Download IV - Net Start Class

IV.
“Integration” BC. Chapter 4. 15 days.
A.
Topics
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
B.
Anti-derivative
Constant of Integration, General Solution
Differential Equation
Anti-differentiation
Indefinite Integration, Integrand, Variable of Integration, Indefinite
Integral
Integration Rules
General Solutions
Initial Condition, Particular Solution
Integration using u-substitution vs Integration using Anti-differentiation
General Power Rule for Integration
Sigma Notation, Index of Summation
Area—Upper Sums, Lower Sums
Circumscribed Rectangle, Inscribed Rectangle
Limit of the Lower and Upper Sums
Definition of the Area of a Region in the Plane
Riemann Sums – left, right, and midpoint sums
Definite Integrals and Riemann Sums
Continuity and Integrability
The Definite Integral as the Area of a Region
Properties of Definite Integrals
The Fundamental Theorem of Calculus
U Substitution and the Change of the Variables and the Intervals of
Integration.
The Mean Value Theorem for Integrals
Average Value of a Function
The Definite Integral of the rate of change of a quantity over an interval
interpreted as the change of the quantity over the interval.
The Second Fundamental Theorem of Calculus
Integration of Even and Odd Functions
Trapezoidal Rule, Simpson’s Rule
Accumulation of Rate of Changes.
Numerical Approximation of the Definite Integral
Integral applications to finding distance.
Teaching Methods and Evaluations.
1.
Each topic presented through lecture, student and group interaction,
2.
3.
4.
5.
graphing calculator usage, projects, supplements, Power Point
presentations, and assignments.
Integration presented through anti-differentiation. Project to solve
differential equations to a general solution, then a particular solution.
Discussion of the role of the Constant of Integration.
Riemann Sums Project. Upper Sums, Lower Sums, Right Hand Sums,
Left Hand Sums and Midpoint Sums explored graphically and
algebraically.
The definite integral developed as a limit of Riemann sums.
Student involvement in the teacher led proof of the Fundamental
Theorem of Calculus.
6.
7.
8.
9.
10.
11.
12.
13.
Student development of skill in integration through anti-differentiation
and u-substitution in assignment problems.
Integration explored as a net accumulation of change.
The definite integral used to illustrate the Fundamental Theorem of
Calculus in the role of solving functional values from graphs.
Understanding the Second Fundamental Theorem of Calculus through its
proof, and its utilization in algebraic and geometric problem solving.
Teacher led and student interaction in the development of the Mean
Value Theorem for Integrals and the Average Value of a Function.
Application of these concepts in AP generated problems of the text and
the College Board.
Trapezoidal and Simpson’s Rules illustrated with applications to data
analysis in charts and graphs.
Distance applications and its role with definite integrals.
Supplements of Chapter 4.
a.
b.
c.
d.
e.
f.
14.
Evaluations.
a.
C.
Limit of a Riemann Sum as a definite integral.
Riemann sum using left, right, and midpoint evaluations.
Proofs related to Integration topics of Chapter 4.
Indefinite and Definite Integration.
Integration Overview.
Selected problems of AP Test Preparation questions of section XI to
provide:
1.
Integral of a rate of change to give accumulated change.
2.
Integration to find the area of a region.
3.
Integration to find total distance or displacement.
4.
Use of anti-derivatives to discuss motion along a line.
5.
Using tables or graphs of velocity to answer questions
concerning distance, accumulation, or lower and upper
estimate of total accumulations.
6.
First and Second Fundamental Theorem of Calculus Discovery
7.
Problems concerning area, Second Fundamental Theorem of
Calculus, and average rate of change.
8.
Using graphs to find definite integrals given the graph of the
derivative.
9.
Trapezoidal and Simpson Rules to approximate definite
integrals (algebraically, graphically, tables).
Teacher created individual and group tests, projectsb. Multiple Choice
and Free Response questions of the College Board and Fast Track to a
5 listed in XI of the syllabus.
Assignments.
Text: Larson, Ron., Edwards, Bruce and Robert P.Hostetler. Calculus Boston:
Houghton Mifflin, 2006.
1.
2.
3.
4.
5.
4.1: Antiderivatives and Indefinite Integration. 21, 25, 27, 35-71o, 72, 73, 77,
78, 81.* E: 81, 82, 85, 94, 95, 97.
4.2: Area – Summation. 3, 9, 11, 15, 19, 23, 25, 27, 29, 33, 35, 41, 47, 51, 53,
55, 59, 63, 65. *E: 84. 75, 81 in class discussion.
4.3: Riemann Sums and Definite Integrals. 5, 9-12, 13-43o, 47-49.51-54, 55,
57. Supplement.
4.4: Fundamental Theorem of Calculus. 11, 15, 21, 23, 25, 29, 31, 37, 39, 43,
45, 47, 49, 51 53-60, 63, 67-91o. Supplement – Proofs. *E: 97, 98.
4.5: Integration by Substitution. 9, 11, 19, 25, 29, 31-39o, 40, 45-97o, 101105, 107, 111, 113. Supplement. . * E: 135, 136.
6.
7.
8.
9.
4.6: Numerical Integration. 3, 7, 13, 17, 23, 25, 27, 49, 51, 52. Supplement –
Proofs.
Teacher and student presentations of AP Questions.
Selected problems of Section VIII of AP Test Preparation.
Fast Track to 5.
“We are what we repeatedly do. Excellence, then, is not an act, but a habit…” Aristotle.
Parents and Students: Grading.
Major grades: (70%)
Daily grades: (20%). Fast Track; Class Presentations; Supplements; in
Class Activities; Quizes; Free Response; Group work.
Homework grades: (10%). Assignments. (view Calendar)
Parents and students are to be aware that the student receives use of a
solution key to the homework exercises and receives solutions to all
supplements in class.
Grade Sheets issued 2 times per 6 weeks. Gradespeed is updated within 48
hours of an assignment and or test.
Teacher Website updated per week. Calendar of pace on the website/Calendar.
Teacher Contact: [email protected] Use email, NOT Voice Mail please.
Student Signature:
________________________________
Parent Signature:
________________________________