Calculus I

Math 2413: Calculus I

Go here for the extra homework assignment(s) I mentioned in class.

Fall 2008

Synonym: 24145, Section: 004, Northridge 2244
Monday / Wednesday 2:40 pm - 4:20 pm

Synonym: 24147, Section: 006, Northridge 2244
Tuesday / Thursday 10:35 am - 12:15 pm

Course Content:

Course Description : MATH 2413 CALCULUS I (4-4-0).   A standard first course in calculus. Topics include inequalities; functions; limits; continuity; the derivative; differentiation of algebraic functions and trigonometric functions; Newton's method; applications of the derivative; the integral; integration of algebraic functions and the sine and cosine functions; numerical integration; and applications of the integral.

Instructional Methodology : This course is taught in the classroom primarily as a lecture/discussion course.

Course Rationale : This course is the first course in the traditional calculus sequence for mathematics, science and engineering students. It is part of what could be a four-semester sequence in calculus courses. The approach allows the use of technology and the rule of four (topics are presented geometrically, numerically, algebraically, and verbally) to focus on conceptual understanding.  At the same time, it retains the strength of the traditional calculus by exposing the students to the rigor of proofs and the full variety of traditional topics: limits, continuity, derivative, applications of the derivative, and an introduction to the definite integral.

Prerequisites:

Please make sure you have the necessary prerequisites for this course : MATH 2412 with C or better or equivalent. Another option is an appropriate secondary school course (one year of precalculus or the equivalent, including trigonometry, with a B or better) and a satisfactory entrance score on the ACC Mathematics Assessment Test . If I feel you are not prepared for this course, I may choose to withdraw you. If you have any questions about your preparation for the course, please come and talk to me about it.

Course Materials:

Textbook : Calculus : Concepts and Contexts , 3rd ed., by James Stewart, Brooks/Cole 2005

Optional : Student Solutions Manual, Single Variable by Jeffrey A. Cole, Study Guide by Dan Clegg, Scientific Notebook software, single version, Doing Calculus with Scientific Notebook , by Daniel W. Hardy, Carol L. Walker.

Technology required : You must have access to technology which enables you to (1) Graph a function, (2) Find the zeroes of a function.  Most ACC faculty are familiar with the TI family of graphing calculators. Hence, TI calculators are highly recommended for student use.  Other calculator brands can also be used.  Your instructor will determine the extent of calculator use in your class section.

Grading:

There will be 3 or 4 exams and a comprehensive final during the term, each of which will count equally towards your grade. The tests will comprise 90% of your grade. There may also be a few extra projects on calculus applications assigned during the semester as well. The remaining 10% of your grade will be based on your homework assignments and any extra projects.

You may earn bonus points on each test, except for the final test, by correcting all errors and submitting them to me within one week of receiving the graded test back. If you submit these corrections for every test that you make less than a 90, then I will replace your lowest test grade with the average of that grade and your grade on the final exam. If you take any test late for any reason, there will be a penalty of 10 points off your test grade. However, no late tests will be allowed after I hand the graded tests back in class.  

If you miss a test, you must try to take it during this “late” period. If you miss this deadline as well, I may consider allowing you to hand in corrections on all tests and replace all or part of the missed test with your grade on the final, but only in the case of serious illness or emergency.  This is solely at my discretion. Otherwise, you will receive a 0 on the test. All tests and assignments must be turned in on or before the last class meeting.

Grades will be assigned as follows:

A

90% or better and a grade of at least 75 on the final

D

60% - 69%

B

80% - 89% and a grade of at least 65 on the final

F

below 60%

C

70% - 79% and a grade of at least 55 on the final

     

W

Withdrawn by student or instructor prior to last withdrawal date on school calendar

I

Incomplete grades (I) will be given only in very rare circumstances. Generally, to receive a grade of "I", a student must have taken all tests, be passing, and after the last date to withdraw, have a personal tragedy occur which prevents course completion.

Homework:

You should bring your homework to class every day.  It will be collected regularly and graded.  There may also be in-class assignments collected for a grade (as part of your homework grade). There will be a penalty on late homework. Homework that is more than two weeks late might not receive any credit.

Attendance:

Attendance is required in this course.  It is extremely important for you to attend class regularly. Although I may not take regular attendance, I MAY drop you from the course for excessive absences, although I make no commitment to do so.

Withdrawal:

It is the student's responsibility to initiate all withdrawals in this course. The instructor may withdraw students for excessive absences (4) but makes no commitment to do this for the student. (If you decide to stop coming, you had best make sure that you drop the course. While we MIGHT do this, it is YOUR responsibility. If you fail to do so, you could receive an F on your permanent record.) After the withdrawal deadline, neither the student nor the instructor may initiate a withdrawal. If you are withdrawn by mistake, I will only consider reinstating you if you have taken all necessary tests, are current in your homework, and have not missed an excessive number of classes. The withdrawal deadline for Fall 2008 is November 24, 2008.

Classroom behavior:

Classroom behavior should support and enhance learning. Behavior that disrupts the learning process will be dealt with appropriately, which may include having the student leave class for the rest of that day. In serious cases, disruptive behavior may lead to a student being withdrawn from the class. ACC's policy on student discipline can be found in the Student Handbook page 32 or on the web at: http://www.austincc.edu/handbook

Class participation:

All students are expected to actively participate in this class. This can include asking relevant questions in class, participating in class discussions and other in-class activities, helping other students, coming to office hours with questions, and doing other things that contribute to the class.

Keeping up:

Please, try to keep up with the homework and with the lecture in class. There just isn't much time to catch up. This means you have to be sure to allow yourself plenty of time to do the homework and to study.

Ask questions:

Please, please, please, if you don't understand something, or you aren't clear about something, or if you think I (or the book) have made a mistake (it has been known to happen), or if you have any other questions, please ask. Don't let confusion accumulate. If you don't want to ask in class, come to our office hours (or call) and ask. It is much easier to ask a question now than to miss it on the test.  I expect all students to participate in class discussions and other activities. Trust me, you will get much more out of the class if you become actively involved in it.

Always show your work:

It is much more important that you understand the processes involved in solving problems than that you just give me the right answer. If I see from your work that you understand what you are doing, I will usually give partial credit for a problem, even if you made a mistake somewhere along the line. If you don't show your work (unless I believe you could reasonably do it in your head), I may not give you full credit, even if the answer is right. If you can really do something in your head, that's great, but when in doubt, write it down.  It is also very important that you write what you mean. I will correct your notation the first few times, but I will start counting it wrong if you continue to write things incorrectly. In addition, please write clearly and legibly. If I can't read it, I won't grade it.

Time required and outside help:

To do homework and study requires two or three times as much time outside of class as the time you spend in class in order to succeed in this course. If you need more out-of-class help than you can obtain in your instructor's office hours, free tutoring is available in any of ACC's Learning Labs.

Course-Specific Support Services  Sometimes sections  of MATH 0187 (1-0-2) are offered. This lab is designed for students currently registered in Calculus I MATH 2413. It offers individualized and group setting to provide additional practice and explanation. This course is not for college-level credit. Repeatable up to two credit hours.

ACC main campuses have Learning Labs which offer free first-come, first-serve tutoring in mathematics courses. The locations, contact information and hours of availability of the Learning Labs are posted at: http://www.austincc.edu/tutor

Statement on Academic Freedom:

Institutions of higher education are conducted for the common good.  The common good depends upon a search for truth and upon free expression.  In this course the professor and students shall strive to protect free inquiry and the open exchange of facts, ideas, and opinions.  Students are free to take exception to views offered in this course and to reserve judgment about debatable issues. Grades will not be affected by personal views.  With this freedom comes the responsibility of civility and a respect for a diversity of ideas and opinions.  This means that students must take turns speaking, listen to others speak without interruption, and refrain from name-calling or other personal attacks.

Scholastic Dishonesty:

Acts prohibited by the college for which discipline may be administered include scholastic dishonesty, including but not limited to, cheating on an exam or quiz, plagiarizing, and unauthorized collaboration with another in preparing outside work.  Academic work submitted by students shall be the result of their thought, work, research or self-expression.  Academic work is defined as, but not limited to, tests, quizzes, whether taken electronically or on paper; projects, either individual or group; classroom presentations; and homework.

Students who violate the rules concerning scholastic dishonesty will be assessed an academic penalty which the instructor determines is in keeping with the seriousness of the offense. This academic penalty may range from a grade penalty on the particular assignment to an overall grade penalty in the course, including possibly an F in the course. ACC's policy can be found in the Student Handbook page 33 or on the web at: http://www.austincc.edu/handbook .  

College Services:

Testing Center Policies: ACC Testing Center policies can be found at: http://www.austincc.edu/testctr/. Deadlines for all tests will be announced in class. Any tests taken after the announced deadline are considered late.

Student Services: The web address for student services is: http://www.austincc.edu/support. The ACC student handbook can be found at: http://www.austincc.edu/handbook

Statement on Students with Disabilities:

Each ACC campus offers support services for students with documented physical or psychological disabilities.  Students with disabilities must request reasonable accommodations through the Office of Students with Disabilities on the campus where they expect to take the majority of their classes.  Students are encouraged to do this three weeks before the start of the semester.

Students who are requesting accommodation must provide the instructor with a letter of accommodation from the Office of Students with Disabilities (OSD) at the beginning of the semester.   Accommodations can only be made after the instructor receives the letter of accommodation from OSD

 

 

Course Outline and Approximate Calendar:
Please note:  schedule changes may occur during the semester.
Any changes will be announced in class.

Week

Sections

Week

Sections

1

1.1, 1.2, 1.3, 1.4, 1.5

9

3.3, 4.2

2

1.6, 2.1, 2.2

10

4.3, 4.4

3

2.3, 2.4, 2.5

11

4.5, 4.6

4

2.6, 2.7, Test 1

12

4.6, 4.8*, Test 3

5

2.7, 2.8, 2.9

13

4.9, 5.1

6

3.1, 3.2, 3.4

14

5.2, 5.3

7

3.5, 3.6, 3.7

15

5.4, 5.5, Test 4

8

3.8, 4.1, Test 2

16

Review, Comprehensive Final Exam

 

     

Calculus I, MATH 2413, Learning Outcomes  

 

Additional information about ACC's mathematics curriculum and faculty is available on the Internet at:
 
http://www.austincc.edu/math/

 

Prerequisites for Calculus

 

There are two calculus sequences at ACC (and at most colleges) -- Business Calculus and Calculus.  The prerequisite sequence is different for these.  Depending on background, students may start the prerequisite sequence at different places

 

Intermediate Algebra (MATD 0390)

Intermediate Algebra (MATD 0390)

 

 

College Algebra**(MATH 1314)

 

Math for Bus & Eco

(MATH 1324)

College Algebra

(MATH 1314)

*Trigonometry (MATH 1316)

 

↓ ↓ ↓

Business Calculus I (MATH 1425)

Precalculus (MATH 2412)

Business Calculus II (MATH 1426)

Calculus I (MATH 2413)

 

 

Calculus II (MATH 2414)

 

 

Calculus III (MATH 2415)

 

 

 

Where to start :  The only way that students may skip courses in a sequence is to begin higher in the sequence, based on current knowledge of material from high school courses.  

  1. A student who needs a review of high school Algebra II will start in Intermediate Algebra (or below.)  

  1. A student who completed high school Algebra II, but no higher, and whose assessment test score indicates that he/she remembers that algebra, will start in College Algebra or Math for Business & Economics.  A substantially higher assessment test score enables the student to start in Trigonometry.

  1. A student who completed some precalculus, elementary analysis, or trigonometry in high school, and whose assessment test score indicates that he/she remembers algebra, is eligible to start higher in the sequence than College Algebra.  Check the catalog or the math web page.***

 

* The material in the Trigonometry course requires that students are quite adept with the skills from high school Algebra II (Intermediate Algebra).  Some students will achieve that level of skill in the College Algebra course if their placement score is high enough, while others need an additional semester of work on algebra that is done in two courses, Intermediate Algebra and College Algebra.  

 

** Some students who are very successful in College Algebra are tempted to skip either Trigonometry or Precalculus and enroll in Calculus I. That is not acceptable .  Trigonometry topics are essential to success in Calculus, and while it is true that the topic list for Precalculus has only a few additions from the topic list for College Algebra, the level of sophistication of the presentation and the problems on all topics is greater in Precalculus. That increased sophistication is necessary for an adequate background for the Calculus sequence. ***

 

Notes about the Business sequence: Texas State University requires Math for Business and Economics and Business Calculus I. Students who will attend the UT College of Business must complete the entire Business Calculus sequence before transferring. For more information, including requirements for UT economics students, see http://www.austincc.edu/mthdept2/notes/1425.html

*** For additional information, including prerequisite review sheets for most courses, see http://www.austincc.edu/math/

 

Prerequisites for MATH 2413 - Calculus I

In order to succeed in calculus, students need to have taken a trigonometry course and a precalculus course and to have current knowledge of the material in those courses.

If you have forgotten the material in those courses, this sheet can serve as a study guide to remind you of what you need to review. By the time you go to your first calculus class, you should be able to do at least 14 of the problems in Part I and 7 of the problems in Part II. Many instructors will test you on this material at the beginning of your calculus course and that test will be part of your grade in the course.

If you cannot work enough of the problems correctly in each part below, you should take a trigonometry course and/or a precalculus course before you register for calculus.

Part I.

1. Write the equation of a line through (2,-3) and perpendicular to .

2. For , calculate , , and .

3. State the domain of each function:

               

4. For and , find .

5. For , find the inverse function of f.

In problems 6 - 9, solve for x:

6.                        7.               8.

9.                                        10. Simplify:

11. Find all rational roots of .

In 12-18, sketch the graph without using a graphing calculator or computer software. In each, you should be able to describe the general shape and then plot a few crucial points to sketch it.

12.                               13.                               14.

15.                 16.                17.

18.

Part II.

1. Graph:

In 2 - 5, evaluate:

2.                  3.                  4.

5.                          6. Solve:

In 7 - 10, convert each of the expressions on the left to the one on the right using trigonometric identities.

7. ,         8. ,                 9. ,           

10. ,

Answers:

1.                     2. , ,

3. f has domain all real numbers, g: , h has domain all positive real numbers except 2, j has domain all real numbers except 0 or 1.

4.             5.               6.         7. or

8.      9. -3                10.                    11. -2, 3

12. parabola, open to the right, vertex (0,0). See graph.

13.                   14. hyperbola, asymptotes at , foci

15. ellipse, center (4, -2)      16.       17.       18. ellipse, center (3, 0)

Part II.

1. Amplitude 5, horizontal shift , period .                 2.            3. undefined

4.           5. 1      6. | where n is an integer}

7. and 8. Use the basic trig identities         9. use the formula for

10. One possible solution:

 


This webpage was created by Marcus McGuff.
It was last updated on August 29, 2008 .