Winter 2011

Math 112: Calculus 1

 

Professor: Dr. Blake Peterson

Office: TMCB 193B                                     

Office Phone: 422-7784                                                        email: blake@byu.edu

Class Time: MWF 11:00-11:50

Office Hours: MWF 10-10:45, W 1:30-2:30

                                    and by appointment

 

Texts: Single Variable CALCULUS: Early Transcendentals  - 6th Ed. Volume 1, written by James Stewart

 

Prerequisites:

Math 110 and 111 or the equivalent. This includes College Algebra and Trigonometry, but could also be satisŽed with a good course in PreCalculus. Students will also be required to take a pretest in order to exhibit competency in these areas. (See below).

 

Pretest:

Successful completion of Math 112 requires a solid background in both College Algebra and Trigonometry. Students are required to take a pretest on these topics. While the pretest may be worth only one assignment, it is also required before we will grade the Žnal. A pretest review can be found at the site http://mathonline.byu.edu. Log in with your route y id and password. Click on Pretests and placement exams. Scroll down to the Math 112 section. The review is one link, the exam the other. When you are ready to take the pretest, make sure you select the correct link! There are 3 pretests on the site.

 

While you take the pretest, you will notice at the bottom of the page a Ósave without submittingÓ button. Select this after each answer. If you lose your internet connection, you can come back and Žnish the quiz later. Select Ósubmit allÓ when you are done with the exam. You will need to Žnish the pretest before January 17 at 11:55 p.m. You are allowed 2 chances to pass. If your score is below 75% then you do not have the necessary skills to succeed in Calculus. Talk to your instructor about your options, and what you can do to better prepare yourself.

 

Preparation Time:

Adequately prepared students should expect to spend a minimum of two hours of work out of class for each hour in class. This adds up to a minimum of 10 hours per week (plus class time) for math 112. A minimal time commitment is likely to lead to an average grade B-/C+ or lower. Much more time may be required to achieve excellence.

 

Grading:                    Homework                                                      225 pts.

                                    3 Midterms (175 pts each)                              525 pts.

                                    Final                                                                250 pts.

                                                                                                          1000 pts.

 

 

 

Learning Outcomes:

Students are expected to master the Ócore topicsÓ of Math 112, consisting of the material in the Žrst Žve chapters of the text. In particular, students are expected to master the following topics:

Limits of Functions: Students will be able to explain intuitively and graphically the concept of limit of a function, recognize the correct deŽnition of limit, be able to use the deŽnition of limit to prove simple limit statements, recall and use limit theorems in evaluating limits explain and use one-sided limits, limits at inŽnity, and inŽnite limits, apply limits to the description of asymptotes of functions, and Žnd for functions which are not deŽned at a.

Continuity: Students will be able to recognize the deŽnition of continuity at a point, explain the graphical interpretation of continuity, understand dierent types of discontinuities which can be rewritten so as to be continuous, use continuity in evaluating limits of composite functions, apply the Extreme Value and Intermediate Value theorems and know a correct statement of these theorems.

The Derivative: Students will be able to explain and apply the graphical interpretation of the derivative as slope, explain and apply the dynamic interpretation of the derivative as rate of change, know the deŽnition of a derivative and be able to use it to compute the derivative of a function, use the dierentiation formulas to Žnd the derivative of any elementary function (polynomial, rational, root, exponential, logarithmic, trigonometric, inverse trigonometric, hyperbolic, and all combinations and compositions thereof ), recognize and use the common notations for the derivative, recall and use the relationship between dierentiability and continuity, use implicit dierentiation to Žnd the Žrst derivative of an implicitly deŽned function, explain and use the interpretations of the second derivative, compute derivatives of higher order, and be proŽcient in all the dierentiation techniques, including the product rule, and chain rule.

Applications of the Derivative: Students will be able to recall and explain the meaning of RolleÕs Theorem and the Mean Value Theorem, use the derivative to describe the monotonicity of a function, use the second derivative to describe the concavity of a function, use Žrst and second derivative tests to classify extrema, use the derivatives to Žnd critical points, inßection points, and local extrema, use derivatives to aid in sketching, by hand, the graph of a function, solve optimization problems, solve related rates problems, and use LÕHopitalÕs Rules to evaluate limits.

The DeŽnite Integral: Students will be able to explain and apply the graphical interpretation of the deŽnite integral as area, explain and apply the dynamic interpretation of the deŽnite integral as total change (given the velocity or acceleration, how do you Žnd the displacement?), recognize a correct deŽnition of the deŽnite integral, recall and use the deŽnition of the deŽnite integral as a limit of Riemann sums, (that is, Žnd what a certain limit of Riemann sums is in terms of an integral), recognize an integral which corresponds to a sequence of Riemann sums, recall and use linearity and interval properties of deŽnite integrals. ŅInterval propertiesÓ are properties pertaining to the interval of integration like and , recall and explain the Fundamental Theorem of Calculus, Žnd derivatives of functions deŽned as deŽnite integrals with variable limits including situations which will require the use of other rules of dierentiation in conjunction with the fundamental theorem of calculus; use the Fundamental Theorem to evaluate deŽnite integrals by antidierentiation, and use a simple substitution to Žnd an antiderivative.

 

Calculators:

Just like a pencil, paper, or a textbook, a calculator is simply a tool that can be used to better understand mathematics. It is not a substitute for understanding. I will use calculators on a regular basis to aid in the visualization of concepts and you will be allowed to use a calculator on homework and midterm exams. If you already have a graphing calculator, there is no need to buy a new one. If you are going to buy a new one, I would recommend a TI-89 because it is what I will be using for demonstration purposes in class.

 

Homework:

Homework will be collected in class each Monday, Wednesday, and Friday. Any homework not handed in during class is considered late. The lowest four homework scores will be dropped so no late homework will be accepted. Only a portion of the homework assignment will be graded each day so it becomes extremely important that you attempt every problem. Although homework assignments will be handed in individually, I strongly encourage students to discuss homework with your classmates in some form of informal study groups. Solutions should be clearly labeled and in order. The style of your written solutions should be very much like that of a text book example; solutions should contain enough explanation so that one of your classmates would be able to easily understand what you have done. The process of justifying your own solution does a lot for solidifying the concept in your own mind.

 

Midterms:

The midterm examinations will take place about every 4-5 weeks as outlined by the dates below. The midterms will be administered through the testing center. The midterm exams will have two parts: a calculator portion and a non-calculator portion but these exams are closed book and closed note.

 

Exam 1            Thursday-Saturday     January 27-29

Exam 2            Thursday-Saturday     February 24-26

Exam 3            Thursday-Saturday     March 24-26

 

Final:

The final will be common to all sections of calculus 1 and will be on Saturday, April 16 from 7-10 pm. Calculators will NOT be allowed on the final exam.

 

Math Lab:

If you feel that you would like extra help, please take advantage of the free tutoring in the Math Lab on the first floor of the TMCB.

 

 

 

 

 

 

 

 

Grade Distribution: The grades will be distributed according to the scale below. If you obtain the specified percentage indicated below, you are assured the grade associated with that percentage.

 

93% - 100%    A

90% - 92%      A-

87% - 89%      B+

83% - 86%      B

80% - 82%      B-

77% - 79%      C+

73% - 76%      C

70% - 72%      C-

67% - 69%      D+

63% - 66%      D

60% - 62%      D-

Below 60%      E

 

 

 

Preventing Sexual Harassment:

Title IX of the Education Amendments of 1972 prohibits sex discrimination against any participant in an educational program or activity that receives federal funds. The act is intended to eliminate sex discrimination in education and pertains to admissions, academic and athletic programs, and university-sponsored activities. Title IX also prohibits sexual harassment of students by university employees, other students, and visitors to campus. If you encounter sexual harassment or gender-based discrimination, please talk to your professor; contact the Equal Employment Oce at 801-422-5895 or 1-888-238-1062 (24-hours), or http://www.ethicspoint.com; or contact the Honor Code Oce at 801-422-2847.

 

Students with Disabilities:

BYU is committed to providing reasonable accommodation to qualiŽed persons with disabilities. If you have any disability that may adversely aect your success in this course, please contact the University Accessibility Center at 422-2767. Services deemed appropriate will be coordinated with the student and instructor by that oce.

 

Academic Honesty:

BYU students should seek to be totally honest in their dealings with others. They should complete their own work and be evaluated based upon that work. They should avoid academic dishonesty and misconduct in all its forms, including plagiarism, fabrication or falsification, cheating, and other academic misconduct. Students are responsible not only to adhere to the Honor Code requirement to be honest but also to assist other students in fulfilling their commitment to be honest.