). Highly recommended.

Homework 04 (Due October 7, 2022)

• Homework 04, due Friday, October 7

week 05

Class 09 (October 10, 2022): The Second Derivative, The Power Rule

In-class content

• Handouts: [The Second Derivative]   [The Power Rule]
• Video of Class

After-class:

Lab 05 (October 10, 2022): Sine Waves, Limits, Derivatives

In-class content

• Topics: Rational Functions, Graphical views of Average and Instantaneous Speeds, More work on Field Guides
• Lab Handout

Class 10 (October 13, 2022): Derivative of Exponentials, The Product Rule

In-class content

• Handouts [Evaluating a limit!]   [Practice with Exponentials]   [Product Rule Practice]

Homework 05 (Due October 14, 2022)

• Homework 05, due Friday, October 14

week 06

Class 11 (October 17, 2022): More Product Rule, Chain Rule

In-class content

• Handouts: [Product Rule]   [Chain Rule]

After-class:

Lab 06 (October 17, 2022): Newton's Law of Cooling, Exponential Functions

In-class content

• Lab Handout

Class 12 (October 20, 2022): Chain Rule, Derivatives of Logs

In-class content

• Handouts: [More Chain Rule]  
• Handout: [Derivatives of Logs]

Homework 06 (Due Friday, October 21)

• Homework 06, due Friday, October 21

week 07

Class 13 (October 24, 2022): More Logarithms, Derivatives of Trig Functions

In-class content

• Handout: [More Logarithm Practice]   [Differentiating Trig Functions]

Lab 07 (October 24, 2022): More Newton's Law of Cooling, A Murder Mystery

In-class content

• Lab Handout

Class 14 (October 27, 2022): Using Derivatives to Understand Graphs

In-class content

• Handouts:   [Using First and Second Derivatives]   [Optimization]

Homework 07 (Due October 28, 2022)

• Homework 07, due Friday, October 28, 2022

week 08

Class 15 (October 31, 2022): Optimization

In-class content

• Handout: Optimization

Lab 08 (October 31, 2022): An Optimal Cone

In-class content

• Lab Handout

Class 16 (November 3, 2022): More Optimization

In-class content

• Handout: More Optimization

Homework 08 (Due November 4, 2022)

• Homework 08, due Friday, November 4

week 09

Class 17 (November 8, 2022): Related Rates and Implicit Differentiation

In-class content

• Handout: Related Rates and Implicit Differentiation
• Video of Class

Lab 09 (November 8, 2022): Related Rates Practice

In-class content

• Lab Handout

Class 18 (November 10, 2022): Applications to Economics, Marginality

In-class content

• Handout: Applications to Economics, Marginality
• Video of Class

Homework 09 (Due November 11, 2022)

• Homework 09, due Friday, November 11

week 10

Class 19 (November 14, 2022): Do Dogs Know Calculus?

In-class content

• Do dogs know calculus? by Timothy J. Pennings, The College Mathematics Journal, 24:3 (2003).
• Do dogs know related rates rather than optimization? by Pierre Perruchet and Jorge Gallego, The College Mathematics Journal, 37:1 (2006).

Homework 10 (Due November 18, 2022)

• Homework 10, due Friday, November 18

Final Synthetic Homework (Due November 18, 2022)

• Final Synthetic Homework, due Friday, November 18