Course Curriculum and Syllabus for Mathematics
Course Outline Calculus I (College Preparation
Mathematics )
Course Objectives: Students will use a graphical, analytical, and numerical
approach as they are introduced to limits, Derivatives, and Integral Calculus.
Students will analyze graphs of various functions, and apply concepts of limits
and derivatives.
Students will:
• Apply a graphical, analytical, and numerical approach to limits. (NCTM
Representation Standard)
• Perform operations using the first derivative. (NCTM Algebra Standard )
• Investigate the nature of graphs. (NCTM Geometry Standard)
• Develop curve-sketching techniques. (NCTM Geometry Standard)
• Be introduced to integral Calculus, Riemann Sums , and Area under a curve.
(NYS Representation Strands).
Weekly listing of reading assignments, tests, labs, projects, including due
dates:
Course Content (40 weeks of instruction)
Week
|
Text
Sections |
Topic
|
Page
|
Week
|
Ch.
|
Homework
|
| 1 |
P.1 |
Graphs and Models |
2 |
1 |
P |
|
2 - 3
|
P.2
|
Linear Models and
Rates of Change |
10
|
2
|
P
|
|
|
|
P.3
|
Functions and their
Graphs |
19
|
3
|
P
|
|
| |
|
Entrance Exam |
| 4 |
1.1 |
Preview of Calculus |
42 |
4 |
1 |
|
| 5 |
1.1 |
Limits |
48 |
5 |
1 |
|
|
|
1.2
|
Finding Limits
Graphically |
48
|
6
|
1
|
|
|
|
1.3
|
Evaluating limits
analytically |
59
|
7
|
1
|
|
6
|
1.4
|
Continuity and One
Sided Limits |
70
|
8
|
1
|
|
|
|
1.5 |
Infinite Limits |
83 |
9 |
1 |
|
| |
|
Ch. 1 Exam |
| 8 |
2.1 |
The derivative and the
Tangent Line
Problems |
96 |
10 |
2 |
|
|
9 -12 |
2.2 |
Basic Differentiation
Rules and Rates of
Change |
107 |
11 |
2 |
|
|
13 |
2.3 |
Product and Quotient
Rules and Higher
Order Derivitives |
119 |
12 |
2 |
|
|
|
2.4 |
The Chain Rule |
130 |
13 |
2 |
|
|
|
2.5 |
Implicit Differentiation |
141 |
14 |
2 |
|
|
15 |
2.6 |
Related Rates |
149 |
15 |
2 |
|
|
|
Ch.2
Rvw. |
Chapter 2 Review
|
158
|
16
|
2
|
|
17
|
3.1
|
Extrema on an
Interval |
164
|
17
|
3
|
|
|
|
3.2 |
Rolle’s Theorem |
164 |
18 |
3 |
|
|
|
3.2
|
The Mean Value
Theorem |
172
|
19
|
3
|
|
|
19
|
3.3
|
The First Derivative
Test:
Increasing/Decreasing
Functions |
179
|
20
|
3
|
|
|
|
3.4
|
The Second Derivative
Test: Concavity |
190
|
21
|
3
|
|
|
|
3.5 |
Limits at Infinity |
198 |
22 |
3 |
|
|
24 |
3.6 |
Curve Sketching |
209 |
23 |
3 |
|
|
|
3.7 |
Optimization Problems |
218 |
24 |
3 |
|
|
|
3.7 |
Business Applications |
218 |
25 |
3 |
|
|
27 |
3.8 |
Newton’ s Method |
219 |
26 |
3 |
|
|
|
3.9 |
Differentials |
235 |
27 |
3 |
|
|
|
Ch.3
Rvw |
Review Exercises
|
242
|
28
|
3
|
|
29
|
4.1
|
Antidervitives and
Indefinite Integration |
248
|
29
|
4
|
|
|
|
4.2 |
Area |
259 |
30 |
4 |
|
|
31 |
4.3 |
Riemann Sums |
271 |
31 |
4 |
|
|
|
4.3 |
Definite Integrals |
273 |
32 |
4 |
|
|
|
4.4
|
The Fundemental
Theorem of Calculus |
282
|
33
|
4
|
|
33
|
4.5
|
Integration by
Substitution (usubstitution) |
295
|
34
|
4
|
|
35
|
Ch. 4
Rvw |
Review Exercises
|
316
|
35
|
4
|
|
| 36 |
7.1 |
Area between Curves |
446 |
36 |
7 |
|
|
37 |
7.2 |
Volume: Disc Method |
456 |
37 |
7 |
|
|
|
7.3 |
Volume: Shell Method |
467 |
38 |
7 |
|
39
|
Ch. 7
Rvw |
Select Review
Exercises |
513
|
39
|
7
|
|
40
|
Ch. 7
Rvw |
|
|
|
|
|
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