Department of Mathematical Sciences CARNEGIE MELLON UNIVERSITY 21-120 Differential and Integral Calculus, 10 units, Fall, 2018 Instructor: Dr. Russ Walker, Wean Hall 6219, ext. 8-9657, rw1k@andrew.cmu.edu Text: Hartman, Gregory, A P EX CALCLUS, Version 4.0, an online text Course website: http://www.math.cmu.edu/ rw1k/120/21120.html 1. Introduction. Calculus is classical mathematics rooted in the physical sciences and Seventeenth Century problems: gravitation, optics, mechanics, heat flow, etc. Despite its classical origins, modern applications abound. In this course we will develop the main ideas of both differential and integral calculus for the full range of transcendental functions. A good background with algebraic, logarithmic, exponential and trigonometric functions is essential. Diagnostic tests are available at the beginning of the text. 2. Recitations, TA information Lecture 1: MWF 8:30 PH 100 Walker Lecture 2: MWF 9:30 PH 100 Walker A TuTh 8:30 WEH 5312 Ramazanli, I. F TuTh 8:30 PH A22 Zhang, J. B TuTh 9:30 WEH 5312 Ramazanli, I. G TuTh 9:30 PH A22 Zhang, J. C TuTh 11:30 WEH 5320 Kehne, G. H TuTh 12:30 PH A22 Chen, D. Q. D TuTh 12:30 WEH 4623 Kehne, G. I TuTh 2:30 SH 208 Koganemaru, J. E TuTh 3:30 WEH 4709 Chen, D. Q. J TuTh 4:30 DH 2105 Koganemaru, J. Some students qualify for special accommodations such as extra time on tests. Please present documentation supporting such a request as soon as possible, and certainly at least three working days before the first test. I will try to assist, but may not be able to help with last minute requests. If you suspect that you may have a disability and would benefit from accommodations but are not yet registered with the Office of Disability Resources, I encourage you to contact them at access@andrew.cmu.edu. Teaching Assistant Information. All TAs and the lecturer have mailboxes in Wean 6113. Teaching Assistant contact information is given below: Name Office Email Office hours Da Qi Chen Wean 6203 daqic@andrew.cmu.edu Gregory Kehne Wean 6213 gkehne@andrew.cmu.edu Junichi Koganemaru Wean 7102 jkoganem@andrew.cmu.edu Ilqar Ramazanli Wean 8209 iramazan@andrew.cmu.edu Jing Zhang Wean 6213 jingzhan@andrew.cmu.edu 3. Learning objectives. Following successful completion of the course, the student should Understand the concept of a continuous function and be able to apply the Intermediate Value Theorem. Be able differentiate algebraic and transcendental functions. Be able to determine the derivative of a basic function using the definition of derivative. Be able to evaluate limits including indeterminate forms. Be able to translate verbal descriptions of relationships into equations.
21-120 Syllabus 2 Be able to apply derivatives to graph a function, solve related rates problems, and solve applied extrema problems. Know and understand the Mean Value Theorem and some of its basic applications. Understand the definition of the definite integral as the limit of Riemann sums. Be able to use the Fundamental Theorem of Calculus Part I to determine the derivative of a function defined as an antiderivative. Be able to use the Fundamental Theorem of Calculus Part II to evaluate definite integrals involving algebraic and transcendental functions. Be able to use the methods of substitution and integration by parts to determine antiderivatives. Be able to apply the definite integral to calculate areas and volumes of revolution. 4. Conduct of the course. There will be three tests. No calculators or other electronic devices will be permitted during tests. A make-up test will be scheduled for each test at 7:30 AM on a day before the test is returned. Permission to take a make-up can be given only by the lecturer, not by a TA. A make-up will be given only for documented illness, family emergency, or University sponsored event. We reserve the right to refuse to give a make-up or to impose a penalty on a makeup for a student without a valid reason for missing the test. To help students get off to a good start, a retest will be given on Test 1, and only Test 1, for students scoring less than 75%. If you take the retest, your recorded score on Test 1 will be the smaller of 75% and the maximum of your two scores on the test. Thus, the retest can raise your grade to at most 75%. This is a great deal! You should take advantage of it if you qualify. Homework will be collected in recitation nearly every Thursday. Searching for solutions on the internet can be hazardous to your understanding you do the work, you get the benefit. The official place for information on homework and due dates is on the course website. Quizzes will be given in recitation most Tuesdays. Questions for recitation quizzes will be posted in advance on the course website so perfect scores should be very common. There will be no make ups on quizzes. Your two lowest quiz scores will not count because students must on rare occasions miss class. Homework and quizzes will each count 10%. The standards of academic honesty found at https://www.cmu.edu/student-affairs/theword/acad standards/creative/academic integrity.html will be strictly enforced. Unannounced questions were asked in lecture on eight occasions in the Fall of 94, and the table indicates the relationship between attendance and grades in the course. These questions counted for only 5% of the grade. Evidently, the most successful students attend the most regularly. Nuf said! Average attendance by grade (out of eight (8)) A 6.89 86% B 5.93 74% C 4.37 55% D 3.70 46% R 2.94 37% Everyone involved must contribute to establishing a positive learning environment. Arrive on time, and do not leave early. Keep cell phones and other electronic devices silent, and use laptops only for note-taking. We reserve the right to inspect the activity on a laptop and insist that it be turned off if it is not used for course related activity.
21-120 Syllabus 3 5. Evaluation. Assessment is designed to measure understanding according to the following qualitative grade definitions: A B C D R A superior level of understanding has been achieved. The student goes well beyond an understanding of the computational aspects of calculus by regularly solving problems that require the use of calculus in novel circumstances or an understanding of the more theoretical aspects of calculus. A high level of understanding has been achieved. The student can apply the computational aspects of calculus to solve problems, and solve routine problems that require understanding the more theoretical aspects of calculus. The student has achieved an average level of understanding, can consistently carry out the basic calculations of calculus, and should be able to complete subsequent calculus courses. A minimum level of understanding. The student is warned that continuing in calculus without strengthening his or her background might not be wise. CIT majors will not permitted to take 21-122 without at least a C in 21-120. Unsatisfactory. The course must be repeated. Your course average will be calculated according to the weights to the right. The highest Grading weights Each of the two high test scores: 20% possible grade cutoffs will be 90% for an A, The low test score: 15% 80% for B, 70% for C, and 60% for a D. These Homework and quizzes: 20% cutoffs may be lowered slightly, but will not be The Final: 25% increased. There is a sample Excel spreadsheet on the course website which you should download to maintain your own scores. It allows What if? games not otherwise possible! Pick up and retain all of your graded work. This is a large class, and occasionally a score goes astray. You should have your work available both to study from and to facilitate any needed correction in your record. 6. Take care of yourself. Do your best to maintain a healthy lifestyle by eating well, exercising, avoiding drugs and alcohol, getting enough sleep and taking some time to relax. This will help you achieve your goals and cope with stress. All of us benefit from support during times of struggle. You are not alone. There are many helpful resources available on campus and an important part of the college experience is learning how to ask for help. Asking for support sooner rather than later is often helpful. If you or anyone you know experiences any academic stress, difficult life events, or feelings like anxiety or depression, we strongly encourage you to seek support. Counseling and Psychological Services (CaPS) is here to help: call 412-268-2922 and visit their website at http://www.cmu.edu/counseling/. Consider reaching out to a friend, faculty or family member you trust for help getting connected to the support that can help. 7. Schedule. Dates and times for all tests, the retest on Test 1, make-up tests, quizzes, and assignments are indicated below. Specific topics for classes may vary slightly and revisions will be provided as necessary. Do not plan your end of the semester trip home until you have seen your final exam schedule! Mon, Aug 27 Introduction to the course. Tue, Aug 28 1.2 Composition of functions, the quadratic formula, and additional algebra basics. Understanding composition is essential. Participate in recitations!
21-120 Syllabus 4 Wed, Aug 29 1.1 Limits. Thu, Aug 30 Assignment 1 Fri, Aug 31 1.2 Precise definition of limit and 1.3 an important trigonometric limit. Mon, Sep 3 Labor Day - No class. Enjoy the break! Tue, Sep 4 Quiz 1 Wed, Sep 5 1.5 Continuity and the Intermediate Value Theorem. Thu, Sep 6 Assignment 2 Fri, Sep 7 1.6 Limits involving infinity. Making asymptotes precise. Mon, Sep 10 2.1-2 Derivatives. Tue, Sep 11 Quiz 2 Wed, Sep 12 2.3-4 Basic differentiation formulas. Thu, Sep 13 Assignment 3 Fri, Sep 14 2.4-5 Differentiation formulas for the trigonometric functions and the Chain Rule. We do Chain Rule first because that is the way to go! Mon, Sep 17 2.6 Implicit Differentiation. Tue, Sep 18 Quiz 3 Wed, Sep 19 4.2 Related rates. Thu, Sep 20 Assignment 4 Fri, Sep 21 4.4 Linear approximation and differentials. Definition 4.4.1 is the key fact. Mon, Sep 24 Exponential functions and inverse functions. Tue, Sep 25 Quiz 4 Wed, Sep 26 Logarithms and their derivatives. Differentiation of inverse functions is discussed in 2.7. Fri, Sep 28 Review. Mon, Oct 1 Test 1. The test will be in McConomy Auditorium. Tue, Oct 2 No recitation. Wed, Oct 3 Exponential growth and decay. Online notes. Thu, Oct 4 Test 1 Make-up, 7:30 AM, Location TBA. Thu, Oct 4 Assignment 5 Fri, Oct 5 2.7 Inverse trigonometric functions. Mon, Oct 8 6.7 Indeterminate forms by l Hospital s Rule. Tue, Oct 9 Quiz 5 Wed, Oct 10 6.7 More indeterminate forms, especially the three exponential versions at the end of the section.
21-120 Syllabus 5 Thu, Oct 11 Test 1 ReTest, 7:30 AM Location TBA. Thu, Oct 11 Assignment 6 Fri, Oct 12 3.1-2 Maximum and minimum values and the Mean Value Theorem. Be able to state the Extreme Value Thm and the Mean Value Thm. Mon, Oct 15 4.2-3 Derivatives and the shapes of curves. The two derivative tests and the concavity tests are essential! Tue, Oct 16 Quiz 6 Wed, Oct 17 3.5 Curve sketching. Introduction to optimization. Thu, Oct 18 Assignment 7 Fri, Oct 19 Midsemester Break - No class, but 4.3 is really important! Mon, Oct 22 4.3 Optimization problems. Tue, Oct 23 Quiz 7 Wed, Oct 24 Mostly review. Fri, Oct 26 No class President s installation. Mon, Oct 29 Test 2 The test will be in McConomy Auditorium. Tue, Oct 30 No recitation. Wed, Oct 31 5.1 Antiderivatives. We begin to reverse the differentiation process. Thu, Nov 1 Test 2 Make-up, 7:30 AM, Location TBA. Thu, Nov 1 Assignment 8 Fri, Nov 2 5.1 More on antiderivatives. Mon, Nov 5 5.2-3 Evaluating definite integrals. Tue, Nov 6 Recitation but no quiz - Vote! Wed, Nov 7 5.4 The Fundamental Theorem of Calculus. Must know both parts of the Fundamental Theorem. Thu, Nov 8 Assignment 9 Fri, Nov 9 6.1. Integration by substitution. This method is a reversal of the Chain Rule, and will be used through out the rest of the year not just this semester! Mon, Nov 12 6.1. Integration by substitution. Do lots of Exercises at the end of Section 6.1! Tue, Nov 12 Quiz 8 Wed, Nov 14 6.1 Integration by parts. A powerful method from reversing the Product Rule. Thu, Nov 15 Assignment 10 Fri, Nov 16 Integration with inverse trigonometric functions. Online notes Mon, Nov 19 6.6 Hyperbolic functions. The only time some will see this topic. Don t miss it! Tue, Nov 20 Recitation, but no quiz.
21-120 Syllabus 6 Wed, Nov 21 No class! Travel safe! Thu, 22 Thanksgiving! Mon, Nov 26 More integration. Tue, Nov 27 Quiz 9 Wed, Nov 28 Review Fri, Nov 30 Test 3 The test will be in McConomy Auditorium. Mon, Dec 3 7.1 Areas between curves. We will have the absolute value involved in our version! Tue, Dec 4 Test 3 Make-up, 7:30 AM, Location TBA. Tue, Dec 4 Assignment 11 Wed, Dec 5 7.2-3 Volumes. You need to know both the shell and the disk method. Fri, Dec 7 Volumes, etc. Just how big is a donut anyway? Mon, Dec 10-Mon 17 Final exam TBA