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 |
|
|
|
|
|
Start solving your Algebra Problems
in next 5 minutes!
 |
 |
 |
|
Algebra Helper
Download (and optional CD)
Only $39.99
|
|
Click to Buy Now:
OR
|
|
|
 |
 |
 |
|
2Checkout.com is an authorized reseller
of goods provided by Sofmath
|
|
Attention: We are
currently running a special promotional offer
for Algebra-Answer.com visitors -- if you order
Algebra Helper by midnight of
December 22nd
you will pay only $39.99
instead of our regular price of $74.99 -- this is $35 in
savings ! In order to take advantage of this
offer, you need to order by clicking on one of
the buttons on the left, not through our regular
order page.
If you order now you will also receive 30 minute live session from tutor.com for a 1$!
|
You Will Learn Algebra Better - Guaranteed!
Just take a look how incredibly simple Algebra Helper is:
Step 1
: Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:
Step 2 :
Let Algebra Helper solve it:
Step 3 : Ask for an explanation for the steps you don't understand:
Algebra Helper can solve problems in all the following areas:
- simplification of algebraic expressions (operations
with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots
(radicals), absolute values)
- factoring and expanding expressions
- finding LCM and GCF
-
(simplifying, rationalizing complex denominators...)
- solving linear, quadratic and many other equations
and inequalities
(including basic logarithmic and exponential equations)
- solving a system of two and three linear equations
(including Cramer's rule)
- graphing curves (lines, parabolas, hyperbolas, circles,
ellipses, equation and inequality solutions)
- graphing general functions
- operations with functions (composition, inverse, range, domain...)
- simplifying logarithms
- basic geometry and trigonometry
(similarity, calculating trig functions, right triangle...)
- arithmetic and other pre-algebra topics
(ratios, proportions, measurements...)
ORDER NOW!
|
|
|
|
Algebra Helper
Download (and optional CD)
Only $39.99
|
|
Click to Buy Now:
OR
|
|
|
|
|
|
|
|
2Checkout.com is an authorized reseller
of goods provided by Sofmath
|
|
|
 |
| |
| "It
really helped me with my homework. I was
stuck on some problems and your software walked me
step by step through the process..." |
| C. Sievert, KY
| |
| |
 |
| |
Sofmath
19179 Blanco #105-234
San Antonio, TX 78258
|
Phone:
(512) 788-5675
Fax: (512) 519-1805
| | |
