Calculus with calculators

Gratuitous baby picture!

 

Hey folks, I hope class is going well. Keep taking good notes and working on the practice problems in class. I'll be back next week!

Objectives:

• Become familiar with the functions of the TI83 / TI84 calculators and their applications to Calculus.

Lesson:

1. Read through and complete the following lessons taken from the Texas Instruments website.
2. Work together in your groups to complete each lesson and corresponding self test questions in your notes composition book.
3. You will work on these lessons in class for the next two (1/31 & 2/2) class periods, and take a calculator quiz this Friday.
4. In addition to these lessons there are many more available for free at: 
   http://education.ti.com/html/t3_free_courses/calculus84_online/index.html
   if you would like to become more effective and efficient when using your calculator.

• Module 2, lesson 2.2 (scatterplots)

• Self test questions 4, 5, 6

• Module 10, lesson 10.1 (derivative of a function at a point using the nDerive function)

• Self test question 3

• Module 12, lesson 12.1, 12.2 (Rules of differentiation)

• Self test questions 2, 3, 4, 5

• Module 13, lesson 13.4 (extreme values with the TI84)

• Self test questions: 5

• Module 17, lesson 17.1, 17.2, 17.3 (Definite Integrals)

•  Self test questions: 1, 2, 3, 4, 5

• Module 19, lesson 19.1, 19.2 (Net Area / Area between two curves)

• Self test questions: 1, 2, 3, 4

7.7: Approximate Integration

Objectives:

• Use Riemann and Trapezoidal sums to approximate definite integrals of functions represented algebraically, geometrically and by tables of values.

Read:
pgs. 495 - 500 (stop at Simpson's Rule)

Definitions:

• Error

Formulas:

• The Trapezoidal Rule

• Error Bounds (of both Trapezoidal and Midpoint Rules)

Flashcards:

• The Trapezoidal Rule

Examples:
Explanation of Trapezoidal approximation


Ex1. The Midpoint Rule (refer to 5.2a ex4)

Ex2. The Trapezoidal Rule

Student Example


Ex3. Error Bounds

Student Example


Practice Set:
7.7 #1, 8a/b,13a/b, 20

Reminder:
Quiz 5.1, 5.2, 7.7 Monday

5.2b: The Definite Integral

Read:

• pg. 373 - 376
  

Definitions:

• Properties of the Definite Integral (2 red box mid-page 373)
• Properties of the Integral ( 5 properties pgs. 373-374)
• Comparison Properties of the Integral (pg. 375)

Formulas:

 N/A

Flashcards:

• Properties of the Definite Integral (2 red box mid-page 373)
• Properties of the Integral ( 5 properties pgs. 373-374)
• Comparison Properties of the Integral (pg. 375)
  

Examples: 

Ex1. Comparison properties of integrals

Student Example

Ex2. Using properties of integrals to evaluate

Student Example

Ex3. Using the upper and lower limit properties to evaluate an integral

Student Example

Practice Problems:

5.2b: # 33, 36,41, 43, 47, 52, 57

5.2a: The Definite Integral

Read:
 pg 366 - 372 (Through the Midpoint Rule)


Defintions:

• Definition of a definite integral (also called Riemann sum)
• Theorem 3
• Theroem 4

Formulas:

•  Sigma Formulas (7 of them on pg. 369)
• The Midpoint Rule

Flashcards:

• Theorem 4
• Front: Integral
• Back: Sigma notation / delta x and x_i
•  The Midpoint Rule

Examples:

Ex1.  Expressing a Riemann sum as an integral

Student example *there is a mistake in the final answer, see the comments below for the correction*

Ex2a. Evaluating Riemann sums

Student Example

Ex2b. Evaluating integrals using Theorem 4 and the Sigma Properties

Student Example

Ex3. Evaluating integrals by interpreting areas.

Student Example

Ex4. The Midpoint Rule

Student Example



Practice Problems:
5.2a #1, 6, 8, 9, 18, 23, 26, 33, 36

5.1b: The Distance Problem

Read:
5.1b pg. 362 -363 "The Distance Problem". 

Definitions: 
N/A

Formulas:
N/A

Flashcards:
N/A

Examples:

The Distance Problem (an explanation)


Running the distance



Practice Problems:
5.1 # 12, 15, 18  

5.1a: The Area Problem

Read:
 pg. 354 - 362 (Stop at "The Distance Problem)

Define:

1. Area of a region S.
2. Sample points
3. Sigma notation
4. Sum of the first n squares formula

Examples:
A note on sigma notation.

Ex1.   Approximate Area Under a Curve (ex1 in the book).

Student Example

Ex2. Sigma Notation/ Area Under a Curve

Student Example

Practice Problems (in class Friday):
5.1 # 2, 5, 18, 19

Hello World!

Hello AP Calculus students,

This is where you will come to find the lesson plan notes, and video examples for each section. Please email me with any questions at robert.tolar@kippking.org.