MATH 1634 Calculus I

Class Log and Announcements
 Apr. 18:
Lecture: Continue reviewing the final exam.
Announcement: We will review Geometry in Substitution this Friday
 Apr. 16:
Lecture: Start reviewing the final exam.
Announcement: We will have a "sort" of a quiz on Geometry in Substitution this Friday. But it's not going be graded as we don't have a meeting time before the final exam and you will not have a chance to get back your graded quiz. As soon as you finish the question, we will go through the solution together.
 Apr. 9:
Lecture: Section 5.5, Part II. Geometry in Substitutions. See the handout.
Homework: Section 5.5 Exercise #74. Do the problems in the handout
Announcement: Review for the hour exam 4. Please pick up a copy of the hour exam 4 from last year from my office, which is different from this review sheet.
 Apr. 6:
Lecture: Sections 5.2 Part III, Section 5.4 Part III. Geometric meaning of Definite integrals; Area.
Homework: Section 5.4 Exercises #43(optional),44(optional), 47,48.
 Apr. 4:
Lecture:
 Section 5.2, Part II. The Properties of Definite Integrals.
 Sections 5.2 Part III, Section 5.4 Part III. Geometric meaning of Definite integrals; Area, halfway.
Homework:
 Section 5.2 Exercises #47,49 (These are just for fun.)
 Section 5.2 Examples 4, Exercises odd #3539. (#37 might be challenging depending on whether you can draw the necessary graph of the curve.)
Quiz 9 this Friday will be based on the materials on
 Fundamental Theorem of Calculus 1 (Section 5.3, Part II.)
 Riemann Sums and Definite Integrals (Section 5.1. & Section 5.2, Part I.)
 Geometric meaning of Definite integrals (During class, two types of problems that you will see in Geometry in Definite Integrals were specified. Quiz 9 requires only the first type that corresponds to Section 5.2 Part III)
 Apr. 2:
Lecture: Section 5.1. & Section 5.2, Part I. Riemann Sums and Definite Integrals.
Homework:
 Section 5.1 Examples 3(b), Exercises #5
 Section 5.2 Examples 5 (Optional; this is basically the same question as Section 5.1 Example 3 (b) with a different function.)
 Section 5.2 Exercises #1720, #2930.
 Mar. 30
Lecture:
 Section 5.3, Part II. Fundamental Theorem of Calculus 1.
 Section 5.1. & Section 5.2, Part I. Riemann Sums and Definite Integrals, started.
Homework:
 Section 5.3 odd #718 (In class, I directly wrote in d/dx integral f(t) dt. For example, #7 asks to find d/dx integral_1^x 1/(t^3+1) dt. #9 asks to find d/dy integral_2^y t^2 sin t dt.)
Announcement: Quiz 8 next Monday will be held in the beginning of the class.
 Mar. 28
Lecture: Section 5.5, Part I. The Substitution Rule, finished.
Homework: Section 5.5. Exercises #146 and #5170 EXCEPT for 28,41,43.(#42,44,46 are ``hard`` substitution problems, which are optional. "Hard" in the sense NOT that the substitutions are hard BUT that more algebra is involved.)
Quiz 8 next Monday will be based on the materials covered from Sections 5.4, Part I (Indefinite Integrals), 5.3 Part I & 5.4 Part II (Definite Integrals; Fundamental Thm of Calc 2) and 5.5, Part I (The Substitution Rule).Presentation counts!!!
 Mar. 26
Lecture:
 Section 5.4, Part I. Indefinite Integrals, finished.
 Section 5.3, Part I & Section 5.4, Part II. Evaluating Definite Integrals (Fundamental Theorem of Calculus 2)
 Section 5.5, Part I. The Substitution Rule, started. (You need to know how to find Differentials in Section 3.10. as a base for substitution rules.)
Homework:
 Section 5.4 Exercises #511, 1418, 2139
 Section 5.3 Exercises #1940 except 34,36,37,38.
 Section 3.10 Exercises odd #1114 (find dy)
 Mar. 14
Review for the hour exam 3
 Mar. 12
Lecture: Section 5.4, Part I. Indefinite Integrals, started. (Section 4.9 Antiderivatives is essentially the same.)
Homework: We practiced several examples in indefinite integrals (equivalently, antiderivatives) in class. The textbook does not have such simple exercises. Go through what we did in class today.
Announcement:Review for the hour exam 3.
 Mar. 7
Lecture: Section 4.7. Optimization problems.
Homework: Section 4.7 Exercises #9,11,16,24,26(Optional: #13,17,19,35 ) Do the problems in the way we did in class, that is,
 (a) Picture and Variables
 (b) Set up Max/Min (object = in terms of two variables), Restriction (equation in your current two variables)
 (c) Set up Max/Min (object = in terms of a single variable), Restriction (interval on your current single variable)
 (d) Find the optimum value in (c) (Notice that the problem has been converted into the absolute max/min of a function over a given interval)
 (e) Interpret what you have found.
Quiz 7 next Monday will be based on Sections 4.4, 4.5 & 4.7.
Regarding 4.5, I will ask only finding horizontal asymptotes and draw them on the xyplane (i.e, the item (d) among (a)(d) in sketching curves)
 Mar. 5
Lecture:
 Section 4.5 Sketching curves with horizontal asymptotes. For the problems on sketching curves, you will be asked (a)(b)(c) as seen on the last quiz, AND one more item (d): Find horizontal asymptotes if exit. Write the equations of the asymptotes and draw in (c).
 Section 4.1, Part II Absolute maximum/minimum.
Homework: Let me write all the homeworks for Sections 4.34.6 here. Some of them have been assigned and some are new.
 Section 4.5. For the functions in Exercises #13,14,17,23(; Problems upto this point are easier than the example that I did in class today, and they are in the level that you will be tested on the exams),#49,51(; these are similar to what I worked on during class today, and will not be on the exams).
do the followings.
 (a) Find local maxima/minima.
 (b) Find the inflection points.
 (c) Sketch the curve of f.
 (d) Find a horizontal asymptote if exits. Write the equation of the asymptotes and draw in (c).
 Section 4.1 (Absolute max/min) Exercises odd #4754; Note that all the intervals in these exercises are closed bounded intervals. The other type of interval in absolute max/min. problems that you will see often in Section 4.7 (optimizations) is open with only critical points. Unfortunately, There is no exercise questions that I can assign in the textbook. Please see the examples done in class.
Announcement: All math classes will be canceled this Friday, including ours, due to Math Day. Quiz 7 will be held next Monday, in the beginning of the class.
 Mar. 2
Lecture: Section 4.4 L` Hospital `s rule
Homework: Section 4.4 Exercises odd #521, 29(; easy upto this point),#39,43(;need an ``trivial manipulation'' to apply L'Hospital's rule),#49,51(;You can use L'Hospital's rule to them. But I don't see a benefit to apply L'Hospital's rule hence I will NOT ask on the exam on the subject of L'Hospital's rule)
 Feb. 29
Lecture:
 Section 4.3. Part III. Sketching curves; Big Table with f ` and f `` We did them in the following way, and this is how you will be asked in quizzes.
 (a) Find local maxima/minima.
 (b) Find the inflection points.
 (c) Sketch the curve of f.
 Section 4.3. Part IV. Second derivative test: Comparison of First derivative test vs. Second derivative test (Note that both are to find local maxima/minima).
Homework:
 Section 4.3. For the functions in Exercises #912(``easy''), #15,#17(``intermediate'') #13,#14(``hard''), do the followings.
 (a) Find local maxima/minima.
 (b) Find the inflection points.
 (c) Sketch the curve of f. (You must give the Big table with f` and f`` in the way we did in class, and then sketch the curve. Again, if you want to solve in different ways, your work must be clear )
 Section 4.3 Exercises #1921: Find the local maxima or minima by any method that you like (i.e, the first derivative test or the second derivative test.)
 Note that, on the exams, I will not specify which table or method to use. You should figure out appropriate methods and show your work.
Quiz 6 this Friday will be based on Sections 4.1 & 4.3 that we have covered (mostly on 4.3). It will be ok not to know the second deriv. test for the quiz though.
 Feb. 27
Lecture:
 Section 4.3. Part I. Finding local maxima/minima; Small table of f '.
 Section 4.3. Part II. Finding inflection points; Small table of f '' .
Homework:
 Section 4.3. Find the local max./min. in
 Exercises odd #912; These are ``easy'' ones and I usually ask this level in exams.
 Exercises #15,#17; These are in an ``intermediate'' level. Sometimes this level can be asked in exams.
 Exercises #13,#14; These are ``hard''. Try if you want to. Dealing with trig. functions is harder when you determine the signs of f '.
(Find the local max./min. in the way we did in class, i.e., give a small table of f '. If you want to solve in different ways, your work must be clear how you find the local extreme points; don't scribble your answer.)
 Section 4.3. Find the inflection points in Exercises odd #912(``easy''), #15,#17(``intermediate'') #13,#14(``hard'')
(Find the inflection points in the way we did in class, i.e., give a small table of f ''. If you want to solve in different ways, your work must be clear how you find the inflection points.)
 Feb. 22
Lecture: Review for the 2nd hour exam.
Announcement My office hours are canceled this Friday.
 Feb. 20
Lecture:
 Section 4.1. Definitions of local max./min. and absolute max./min., Critical points.
 Section 4.3. Part I. Finding local maxima/minima; Small table of f ', started.
Homework: Section 4.1. Exercises odd# 2944 (3744 are for those who want to deepen their knowledge).
Announcement Review for the hour exam 2.
 Feb. 17
Lecture: Section 3.10 Linear Approximations and Differentials.
Homework: Section 3.10 Example 3, Exercises odd #1518
 Feb. 15
Lecture:
 Section 3.9 Related rates.
Do problems in Related Rates in the following order. You MUST give accurate answers to all these items as we did class:
 (a) Picture and Parameters(or Variables)
 (b) Known rate(s)
 (c) Unknown rate to find out
 (d) An equation that relates the parameters in (a)
 (e) Differentiate the equation of (d) implicitly w.r.t. an appropriate parameter
 (f) Find the unknown rate. Give units too.
Homework:
 Section 3.9
 Examples 14 (You don't have to memorize the formula for the sphere in Example 1 nor the formula for the cone in Examples 3.)
 Exercises #16,#1114,#22. (#13 is optional; it's more difficult than the others.)
You must know ALL the required equations relating parameters (that are asked in the item (d)) in these exercises.
Quiz 5 this Friday will be based on Sections 3.5 and 3.9.
 Rg. Section 3.9, for this upcoming quiz, it will be enough to study the four examples done in class and exercises #14. (You must do all the exercises for the hour exam and the final exam.)
 You will not see any question from Section 3.7.
 Feb. 13
Lecture:
 Section 3.5 Implicit differentiation.
 Section 3.7 Rates of changes.
Homework:
 Section 3.5 Exercises #520, 2530(Do the odd numbers first, and then try even numbers if you have time)
 Section 3.7 Example (not Exercise) 1 (a)(b)(g)(h)
 Feb. 8
Lecture:
 Part of Section 3.6 Derivatives of logarithmic functions.
 Higher derivatives and the notation d/dx in Sections 3.13.3, 3.4, and 3.6; Get used to the notation d/dx
 Tangent lines in Sections 3.13.3,3.4, and 3.6
 Section 3.5 Implicit differentiation, started.
Homework:
 Section 3.1 exercises #33,51,55.
 Section 3.2 exercises #31.
 Section 3.3 exercises #26(a),33
 Section 3.4 exercises #52,54,60
 Section 3.6 exercises odd #216, #36 (You don't have to the "graphing" part.)
Announcement: We retake the first hour exam this Friday. If you don't need to take the exam again, you don't have to come for the class.
Quiz 4 next Monday will be based on Sections 3.13.4 and 3.6 Nothing on Section 3.5!!!
 Feb. 6
Lecture: Section 3.4 Chain rule
Homework:Section 3.4 Examples 14. Exercises odd #745
Announcement: We retake the first hour exam this Friday. Quiz 4 that is supposed to be taken this Friday will be held next Monday, for the first 15 minutes in the beginning of the class.
 Feb. 3
Hour Exam 1
 Feb. 1
Lecture:
 Sections 3.1 Derivatives of polynomials and exponential functions, Section 3.2 The product and quotient rules, Section 3.3 Derivatives of trigonometric functions ; Part 1, Basic differentiation rules.
 We went through last year's 1st hour exam.
Homework:
 Section 3.1 exercises #330.
 Section 3.2 exercises #326 (#52 is challenging. Try!).
 Section 3.3 exercises #116.
 Jan. 30
Lecture:
 Section 2.7 The meanings of the derivatives in Physic (and real life).
 Chapter 3, started. Warmup examples.
Homework:Section 2.7 Exercises #37 (Optional.)
Announcement: Review for the hour exam 1. Note that the differentiation rules in Chapter 3 are NOT on the exam this Friday.
 Jan. 27
Lecture: Section 2.8 Geometric meaning of the derivative (=slope). The limit definition of the derivatives.
Homework: Section 2.8 Exercises odd #1928 (you don`t have to state the domains.)
 Jan. 25
Lecture: Section 2.6 Computation of lim_{x > \finity} f(x). Two handouts have been distributed handout 1, handout 2.
Homework: Section 2.6 Exercises odd # 1525, #29 (The highest power terms in the numerator and the denominator are different. Which one would you go for? Both will work. Which one do you prefer?), #33 (What is the ``highest power term'' here though they are not exactly polynomials?)
Quiz 3 this Friday will be based on Part of Sections 2.3 and 3.3 (The cases #4#6 of the handout for 2.3) and Section 2.5 (Continuity). Nothing on Section 2.6!!!
Announcement: There is a tiny change of the office hours. The new offices hours are on the syllabus (links on top of this page). You may not even notice the difference.
 Jan. 23
Lecture:
 Section 2.3 The limit of a function: Algebraic approach, finished.
 Section 3.3 The limit of a function: lim_{\theta>0} sin \theta / \theta = 1.
 Section 2.5 Continuity.
Homework:
 Section 2.3 Examples 7,8,11. Exercises #3638, #39, #40, #42, #43, #44, #57(This is a challenging problem. Be aware that you cannot simply replace f(x) by x^2 nor 0 in lim_{x>0) f(x). Why?)
 Section 3.3 Exercises odd #3946.
 Section 2.5 Exercises #11,17,19,20(You do not have to sketch the graph for #20. You can try, though, if you want to.)
Announcement: #2 of Quiz 2 has been graded differently than I intended. If you've chosen three (a)(b)(c), then 6 points. If you have chosen, say, (a)(c)(d), then it's credited 4 points (rather than 2 points) because: 2 points since you are correct to choose (a)(c), and another 2 points since you are correct not to choose (e)(f); basically you lose 2 points on (b)(d). If you have a question on your score of #2, talk to me.
 Jan. 20
Lecture: Section 2.3 The limit of a function: Algebraic approach, the case #4.
Announcement: The syllabi have been updated. Check out the links above.
 Jan. 18
Lecture: Section 2.3 The limit of a function: Algebraic approach, started. A handout distributed. We covered the cases 1,2, and 3(a)(b) from the handout.
Homework: Section 2.3 Examples 36 and 9. Exercises odd #1129, #48((b) is optional but it will help you understand the problem).
Quiz 2 this Friday will be based on what we learned today: Part of Section 2.3
 Jan. 11
Lecture: Section 2.2 The limit of a function: Graphical approach.
Homework: Section 2.2 Examples 3,9,10 (Refer to the graphs given in the textbook). Exercises 7,12
Quiz 1 this Friday will be based on the Basic functions and their graphs and Section 2.2.
Announcement: My office hours and our TA's MTC hours have been set. They can be found on the Course Information that have links above.
 Jan. 9
Lecture: Basic functions and their graphs. Click here to see the list of functions.
Homework: No specific problems from the textbook today. Just review what we did in in class today.
Homework won't be collected or graded as written in the syllabus. However, you should do homeworks to master the material and to be prepared for weekly quizzes and the exams.