# Math 372 - Differential Equations

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```					                            MTH 184 – Calculus I
Fall 2008

Class Meetings: MWF 10:00am / Tues 1:30-2:30
Location: RTC 127
Instructor: Dr. Jerome Reyes
Office Location:      Brown Memorial Hall (BMH) B165
Phone Number:         823-9560
E-mail:       jreyes@nsu.edu

Office Hours: Monday & Wednesday 2 – 4pm       Tuesday & Thursday 11 – 12:30   4 – 5pm

Department Telephone Number: 823-8820
Location: Brown Hall, Suite B168

Credits:              4 Semester Hours
Prerequisite:         Math 153 or equivalent

Course Description:

This is a first course in the essentials of Calculus, necessary for more advanced study in the
natural sciences and mathematics. The topics include limits, continuity, derivatives and
applications, antiderivatives and the Fundamental Theorem of Calculus. The course integrates
some calculus applications with computer activities.

Course Rationale:

The fundamental notion of rate of change, in all its various guises, is emphasized. This idea is
basic, and should be kept in mind, as one moves from one topic to the next while the course
unfolds. We emphasize graphing, as a way to study the behavior of functions, and this is
facilitated through the use of the derivatives of the functions under consideration. Much of the
applications are directed towards optimization problems, and these are studied in great detail.

The inverse problem of recovering a function, given its rate of change, leads to anti-
differentiation. This, in turn, steers us to an unexpected connection between the problem of
finding areas (by way of the definite integral) and differentiation. This connection is afforded by
the Fundamental Theorem of Calculus. The techniques of integration are then applied to shed
light on the solution of several classical problems involving areas, volumes, motion, and, more
generally, accumulation.
Course Goals and Measurable Intended Student Learning Outcomes:

To study limits, differentiation, anti-differentiation and their application to real world problems.
Students, on completing this course, will be able to:
1. Construct functions and analyze them for continuity;
2. Find the limits of certain functions, as the independent variable approaches some fixed
number;
3. Understand the definition of the derivative, and master the techniques of differentiation,
explicit and implicit;
4. Use the chain rule to find derivatives of composite functions;
5. Understand the connection between the sign of the first derivative of a function and
whether that function is increasing or decreasing;
6. Determine the concavity of the graph of a function, depending on the sign of the second
derivative;
7. Set up and solve problems involving related rates;
8. Find critical points for a function, and use them to find extreme values (maximum or
minimum);
9. Understand the Mean Value Theorem, analytically and geometrically;
10. Find antiderivatives (indefinite integrals) by inspection, or by substitution;
11. Evaluate definite integrals by using the Fundamental Theorem of Integral Calculus;
12. Find the areas between curves by integration;
13. Use integration to solve problems of accumulation, via Riemann sums.

Course Materials/Required Text/Requirements:
Each student should:
1. prepare for each lecture by reading the appropriate topic(s).
2. devote a minimum of 10 hours per week for preparation.
3. attend all lectures and keep a notebook of lecture notes and solved problems.
4. complete and turn in all assignments (if required) on time.

Text:       University Calculus by Hass, Weir, and Thomas

Available Supplements:

Solutions manual can be ordered through the bookstore. The following computer software are
available: My Math Lab, Maple, Mathcad, and Mathematica. The School of Science website for
gateway courses will also be used (http://sst.nsu.edu).

Primary Methods of Instruction/Methods to Engage Students:

1. Students will be required to complete an exercise or to engage in a discussion related to
the topic(s) covered previously for a period of five minutes at the beginning of each
lecture.
2. There will be three hours of lecture and discussion and one hour of intense problem
solving (drill session) per week.
3. Students are required to complete 8 labs online (My Math Lab software assignments.)
Topical Outline:

Week Number                   Topics                                       Sections

1            Preliminaries: Lines and Functions,                   1.1 – 1.5
Solving equations, Trigonometric Functions,
Exponential and Logarithmic Functions,
Preview of Calculus

2            Rates of change and limits, Computation of Limits,    2.1 – 2.2
One-Sided Limits and Limits at Infinity               2.4

3            Infinite Limits, Continuity and Its Consequences,     2.5 – 2.7
Tangents and Derivatives

4            The Derivative as a Function, Differentiation         3.1 – 3.2
Rules for Polynomials, Exponentials, Products
and Quotients (Deadline for Labs 1 and 2)
(Test I: 2.1-2.2 & 2.4-2.7)

5            The Derivative as a Rate of Change,                   3.3 – 3.4
Derivatives of Trigonometric Functions

6            The Chain Rule,                                       3.5 & 3.7
Derivatives of Inverse Functions and Logarithms

7            Implicit Differentiation, Related Rates               3.6 & 3.9

8            Extreme Values of Functions, The Mean Value Theorem   4.1 - 4.3
Monotonic Functions and the First Derivative Test
(Deadline for Labs 3 through 5)
(Test II: 3.1-3.7)

9            Concavity and Curve Sketching                         4.4

10           Curve Sketching                                       4.4 – 4.5
Applied Optimization Problems

11           Antiderivatives                                       4.8
(Deadline for Labs 6 & 7)
(Test III: 3.9, 4.1 – 4.5)

12           Estimating with Finite Sums, Sigma Notation and       5.1 – 5.3
Limits of Finite Sums, The Definite Integral
13               The Fundamental Theorem of Calculus,                     5.4 – 5.5
Indefinite Integrals and the Substitution Rule

14               Substitution                                            5.5
(Thanksgiving Break: Thursday, Nov. 27th, through Sunday, Nov. 30th)

15               Area Between Curves, Review                              5.6
(Deadline for Lab 8)
(Test IV: 4.8, 5.1-5.6)

16               Final Exam

The schedule is subject to change at the discretion of the instructor.

Related University-Wide and Course-Specific Requirements:

 Writing: There are free-response questions where the student will write his/her
explanation.
 Information Technology Literacy: Students will explore various websites to gain a
better understanding of math concepts and problems. Each student is also required to
complete math labs online. Students are encouraged to communicate with the professor
and/or classmates through electronic means.
 Quantitative Reasoning: Most of the math concepts have applications that require
quantitative reasoning.
 Scientific Reasoning: Most of the math applications require the use of scientific
reasoning.
 Oral Communication: Students demonstrate oral communication through classroom
discussions.
 Critical Thinking: Majority of the math concepts and applications require critical
thinking.
 Other Requirements: Students are required to engage in solving an exercise or
participating in a group discussion for approximately five minutes at the beginning of
each lecture. The completion of 8 Math Labs assignments is also required.

Evaluation:     Final grades are determined as follows:

HW / Quizzes:             15%
Labs:                     15%
4 Tests :                 50%
Final Exam:               20%

Grading Standards: A            [90, 100]
B            [80, 90)
C            [70,80)
D            [60, 70)
F            Below 60
Class Policies And Procedures:

1.   No Make-Ups except in cases of extreme emergencies.
2.   All tests will be announced.
3.   Cheating of any kind will not be tolerated and will result in an automatic grade
of “F” for the semester (further disciplinary actions may be taken by the
university).

Students are expected to attend all class sessions. Information regarding academic or
academically related misconduct, and disciplinary procedures and sanctions regarding such
misconduct, may be obtained by consulting the NSU Student Handbook.

Americans With Disabilities Act (ADA) Statement:
In accordance with section 504 of the 1973 Rehabilitation Act and the Americans with
Disabilities Act (ADA) of 1990, if you have a disability or think you have a disability please
make contact with Supporting Students through Disability Services (SSDS) Office.
Location:             2nd floor/Lyman B. Brooks Library, Room 240
Contact Person:       Marin E. Shepherd, Disability Services Coordinator
Telephone:            823-2014

University Assessment Statement:
As part of NSU’s commitment to provide the environment and resources needed for success,
student may be required to participate in a number of university-wide assessment activities. The
activities may include tests, surveys, focus groups and interviews, and portfolio reviews. The
primary purpose of the assessment activities is to determine the extent to which the university’s
programs and services maintain a high level of quality and meet the needs of the students.
Students will not be identified in the analysis of results. Unless indicated otherwise by the
instructor, results from University assessment activities will not be computed in the student
Mathematics
Flowchart

Tutorial
(Any Lab on Campus)

Report to
STARS
and/or      Fail
Instructor             **Lab Assignment
and/or
Resource Center             ON LINE
Room C227 BMH
and/or ACCESS

Pass               Report to
STARS
and/or
Instructor
Proceed to                   and/or
In-Class Test            Resource Center
In-Class Test
Room C227 BMH
and/or
Fail
ACCESS

Pass

Proceed to
Next Assignment

**No Credit will be awarded for Lab Tests not passed (70%).
Lab Tests count for 15% of Final Grade
My Math Lab Instructions:

You are expected to complete ten labs during the semester. You will need:
1. Internet access and an email address
2. A student access code
3. A course ID:   coombs-reyes95477
Getting started:
1. Visit this site: www.coursecompass.com
2. Click Register, click next
3. Type in your six-word access code (do not type the hyphens)
4. Select, No, I am a new user, and Next
5. Type in your course ID number and Next
6. Enter your contact information, click Next
7. Click the drop down arrow next to the Institution Name box
8. Click NSU
9. Enter you desired login name and password (do not use blank spaces or punctuation marks)
10. Click the arrow next to the Question box to select a question that only you can answer to
12. Click, I agree and Next
13. A page will be displayed confirming your registration. Print this page.

Access the My Math Lab Site:
1. Go to http://www.mymathlab.com (save this site as a favorites on your computer)
4. Click on the name of your course
5. Install the plug-ins that allow you to interact with the multimedia. You may already have
these on your computer. Some are Adobe Acrobat, Real Player, Macromedia Flash. There
are 7 plug-ins. Access the Installation Wizard from the Announcements page.
6. Click current users and upgrade plug-ins on the left
8. Repeat the process until all of the plug-ins are downloaded

Now you are ready to use My Math Lab!

Do you want a user’s guide?
1. Go to http://www.mymathlab.com and click Getting Started
2. Under the heading Current Users, you can view and print your user’s guide.
Math 184 – Calculus I, Fall 2008
Lab Test Assessment Form (LTAF)

Lab Test                         Completed (Signature/Date)
1.   Rates of Change, Limits
Sections: 2.1 - 2.2 & 2.4
2.   Continuity, Tangents & Derivatives
Sections: 2.5 - 2.7

Deadline for Labs 1-2: September 17, 2008;
In-class Test #1
3.   The Power, Product, and Quotient Rules
Sections: 3.1 - 3.2
4.   Derivatives as a rate of change, Derivatives of
Trigonometric, The Chain Rule
Sections: 3.3 - 3.5
5.   The Chain Rule, Derivatives of Exponential,
and Logarithmic Functions, Implicit
Differentiation
Sections: 3.5 - 3.7

Deadline for Labs 3-5: October 15, 2008;
In-class Test #2
6.   Related Rates, Extreme Values of Functions,
Increasing and Decreasing
Functions, Mean-Value Theorem
Sections: 3.9, 4.1 - 4.3
7.   Concavity, Asymptotes, Applied
Optimization
Sections: 4.4, 4.5, 2.5

Deadline for Lab 6-7: November 5, 2008;
In-class Test #3
8.   Antiderivatives, Definite and Indefinite
Integrals, Substitution Rule, Area between
Curves
Sections: 4.8, 5.1 - 5.6

Deadline for Lab 8: December 3, 2008;
In-class Test #4
Tests must be taken in consecutive order               No credit awarded for Lab Tests not passed

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