MATH 1634 Calculus I
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Class Log and Announcements
- We still have materials to cover for the semester and will finish them on Monday 11/30. Then will have review sessions for the final exam on Wed. 12/2 and Fri. 12/4.
- On Monday Nov. 23, I will have office hours during 11-12 in the morning, and will not be available in the afternoon.
- Katie will have special Math Tutoring Center hours for the 3rd hour exam, 12:50--1:50 Monday, Nov. 23.
- This Friday Nov. 20, I teach 2--4pm. Hence I will not be in my office during those hours.
- Nov. 18: Review for the hour exam 3.
- Nov. 18: Sec 5.2 The Properties of Definite Integrals. Sec 5.3. Fundamental Theorem of Calculus. Sections 5.3--5.4 Area.
Homework: section 5.2 #47,49; section 5.3 odd #7--18; section 5.3 #51,52; section 5.4 #47,48(The pictures will not be given in exams.)
- Nov. 16: Sec 5.1, Sec. 5.2. Area, Riemann Sum, and Definite Integrals .
homework: sec 5.2 #17-20, #35--40 (You can evaluate the integrals of #35 and #38 using Fundamental Theorem of Calculus 2. Do not use F.T.C. 2 but evaluate them by drawing appropriate pictures.)
- Quiz 10 this coming Friday will be on Definite integrals from Sections 5.2--5.5 (refer to the homework below. If you do not have time, concentrate on sections 5.4 and 5.5.) and Indefinite integrals in Section 5.5.
- Nov. 11: Sections 5.4--5.5 The Definite Integrals and Fundamental Theorem of Calculus 2.
Homework:
- Definite Integrals and FTC 2: section 5.4 #21--39, section 5.5 #51--70 except 60,63,64,68,70. (#57 can be challenging.) If you want to practice more problems, then do section 5.2 #21--25, section 5.3 #19--33 except #34,38,
- If you have trouble to find du in substitutions, then do problems in Differentials: section 3.10 odd #11-14 (find dy)
- Nov. 9: Sec 5.5 The Substitution Rule, (only the Indefinite integral part).
Homework: section 5.5 #1--46 except for 28,41,43. ( Note that #42,44,46 are ``hard`` substitution problems.)
- Quiz 9 this coming Friday will be on Sections 4.9 and 5.4.
- Nov. 4: Sec 5.4 Indefinite Integrals.
Homework: section 5.4 #5--11, 14--18
- Nov. 2: Sec. 4.7. Optimization problems, finished. Sec. 4.9, Sec 5.4 Antiderivatives, Indefinite Integrals, started. We practiced several examples in indefinite integrals (equivalently, antiderivatives) in class. The textbook does not have such simple exercises. However, those examples done in class will be foundations of integrals in advanced levels.
Homework: section 4.7 #17,19
- Oct. 30: Recitation class and Quiz 8
- Quiz 8 this coming Friday will be on Section 4.7 Optimization problems.
- Oct. 28: Sec. 4.7. Optimization problems.
Homework: section 4.7 #21,24,26
- Oct. 26: Sec. 4.7. Optimization problems.
Homework:
- section 4.1 odd #47--58
- section 4.7 #11--14. Do the problems in the way we did in class. That is, (a) Picture and Variables (b) Set up the problems in two ways. (c) Solve the problem (You must show why your critical points yields the optimum value.) (d) Answer: Interpret your numbers in an appropriate way.
- Oct. 23: Hour exam 2
- Review for the hour exam 2.
- Oct. 19: Sec 4.4 L` Hospital `s rule. Sec 4.1 Absolute maximum/minimum.
Homework:
- section 4.4 odd #5--21
- If you want more exercises to sketch curves: section 4.5 #1,5,5,7,13,17
- section 4.1 odd #47--56 (This is for absolute maxima/minima). We have discussed a special case that, if a give function f has a unique critical point x=c on the given interval, then the second derivative test at x=c gives us the absolute maximum or the absolute minimum value. This situation often occurs in Section 7 Optimization Problems. Unfortunately, there is no exercises in the textbook that matches this situation. I will keep mentioning again and again when we learn Optimization.
- Oct. 14:
- Sec 4.3. Part III. Sketching curves where the graphs have asymptotes.
To sketch curves with asymptotes, do in the following order as we did class:
- (a) Find the equations of the vertical/horizontal asymptotes, if exist.
- (b) Find the possible local maxima/minima points.
- (c) Find the possible inflection points.
- (d) Big table.
- (e) Sketch the curve, according to your table in (c).
- (f) Determine the local maxima/minima. Give the answer in ordered pairs.
- (g) Determine the inflection points. Give the answer in ordered pairs.
- Sec 4.3. Part IV. Second derivative test.
Homework:
- Sketch the curves of exercises #12,20 in section 4.3. Do the problem according to (a)--(g) above.
- Find the local maxima or minima of exercises #19--21 in section 4.3 by any method that you like (i.e, the first derivative test or the second derivative test.)
- Oct. 12:
- Sec 4.3. Part II. Finding inflection points (Nickname-- Small Table of f``)
- Sec 4.3. Part III. Sketching curves. (Nickname-- Big Table)
To sketch curves, do in the following order as we did class:
- (a) Find the possible local maxima/minima points.
- (b) Find the possible inflection points.
- (c) Big table.
- (d) Sketch the curve, according to your table in (c).
- (e) Determine the local maxima/minima. Give the answer in ordered pairs.
- (f) Determine the inflection points. Give the answer in ordered pairs.
Homework: Sec 4.3 Sketch the curves of the functions #9--11, #19 (Ignore the question in the textbook). Do the problem according to (a)--(f).
- Oct. 9: Recitation class and Quiz 7
- Quiz 7 this coming Friday will be on Section 3.9 Related Rates and Section 4.1 Critical Points.
First derivative test that we learn on Wed. 10/7 will NOT be on the quiz this Friday.
- Oct. 7: Sec 4.3. Part I. Finding local maxima/minima through First Derivative Test (Nickname-- Small Table of f`).
Homework: There is no exercise problem that asks only first derivative test in the textbook. So, with the critical points of the functions of exercises #29--37 in Section 4.1 (since you have already found them), determine the local maxima or minima using the first derivative test. You must show the Small Table of f` as we did in class.
- Oct. 5: Sec 3.9 Related rates, finished. Sec. 4.1. Maximum and Minimum values.
When you solve problems in Related Rates, do them in the following order 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.
Homework:
- Sec 3.9 exercises #3--13, 22: Most of ``nontrivial`` formulae that you need, such as the surface area of a sphere, can be found on the first page of the textbook.
- Sec 4.1 exercises #29--37: Give your answers in ordered pairs, as described in class.
- In case you want to study Section 3.9 Related rates during the weekend, please do the followings problems that will be part of homework from Section 3.9 and that will be assigned this coming Monday when we finish the section.
- #3--6: these problems are similar to what did in class on Wed. 9/30.
- #7--9: There is no really ``words`` that you have to interpret to solve the problems.
- Oct. 2: Recitation class and Quiz 6
- Quiz 6 this coming Friday will be on Sections 3.4--3.6. (Note that 3.9 Related rates will NOT be on the quiz this Friday.)
- Sep. 30: Sec 3.5 Implicit differentiation, finished. Sec 3.6 Derivatives of logarithmic functions. Sec 3.9 Related rates, started.
Homework:
- section 3.5 exercises #5--20, 25--30(Do the odd numbers first, and then try even numbers if you have time.)
- section 3.6 exercises #2--16, 41--48(Do the odd numbers first, and then try even numbers if you have time.)
- Sep. 28: Sec 3.4 Chain rule, finished. Sec 3.5 Implicit differentiation, half way through.
Homework: section 3.4 exercises #7--46, 51--54 (Do the odd numbers first, and then try even numbers if you have time.)
- Sep. 25: Recitation class and Quiz 5
- Quiz 5 this coming Friday will be on Sections 3.1--3.3. (Note that 3.4 Chain rule will NOT be on the quiz this Friday.)
- Sep. 23: Sec 3.4 Chain rule.
Homework: section 3.4 exercises #7,9,10,12,33.
- Sep. 21: The equations of tangent lines in Sections 3.1--3.3.
Homework: For the homework in Sections 3.1--3.3, do the odd numbers first, and then try even numbers if you have time.
- section 3.1 exercises #3--30,33,34,51,52.
- section 3.2 exercises #3--26,31,32,52 (#52 is challenging. Try!).
- section 3.3 exercises #1--16, 21--24.
- Sep. 18: Hour exam 1
- Sep. 16: Section 3.2 The product and quotient rules, Section 3.3 Derivatives of trigonometric functions .
Homework: Will be assigned from sections 3.2--3.3 after the 1st hour exam.
- Sep. 14: Brief discussion of meanings of derivatives in physics from Section 2.7.
Sections 3.1 Differentiation formulae .
Homework: section 3.1 exercises #3--30.
- Review for the hour exam 1. Please bring your questions on Wednesday after looking through the review sheet. If you don`t have any question, we will start a new material.
- Sep. 11: Recitation class and Quiz 4
- My office hours 2-3 this Friday 9/11 are canceled. But I will be in my office during the rest of the regular office hours.
- Quiz 4 this coming Friday will be on Section 2.8.
- Sep. 9: Sec. 2.8 Derivatives (using the definition of derivatives). Brief discussion of geometric meaning of derivatives from Section 2.7.
Homework: section 2.8 exercises odd #19--28.
- The Math Tutoring Hours 12-4, Wed., Sep. 9, by Katie Dawson have been canceled.
- Sep. 4: Recitation class and Quiz 3
- Quiz 3 this coming Friday will be on Sections 2.5 and 2.6.
I will be out of town this Friday, and hence office hours are canceled.
- Sep. 2: Sec. 2.6 Computation of lim_{x -> \finity} f(x), finished.
Homework: section 2.6 exercises #15,19,21,23,25,33.
- Aug. 31: Sec. 2.5 Continuity . Sec. 2.6 Computation of lim_{x -> \finity} f(x), started.
Homework: section 2.5 exercises #11,17,19.
- Aug. 28: Recitation class and Quiz 2
- Quiz 2 this coming Friday will be on Sections 2.3 and 3.3.
- Aug. 26: Sec. 2.3 The limit of a function: Algebraic approach. Some of Sec.3.3 lim_{\theta->0} sin \theta / \theta = 1.
Homework: section 2.3 exercises 35--38. section 3.3 odd #39--46
- Aug. 24: Sec.2.3 The limit of a function: Algebraic approach.
Homework: section 2.3 exercises odd #11--29 (25--29 are challenging while simplifying the functions.), odd #39--43, #46 ((d) is challenging), #48 ((b) is optional but it will help you understand what is going on).
- Aug. 21: Recitation class and Quiz 1
- There was a mistake on the section number in last homework. It has been corrected. I apologize.
- Notice about tutoring center. Math Tutoring Center is Boyd 205, as written on the syllabus. However, there will be workers in Boyd 205 on Thursday & Friday upgrading the
networking 7 wiring.
Therefore the tutoring center will be temporarily relocated for those two
days starting tomorrow.
We will be located in Cobb Hall room 130. The building is on front campus
drive.
You can walk out the main Boyd doors and continue across going between
calloway and college of business, then up the steps and fork left and
continue over the Cobb. You can enter the right side doors and it is on
that hallway, you do not need to go to the main entrance where the deck is.
- Quiz 1 this coming Friday will be on everything so far.
- Aug. 19: Sec. 2.2 The limit of a function: Graphical approach. Sec. 2.3 The limit of a function: Algebraic approach, started.
Homework: sec 2.2 exercises #4,5
- Aug. 17: Review 9 basic functions and practice limit of functions.
Homework: No specific problems from the textbook today. Just review what we did in in class today.
- Aug. 14: Review basic functions, started -- you are expected to remember the graphs of these 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.