MATH 1634 Calculus I

Class Log and Announcements
 Nov. 21, Fri.
Lecture: Sections 5.2 Part III, Section 5.4 Part III. Geometric meaning of Definite integrals; Area.
Homework: Section 5.4 Exercises #49,50.
 Nov. 19, Wed.
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 #17,19,20 (In addition, evaluate the areas represented by the given Riemann sums), #2930. Exercises #47,49 (These are just for fun.)
 Section 5.2 Examples 4(a), Exercises odd #3539. (#37 might be challenging depending on whether you can draw the necessary graph of the curve.)
 Section 5.2: Evaluate the definite integrals of #44, #46 by interpreting in terms of areas.
Announcement: Review for the hour exam 4.
 Nov. 17, Mon.
Lecture:
 Section 5.3, Part II. Fundamental Theorem of Calculus 1.
 Section 5.1. & Section 5.2, Part I. Riemann Sums and Definite Integrals.
Homework:
 Section 5.3 #7,8,10,13,15,16 (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.)
Quiz 9 this coming Wednesday will be based on 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!!! What we learned today will NOT be on Quiz 9.
 Nov. 14, Fri.
Lecture: Section 5.5, Part I. The Substitution Rule, finished.
Homework:
 Section 3.10 Exercises odd #1114 (find dy)
 Section 5.5. Exercises #148 and #5373 EXCEPT for 30,37,43.(#44,46,48 are ``hard`` substitution problems; "Hard" in the sense NOT that the substitutions are hard BUT that more algebra is involved.)
Quiz 9 this coming Wednesday will be based on everything in Integrals covered so far. That is, 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!!!
 Nov. 12, Wed. Exam 3
 Nov. 10, Mon. Review for the hour exam 3
 Nov. 7, Fri.
Lecture: Section 5.5, Part I. The Substitution Rule, continued.
 Nov. 5, Wed.
Lecture: 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.)
Announcement:Review for the hour exam 3.
 Nov. 3, Mon.
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)
Homework:
 Section 5.4 Exercises #518 (except 12, 13), #2142(except 34, 35, 40, 41)
 Section 5.3 Exercises #1942 except 38, 39, 42.
Quiz 8 this Wednesday will be based on 4.7 Optimization.
 Oct. 31, Fri.
Lecture:
 Section 4.7. Optimization problems, finished.
 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.
 Oct. 29, Wed.
Lecture: Section 4.7. Optimization problems, continued.
Homework:
 Always first review the examples done in class.
 Section 4.7 Exercises #7, 11, 13, 14, 15, 23(the equation of the circle with radius r is x^2+y^2=r^2), 25 (Optional: #19, 20, 21). 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.
 Oct. 27, Mon.
Lecture: Section 4.7. Optimization problems, halfway through.
Quiz 7 this Wednesday will be based on
 Section 4.4 L` Hospital `s rule
 Sections 4.3 and 4.5 Sketching curves with horizontal asymptotes.
 Section 4.3 Second derivative test (though I will not specify the methods between First derivative test (aka. Small table of f') and Second derivative test)
 Oct. 24, Fri.
Lecture:
 Section 4.4 L` Hospital `s rule
 Section 4.5 Sketching curves with horizontal asymptotes. For the problems on sketching curves, you will be asked as done in class (which is written in the homework below)
Homework:
 Section 4.4 Exercises odd #521
 Section 4.5. For the functions in Exercises #14, 15, 19("easy" and they are in the level that you will be tested on the exams), do the following (a)(d). Most of the other problems have vertical asymptotes, and they 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).
 Oct. 22, Wed.
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 #19 (''easy''), #20(''intermediate''),#21(''difficult''): 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.
 Oct. 20, Mon.
Lecture:
 Section 4.3. Part II. Finding inflection points; Small table of f ''.
 Section 4.3. Part III. Sketching curves; Big Table with f ` and f ``, halfway through.
Homework: 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.)
Quiz 6 this Wednesday will be based on 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 ''. Section 4.1. critical points is part of the process finding local maxima/minima and inflection points (Sketching curves with Big table will NOT be on the quiz.)
 Oct. 17, Fri.
Lecture: Section 4.3. Part I. Finding local maxima/minima; 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.)
 Oct. 13, Mon.
Lecture:
 Section 4.3. Part I. Finding local maxima/minima; Small table of f ', started.
 Go through the Trial Test
 Oct. 10, Fri.
Lecture:Section 4.1. Critical points, finished. Section 4.3. How to read/create reasonable tables.
Homework: Section 4.1. Exercises odd# 2944 (3744 are for those who want to deepen their knowledge).
Announcement: The exam 2 next week will on Chapter 3 (Chapter 4 will NOT be on the test as you can find on the review sheet.) Trial test has been distributed.
 Oct. 8, Wed.
Lecture:
 Differentials.
 Section 4.1. Definitions of local max./min. and absolute max./min., Critical points, started.
Homework: Section 3.10 Example 3, Exercises odd #1518
Announcement: Review for the hour exam 2.
 Oct. 6, Mon.
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 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 Wednesday will be based on Tangent lines, Mix of chain rules and product/quotient rules, and velocity and accelerations. NO problems from related rates.
Announcement: If you want an extra copy of the today's handout (the examples of related rates) to practice later, please ask for one.
 Oct. 3, Fri.
Lecture:
 Section 3.5 Implicit differentiation.
 Section 3.7 Rates of changes.
Homework:
 Section 3.5 Exercises #520, 2532(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)
 Oct. 1, Wed.
Lecture:
 Tangent lines in Sections 3.13.3,3.4, and 3.6
 Section 3.5 Implicit differentiation, started.
Homework:
 Section 3.1 exercises #33,35(do only the tangent line),37 (You don't have to the "graphing" part.),51.
 Section 3.2 exercises #31,33.
 Section 3.3 exercises #26(a),33
 Section 3.4 exercises #52,54,60
 Section 3.6 exercises #33,34
 Sep. 29, Mon.
Lecture:
 Section 3.4 Chain rule.
 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 I thought the section number for the higher derivatives was 3.8 but it is spread all over Sections 3.13.4 and 3.6).
 Tangent lines, started
Homework:
 Review the contents and examples from the lecture, then start exercise problems.
 Section 3.4 Examples 19. exercises odd #745
 Section 3.6 Examples 15. exercises odd #216
Quiz 4 this Wednesday will be based on Product, Quotient and Chain rules from Sections 3.13.4 and 3.6. No questions from tangent lines.
 Sep. 24, Wed.
Lecture:
 Sections 3.1 Section 3.3; Part 1, Basic differentiation rules. The product and quotient rules
 Section 3.4 Chain rule, started.
Homework:
 It is always assumed that you review the contents and examples from the lecture first, before starting exercise problems.
 Section 3.1 exercises #330.
 Section 3.2 exercises #326.
 Section 3.3 exercises #116.
 Sep. 22, Mon.
Lecture:Sections 3.13.3, started. Warmup examples. "Intuitive" diff. rule. "Nonintuitive" diff. rule; Product rule, started.
Quiz 3 this Wednesday will be based on what we did today EXCEPT the product rule.
Announcement: Makeup exam this Friday.
 Sep. 15, Mon.
Lecture:
 Section 2.7 The meanings of the derivatives in Physic (and real life).
 Review for the hour exam 1
Homework: Study the example that we did in class. Section 2.7 Exercise #13
 Sep. 12, Fri.
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.)
Announcement: Review for the hour exam 1.
 Sep. 10, Wed.
Lecture:Section 2.6 Computation of lim_{x > \finity} f(x). A handout have been distributed Limit when x> infinity; Cases.
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?), #35 (What is the ``highest power term'' here though they are not polynomials?)
 Sep. 8, Mon.
Lecture:
 Section 3.3 The limit of a function: Algebraic approach, case 6, Using the result of lim_{\theta>0} sin \theta / \theta = 1, finished.
 Section 2.5 Continuity.
 Section 2.6 Computation of lim_{x > \finity} f(x). A handout have been distributed Limit when x > infinity;Limit Laws .
Homework:
 Section 2.5 Exercises #13,17,18,19,21(Determine the continuity of each function at a given point in the way we did in class; Check the items (1)(2) and (3).
Quiz 2 this Wednesday will be based on Sections 2.3 & 3.3 The limit of a function: Algebraic approach, cases 36. (Section 2.5 Continuity and Section 2.6 that we did today will NOT be on Quiz 2.)
 Sep. 5, Fri.
Lecture:
 Section 2.3 The limit of a function: Algebraic approach, case 5, Squeeze theorem.
 Section 3.3 The limit of a function: Algebraic approach, case 6, Using the result of lim_{\theta>0} sin \theta / \theta = 1.
Homework:
 Section 2.3 Example 11. Exercises #37,39, #59(Be aware that you cannot simply replace f(x) by x^2 nor 0 in lim_{x>0) f(x). Why?)
 Section 3.3 Examples 5,6. Exercises #3946.
 Sep. 3, Wed.
Lecture: Section 2.3 The limit of a function: Algebraic approach, continued. We covered the cases 3(a)(b) and 4 from the handout. The Squeeze theorem was stated, but we will see examples next time.
Homework: Section 2.3 Examples 7,8,9. Exercises #41,43,48,49,50.
 Aug. 29, Fri.
Lecture: Section 2.3 The limit of a function: Algebraic approach, started. A handout distributed. We covered the cases 1 and 2 from the handout.
Homework: Section 2.3 Examples 3,5,6. Exercises #3,5,7,10,11,13,15,17,19,21,25,27,31.
Quiz 1 Next Wednesday will be based on what we learned so far: basic functions, Section 2.2 The limit of a function: Graphical approach, Section 2.3 The limit of a function: Algebraic approach, cases 1 and 2 in the hand out.
 Aug. 27, Wed.
Lecture:
 Section 2.2 The limit of a function: Graphical approach
 Section 2.3 The limit of a function: Algebraic approach, started.
Homework: Section 2.2 Examples 3,7,9,10 (Refer to the graphs given in the textbook). Exercises 7,11
 Aug. 26
Announcement: In case you wonder: There is no quiz tomorrow Wed 8/27
 Aug. 25, Mon
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.