Calculus I

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Syllabus

MAT 2O1 - CALCULUS 1
PRE-REQUISITES: MAT 2OO, (PRECALCULUS), OR ITS EQUIVALENT BY WAIVER

CATALOG DESCRIPTION: First of a three-quarter sequence designed to provide students with an appreciation of the usefulness and power of calculus. Emphasis will be placed on the application of calculus to various disciplines. Among the topics studied are: functions, limits, derivatives, maxima-minima problems, velocity and acceleration problems, antiderivatives.

ENTRY LEVEL SKILLS: The student should understand the concept of function and have a good algebraic and graphic knowledge of elementary polynomial trigonometric and logarithmic functions. Furthermore, the student should be able to simplify algebraic expressions and solve algebraic equations.

Instructional Objectives:

1. Reinforcement of the student's knowledge of precalculus mathematics.

2. An intuitive presentation of limit and tangent to a curve.

3. Calculation of the derivative by limit techniques.

4. The derivatives of Rational and Trigonometric functions.

5. The formulas of the derivatives of the sum, difference product, quotient and composition of functions.

6. Implicit differentiation.

7. Applications of the derivatives to graphing, optimization and related rate problems.

Performance Objectives:

The student will acquire the following skills:

1. Calculation of the derivative of rational functions.

2. Calculation of the derivative of the sum, difference, product, quotient and composition of functions.

3. Calculations of the derivative by implicit techniques.

4. Application of the derivatives to elementary graphing.

TEXT: CALCULUS. Hughes-Hallet. Third Edition

John Wiley & Sons, Inc.

GRADING: Your grade will be based on your performance on the quizzes and/or tests and final exam, which the instructor may give. The instructor may count solution to homework assignments as a factor in the grade. In any case the student is encouraged to submit solutions to unassigned problems to give him more practice, which is essential for success in mathematics.

ATTENDANCE: By official school policy, attendance is mandatory. It is assumed that absence is always with good reason, but excessive cuts will result in a WU or F grade. You will be urged to meet with the instructor frequently during the quarter to discuss your progress.

LAGUARDIA COMMUNITY COLLEGE
CALCULUS I - COURSE SYLLABUS 

	TOPICS	SECTION	SECTION ASSIGNMENT
1.	How Do We Measure Speed?	2.1	1, 3, 4, 6, 7, 8, 11, 14, 16
2.	Limits (Optional)	2.2	1, 3, 5, 7, 11, 13, 15, 19, 20, 22, 30, 32, 34
3.	The Derivative At A Point	2.3	1, 3, 8, 9, 10, 14, 16 (uses 10), 22 24, 26
4.	The Derivative Function	2.4	5, 8, 11, 15, 22, 24, 31, 33, 38,39
5.	Interpretations Of The Derivative	2.5	2, 6, 7, 9, 12, 15, 19
6.	The Second Derivative	2.6	2 – 6, 12, 14, 18, 19, 20,22
7.	Continuity And Differentiability	2.7	2, 6, 8, 10, 11
8.	Review for Test# 1
9.	Test # 1
10.	Powers And Polynomials	3.1	5, 6, 9, 10, 21, 22, 25, 27, 40, 42 – 44, 59
11.	The Exponential Function	3.2	5, 6, 12, 16, 24, 25, 28, 35, 38, 40, 43, 44
12.	The Product and Quotient Rules	3.3	2, 4, 11, 20, 28, 29, 32, 41, 42, 47
13.	The Chain Rule	3.4	2, 12, 20, 24, 26, 41, 44, 53, 55, 56, 58, 63
14.	The Trigonometric Functions	3.5	4, 5, 11, 18, 20, 25, 27, 37, 46, 47, 48
15.	Applications of he Chain Rule	3.6	3, 4, 8, 18, 20, 22, 25, 32, 41, 45, 47
16.	Implicit Functions	3.7	2, 9, 10, 11, 21,27
17.	Linear Approximation And The Derivative	3.9	2, 4, 10, 11, 15
18.	Using Local Linearity To Find Limits	3.10 (154-7)	2, 4, 6, 13, 14, 19
19.	Review for Test# 2
20.	Test # 2
21.	Using First And Second Derivatives	4.1	2, 4, 9, 10, 18, 19, 24,25, 26, 32, 34, 36, 40, 42
22.	Optimization	4.3	2, 4, 12, 15, 25, 31, 32
23.	Newton’s Newton	Appendix D
24.	Optimization And Modeling	4.5	2, 5,6, 14, 16
25.	Theorems About Continuous And Differentiable Functions	4.7	8-10, 13-15, 18, 22, 26, 30, 31
26.	Review for Test# 3
27.	Test # 3
28.	How Do We Measure Distance Traveled?	5.1	2-4, 6-8, 11, 14
29.	The Definite Integral	5.2	1, 2, 8, 13, 16, 20, 23, 24, 27, 30
30.	Interpretations Of The Definite Integral	5.3	6, 8, 9, 14, 18, 20, 23, 24, 31
31.	Theorems About Definite Integrals	5.4	1, 5, 6, 9, 11, 12, 14, 15
32.	Review for Test# 4
33.	Test # 4
34.	Antiderivatives Graphically And Numerically	6.1	1, 4, 6, 10, 11, 15, 17, 18, 23
35.	Constructing Antiderivatives Analytically	6.2	6, 12, 16, 28, 32, 37, 46, 53, 55, 67, 72, 77, 81, 83
36.	Differentials equations	6.3	2, 4, 7, 12-14, 19, 23
37.	Second Fundamental Theorem Of Calculus	6.4	2, 4, 6, 8, 11, 18, 19, 22, 23
38.	The Equations Of  Motion	6.5	2, 4, 6
36.	Integration by Substitution	7.1	Even #s 4-40, Even #s 49-68, 43, 44, 70, 75
37.	Review for Test# 5
38.	Test# 5
39.	Review for Final