Plus 4.8 Differentials
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Websites to help you with Chapter 5 |
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Wed.,
1/6
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Welcome back to
Second semester.
Homework: Review
your derivatives (all 24) for a quiz on Wednesday, and do the
sample derivative gateway test and get your answers checked. -
test4A with answers - check it out!
Homework:
Read and take notes on 4.8
(p. 271-275), paying special attention to Example 7 and do P. 276 #
4, 6,
9, 14 |
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Fri.,
1/8
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4.8
Differentials
Objectives:
At the end of this lesson you should be able to
- Understand
the concept of a tangent line approximation
- Compare the
value of the differential, dy, with the actual change in
y,
Dy
- Find the
differential of a function using differentiation formulas
- Estimate a
propagated error, relative error, and percent error using a differential
Homework:
Read and take notes on 4.8
(p. 271-275), paying special attention to Example 7 and do P. 276 #
4, 6,
9, 14, 18, 24, 27, 29, 32, 33, 40, 45, 59 - 62, and 35
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Mon., 1/11
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5.1
Antiderivatives and Indefinite Integration
Objectives:
At the end of this lesson you should be able to
- Write a
general solution for a differential equation
- Use
indefinite integral notation for antiderivatives
- Use basic
integration rules to find antiderivatives
Homework:
Read and take notes on 5.1
(p. 284 – 288) and do p. 291 # 3, 4, 6, 9, 11, 14, 15, 18, 20, 23,
25, 26, 28, and 47
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Tues.,
1/12
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 5.1
Antiderivatives and Indefinite Integration (cont.)
Objectives:
At the end of this lesson you should be able to
- Find
general antiderivatives
- Use initial
conditions to solve for
- Use a slope
field to find antiderivatives
- Use
integration to solve vertical and rectilinear motion problems
Activity:
PowerPoint on Slope fields
(if you have PowerPoint)
PowerPoint on Slope fields
(if you don't have PowerPoint)
Homework:
Read and take notes on p. 289 – 291
and do p. 291 # 31, 34, 35, 38-41, 43, 50, 52-54, 57, 60, 61
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Wed.,
1/13 |
 5.1
Antiderivatives and Indefinite Integration (cont.)
Homework: P. 292 # 65, 67, 68, 71,
73, 74, 77-79, 85, 87, 91, 92, 95-100
There will be a
Homework quiz over all problems from 5.1 on Thursday!
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Thurs.,
1/14
HW
Quiz
4.8 & 5.1
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5.2
Area
Objectives:
At the end of this lesson you should be able to
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Use sigma
notation to write and evaluate a sum.
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Understand
the concept of area.
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Approximate
the area of a plane region.
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Find the area
of a plane region using limits.
Activity:
5-2 Area PowerPoint (if you have
PowerPoint)
5-2 Area PowerPoint (if you don't have
PowerPoint)
Homework:
Read and take notes on section 5.2 (p. 295 – 303)
Do p. 303 # multiple of 3’s from 3 to 45 (i.e.
3, 6, 9, 12, …, 39, 42, 45)
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Fri., 1/15 |
NO School - School Improvement Day |
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Mon., 1/18 |
NO School - Martin Luther King Holiday |
Tues.,
1/19 |
5.2 Area
Objectives:
At the end of this lesson you should be able to
-
Use sigma
notation to write and evaluate a sum.
-
Understand
the concept of area.
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Approximate
the area of a plane region.
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Find the area
of a plane region using limits.
Activity:
5-2 Area PowerPoint (if you have
PowerPoint)
5-2 Area PowerPoint (if you don't have
PowerPoint)
Homework:
P. 304 # 46, 49, 52, ...,
73, 74 - 77
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Wed..,
1/20 |
5.3
Riemann Sums and Definite Integrals
Objectives:
At the end of this lesson you should be able to
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Understand
the definition of a Riemann sum.
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Evaluate a
definite integral using limits.
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Evaluate a
definite integral using properties of definite integrals.
Activity:
5-3 Riemann Sum PowerPoint (if you have
PowerPoint)
5-3 Riemann Sum PowerPoint (if you don't have
PowerPoint)
Homework:
Read and take notes on section 5.3 and do p. 314 #
3, 6, 9, …, 45, 47, 49, 53, 65- 70 –
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Friday.,
1/22 |
5.3 Riemann Sums
and Definite Integrals
Objectives:
At the end of this lesson you should be able to
-
Understand
the definition of a Riemann sum.
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Evaluate a
definite integral using limits.
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Evaluate a
definite integral using properties of definite integrals.
Activity:
5-3 Riemann Sum PowerPoint (if you have
PowerPoint)
5-3 Riemann Sum PowerPoint (if you don't have
PowerPoint)
Homework:
Get the Riemann sum program for your calculator
and do p. 316 # 59-64, 71 and then READ and TAKE Notes on section
5-4 and do P. 327 #1, 2, 5, and 8
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Mon., 1/25 |
5.4
The Fundamental Theorem of Calculus
Objectives:
At the end of this lesson you should be able to
-
Evaluate a
definite integral using the Fundamental Theorem of Calculus.
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Understand and
use the Mean Value Theorem for Integrals.
Activity:
5.4 PowerPoint - Day 1 (if
you have PowerPoint)
5.4
PowerPoint - Day 1 (if you
don't have PowerPoint)
Buddy Homework:
Read/take notes on 5.4 (p. 318-321) and do p. 327 #12, 15, 18, 21,
..., 54 (multiples of 3)
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Tues., 1/26 |
5.4 The Fundamental Theorem of Calculus
- part 2
Objectives:
At the end of this lesson you should be able to
Activity:
5.4 PowerPoint - Day
2 (if
you have PowerPoint)
5.4
PowerPoint - Day 2 (if you
don't have PowerPoint)
Buddy Homework: Read/take
notes on 5.4 (p. 322 - 326) and do p.328 # 57, 60, 63 - 66, 74, 77,
79, 81, 87, 90, 93, 96, 99
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Wed., 1/27 |
5.5
Integration by Substitution
Objectives:
At the end of this lesson you should be able to
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Use pattern
recognition to find an indefinite integral.
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Use a change
of variables to find an indefinite integral.
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Use the
General Power Rule for Integration to find an indefinite
integral.
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Use a change
of variables to evaluate a definite integral.
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Evaluate a
definite integral involving an even or odd function.
Activity...Sample
Problems from the SmartBoard! Make sure to look at problem
#8... You sometimes have to go to extremes to get everything in
terms of u!!!
Buddy Homework:
Read/take notes on 5.5 (p. 331 - 339) and do (with a partner!) p.
340 # 1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 35, 41, 45,
48, 51, 54, 57, 60, 63,
66, 69, 72, 75, 78, 81, 84 and review even and odd functions
and how to tell if a function is either even or odd symbolically (p.
26). Then learn a shortcut to evaluating an integral of an
even/odd function and be able to explain why/how it works!
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Thurs.,
1/28
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5.5
Integration by Substitution (cont.)
Objectives:
At the end of this lesson you should be able to
-
Use pattern
recognition to find an indefinite integral.
-
Use a change
of variables to find an indefinite integral.
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Use the
General Power Rule for Integration to find an indefinite
integral.
-
Use a change
of variables to evaluate a definite integral.
-
Evaluate a
definite integral involving an even or odd function.
Buddy Homework:
p. 341 # 85, 87, 90, 95, 100, 105, 110, 113, 119, 124, 125,
129, 137, 139, 149, 152
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Fri.,
1/29
1st Hour - Lab 41
3rd Hour- Lab 43
Quiz
Sections
5.1 - 5.5
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Mon., 2/1 |
5.6
Numerical Integration
Objectives:
At the end of this lesson you should be able to
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Approximate
a definite integral using the Trapezoidal Rule.
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Approximate a
definite integral using Simpson's Rule.
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Analyze the
approximate errors in the Trapezoidal Rule and Simpson's Rule.
Homework:
Read and take notes on 5.6 (p. 345 - 349) and do p. 350 # 3, 6, 16,
24, 44, 46, and 47
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Tues.,
2/2 1st hour - lab 133
3rd Hours-
Lab 41 |
Activity: Riemann Sum Sketchpad Lab |
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Wed.,
2/3 |
5.7
The Natural Logarithmic Function: Integration
Objectives:
At the end of this lesson you should be able to
Homework:
Read and take notes on 5.7 (p. 352 - 357) and do p. 358 # 1, 6, 11,
16, 20, 27, 29, 34, 38, 46, 48, 49, 52, 55
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Thurs.,
2/4 |
5.7
The Natural Logarithmic Function: Integration Objectives:
At the end of this lesson you should be able to
Homework:
p. 359 # 63, 66, 69, 72, 73, 76, 78, 79, 89, 93, 94
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Fri.,
2/5 |
5.8
Inverse Trigonometric Functions: Integration
Objectives:
At the end of this lesson you should be able to
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Integrate
functions whose antiderivatives involve inverse trigonometric
functions.
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Use the
method of completing the square to integrate a function.
-
Review the
basic integration rules involving elementary functions.
Homework:
Read and take notes on 5.8 (p. 361 - 365) and do p. 365 # 1, 6, 11,
16, 21, 26, 29, 30, 34, 35, 37
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Mon.
2/8 |
5.8
Inverse Trigonometric Functions: Integration
Objectives:
At the end of this lesson you should be able to
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Integrate
functions whose antiderivatives involve inverse trigonometric
functions.
-
Use the
method of completing the square to integrate a function.
-
Review the
basic integration rules involving elementary functions.
Homework:
Page 366 # 41, 43, 44, 54, 55, 59, 62, 64, 67, and (due
Tuesday 2/17) and begin your
Take-Home Exam - chapter 5
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Homework:
Page
380-382: You create your own review from these problems!!! 
Homework:
Finish your Take-Home Exam - chapter 5 with
4.8
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Tues.,
2/9 1st Hour -
Lab 43 3rd Hour -
Lab 43 |
Wed.,
2/10 |
Review
Homework:
Finish your Take-Home Exam - chapter 5 with
4.8 |
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Thurs., 2/12 |
with problems from 4.8
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Websites that might be helpful this
chapter….
http://education.yahoo.com/homework_help/math_help/problem_list?id=minicalcgt_5_1 |
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