## MATH 1634 Calculus I

• #### Class Log and Announcements

• Apr. 13, Mon: Hour Exam 4
Announcement: Review for the final exam We will review for the final exam this Wed and Fri. Bring all the hour exams with you.

• Apr. 10, Fri:
Lecture:
• How to integrate the absolute value of a function \int_a^b |f(x)| dx algebraically
• Section 5.5, Part II. Geometry in Substitutions. See the handout.
Homework:
• Section 5.4 Exercises #43(optional),44(optional)
• Section 5.5 Exercise #74. Do the problems in the handout
Announcement: Geometry in Substitution that we did today will not be on the hour exam 4 this Monday but will be on the final exam.

• Apr. 8, Wed:
Lecture: Sections 5.2 Part III, Section 5.4 Part III. Geometric meaning of Definite integrals; Area.
Homework:
• All the examples done in class, as usual.
• Section 5.4 Exercises #49,50.
Announcement:

• Apr. 6, Mon:
Lecture:
• Section 5.1. & Section 5.2, Part I. Riemann Sums and Definite Integrals. See the revised handout; #3 has been removed.
• 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, half-way.
Homework:
• Section 5.2 Exercises #17,19,20 (In addition, evaluate the areas represented by the given Riemann sums), #29--30. Exercises #47,49 (These are just for fun.)
• Section 5.2 Examples 4(a), Exercises odd #35--39. (#37 might be challenging depending on whether you can draw the necessary graph of the curve.)
Quiz 7 solution

• Apr. 3, Fri:
Lecture: Section 5.1. & Section 5.2, Part I. Riemann Sums and Definite Integrals
Homework: Not ready to assign homework for Riemann Sums
Quiz 7 next Monday will be based on The Substitution Rule and Fundamental Theorem of Calculus 1

• Apr. 1, Wed:
Lecture:
• Section 5.5, Part I. The Substitution Rule, finished.
• Section 5.3, Part II. Fundamental Theorem of Calculus 1.
Homework:
• Section 5.5. Exercises #53--73
• 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.)

• Mar. 30, Mon:
Lecture: Section 5.5, Part I. The Substitution Rule, half-way through.
Homework:
• Review Examples done in class
• Section 5.5. Examples 1--6
• Section 5.5. Exercises #1--48 EXCEPT for 30,37,43.(#44,46,48 are hard substitution problems, which we will do this Wednesday; "Hard" in the sense NOT that the substitutions are hard BUT that more algebra is involved.)

• Mar. 27, Fri: Hour exam 3 Make-up on Optimizations Solution

• Mar. 25, Wed:
Lecture:
• 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 5.3 Exercises #19--42 except 38, 39, 42.
Announcement: No class this Friday 3/26 due to Math Day
Quiz 6 next Monday will be based on Indefinite integrals and Definite integrals upto substitution rule, i.e, No substitution rule will be on the quiz.

• Mar. 23, Mon:
Lecture:Section 5.4, Part I. Indefinite Integrals.
Homework: Section 5.4 Exercises #5--18 (except 12, 13), #21--42(except 34, 35, 40, 41)
Announcement:

• Mar. 13, Fri: Special lecture on challenging problems.

• Mar. 11, Wed: Hour exam 3

• Mar. 9, Mon:
Lecture: Section 4.7. Optimization problems, finished.
Homework:
• Always first review the examples done in class.
• Section 4.7 Exercises #23(the equation of the circle with radius r is x^2+y^2=r^2), 25, 19, 20, 21. The problems will be asked 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.

• Mar. 6, Fri:
Lecture: Section 4.7. Optimization problems, half-way through.
Homework:
• Always first review the examples done in class.
• Section 4.7 Exercises #7, 11, 13, 14, 15, 25. The problems will be asked 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.
Announcement:

• Mar. 4, Wed:
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 #7--25
• 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).
Announcement: Hour Exam 3 will be held on 3/11 Wed. (instead of 3/9 Mon.)

• Mar. 2, Mon:
Lecture: 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 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.

• Feb. 27, Fri:
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 . We did them in the following way, and this is how you will be asked in exams.
• (a) Find local maxima/minima.
• (b) Find the inflection points.
• (c) Sketch the curve of f.
Homework: Section 4.3. For the functions in Exercises #9--12(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 way must be mathematically clear )
Quiz 5 next Monday will be based on everything covered in Chapter 4 so far, including Big Table and sketching curves.

• Feb. 16, Mon:
Lecture:
• How to read/create reasonable tables.
• 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 '', started.
Homework: Section 4.3. Find the local max./min. in
• Exercises odd #9--12; Easy'', the level that you will be asked on the exams.
• Exercises #15,#17; Intermediate'' level, sometimes asked on the exams.
• Exercises #13,#14; Hard'' level. Try if you want to. Dealing with trig. functions can be quite hard 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.)

• Feb. 20, Fri: The graded hour exam 2 has been distributed back. Here's the solution
Announcement: There will be NO quiz next Monday. However, do the homework assigned on Section 4.1, at least non-challenging ones. Otherwise, you will have difficult time to follow the lecture next week.

• Feb. 18, Wed:
Lecture: Section 4.1. Definitions of local max./min. and absolute max./min., Critical points.
Homework: Section 4.1. Examples 1--4, 7. Exercises odd# 29--44 (37--44 are more challenging).

• Feb. 16, Mon: Hour Exam 2.

• Feb. 13, Fri:
Lecture:
• Section 3.9 Related rates, finished.
• Section 3.10 Differentials.
Homework: Understand what we did in class. If you want, try Section 3.10 Example 3, Exercises odd #15--18

• Feb. 12, Thurs:
Hour Exam 2 last semester, blankcopy and its solution. A problem regarding a horizontal tangent was not asked last semester. This time, it may.
There were no challenging problems on chain rule with product/quotient rule or implicit differentiation on a quiz. Here are links to practice those problems and its solution.

• Feb. 11, Wed:
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 1--4 (You don't have to memorize the formula for the cone in Examples 3.)
• Exercises #1--6,#11--14,#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.
Announcement: Review for the hour exam 2.

• Feb. 9, Mon:
Lecture:
• Section 3.5 Implicit differentiation.
• Section 3.7 Rates of change.
Homework:
• Section 3.5 Examples 1--3. Exercises #5--20, 25--32(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. 6, Fri:
Lecture:
• Trigonometry
• Tangent lines in Sections 3.1--3.3,3.4, and 3.6, finished.
• Higher derivatives and the notation d/dx in Sections 3.1--3.3, 3.4, and 3.6; Get used to the notation d/dx.
Homework: Section 3.6 exercises #23--26
Quiz 4 next Monday will be based everything in differentiation covered so far.

• Feb. 4, Wed:
Lecture:
• Section 3.4 Chain rule, finished.
• Part of Section 3.6 Derivatives of logarithmic functions.
• Tangent lines in Sections 3.1--3.3,3.4, and 3.6 (Almost finished. I will wrap up the subject this Friday.)
• Trig values at special angles (A handout has been distributed. An undated version will be distributed this Friday.)
Homework:
• Review the contents and examples from the lecture, then start exercise problems.
• Section 3.4 Examples 1--9. exercises odd #7--45
• Section 3.6 Examples 1--5. exercises odd #2--16
** The following problems are for tangent lines.**
• Section 3.1 exercises #33,35(do only the tangent line),37 (You don't have to the "graphing" part.),51(Do this problem after we finish the whole tangent lines this Friday) .
• Section 3.2 exercises #31,33.
• Section 3.3 exercises #26(a),33(A problem on horizontal tangent lines of trigonometric functions. Try it if you want to challenge, and come by my office to discuss.)
• Section 3.4 exercises #52,54,60(A problem on horizontal tangent lines of trigonometric functions. Try it if you want to challenge, and come by my office to discuss.)
• Section 3.6 exercises #33,34

• Feb. 2, Mon:
Lecture:
• Sections 3.1-- Section 3.3; Part 1, Basic differentiation rules. "Intuitive" diff. rules, and "Non-intuitive" diff. rules (The product and quotient rules)
• Section 3.4 Chain rule, half-way.
Homework:
• It is always assumed that you review the contents and examples from the lecture first, before starting exercise problems.
• Section 3.1 exercises #3--30.
• Section 3.2 exercises #3--26.
• Section 3.3 exercises #1--16.

• Jan. 30, Fri
Lecture: Sections 3.1--3.3, started. Warm-up examples.
Homework: Nothing from Exercises but understand what we did in class
Quiz 3 next Monday will be based on only on warm-up examples (nothing from slopes or rates of change - these will be asked later)

• Jan. 28, Wed
Lecture:
• Section 2.7 Derivatives; Geometric meaning - slope of a tangent line.
• Section 2.7 Derivatives; Physics - rates of change (for example, position, velocity, and acceleration).
Homework: As I said in class, you will be asked only the final results on exams after we learn differentiation formulae in Chapter 3. It will be good for you if you can understand the whole process how to get those final results in order to improve your mathematical thought process, though. For those who want to practice all these concepts now (rather than postpone in Chapter 3), try Section 2.7 Exercises#9, 13, 33

• Jan. 26, Mon: Exam 1
• Jan. 23, Fri
Lecture: Section 2.8 The limit definition of the derivatives.
Homework: Section 2.8 Exercises odd #21--28 (you dont have to state the domains.)
Announcement: The solutions for the first hour exams from last semester Version 1 (Section 03) and Version 2 (Section 05).

• Jan. 21, Wed
Lecture: Section 2.6 Computation of lim_{x -> \finity} f(x). Two handouts have been distributed Limit when x -> infinity;Limit Laws and Limit when x-> infinity; Cases.
Homework: Section 2.6 Examples 3,6; Exercises odd # 15--25(Try #25 after this Friday's class), #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?)
Announcement: Review for the hour exam 1.

• Jan. 16, Fri
Lecture:
• Section 3.3 The limit of a function: Algebraic approach, case 6, Using the result of lim_{\theta->0} sin \theta / \theta = 1.
• Section 2.5 Continuity.
Homework:
• Section 3.3 Examples 5,6. Exercises #39--46.
• Section 2.5 Determine whether the function is continuous at a given point in Exercises #13,17,18,19,21 in the way we did in class; Check the items (1)(2) and (3).
Quiz 2 next Wednesday will be based on Sections 2.3 & 3.3 The limit of a function: Algebraic approach, cases 1--6, and Section 2.5 Continuity.

• Jan. 14, Wed
Lecture: Section 2.3 The limit of a function: Algebraic approach. More on case 4, and case 5 (Squeeze theorem).
Homework:
• Study the lecture note and understand the examples coved in class first before start exercise problems.
• Section 2.3 Example 11. Exercises #37,39,40, 59(#59 can be challenging. Be aware that you cannot simply replace f(x) by x^2 nor 0 in lim_{x->0) f(x). Why?)

• Jan. 12, Mon
Lecture: Section 2.3 The limit of a function: Algebraic approach, continued. We covered the cases 2, 3(a)(b) and 4 from the handout.
Homework:
• Study the lecture note and understand the examples coved in class first before start exercise problems.
• Section 2.3 Examples 6,7,8,9. Exercises #25,27, 41,43,48,49,50

• Jan. 9, Fri
Lecture: Section 2.3 The limit of a function: Algebraic approach, started. A handout distributed. We covered the case from the handout.
Homework:
• Study the lecture note and understand the examples coved in class first before start exercise problems.
• Section 2.3 Examples 3,5, Exercises #3,5,7,10,11,13,15,17,19,21,31>
Quiz 1 Next Monday 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, case 1 in the handout.

• Jan. 7, Wed
Lecture: Section 2.2 The limit of a function: Graphical approach
Homework:
• It is and will be assumed that you study the lecture note first before start exercise problems.
• Section 2.2 Examples 3,7,9,10 (Refer to the graphs given in the textbook). Exercises 7,11

• Jan. 5, 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.