## MATH 1634 Calculus I

• #### Class Log and Announcements

• Feb, 10, Wed.
Lecture:
• Sections 3.1--3.3, started. Warm-up examples.
• Sections 3.1-- Section 3.3; Part 1, Basic differentiation rules. "Intuitive" diff. rules, and "Non-intuitive" diff. rules (The product and quotient rules), almost done.
Homework: Study the lecture note and understand the examples coved in class.

• Feb, 8, Mon.
Lecture:
• Section 2.4 The epsilon-delta definition of a limit, finished -- all the Examples in the handout "e-d-Game; Version 1". Briefly discussed in the handout "e-d-Game; Version 2".
-- I have shown you how to write the proof of a limit using e-d arguments logically as in any math book.
• 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).
-- The meanings of derivatives (geometric & physics) will appear again in Chapter 3 later.
• Trig values at various angles (more than 90 degrees) in the second handout Trigonometry, reviews, distributed in the beginning of the semester.
Homework: Practice how to write the proof of the limit using e-d arguments using the examples in "e-d-Game; Version 1"
Quiz 3 next Wednesday will be based on the epsilon-delta definition of a limit and trig values at various angles.

• Feb, 5, Fri.
Lecture: Section 2.4 The epsilon-delta definition of a limit. Examples 1 and 2 in the handout "e-d-Game; Version 1"
Homework: Finish the example 3 in the handout, and try the examples 4--6.

• Feb, 3, Wed. Exam 1

• Feb, 1, Mon.
Lecture:
• Section 2.8 The limit definition of the derivatives, finished.
• Review for the upcoming exam
Homework:
• Study the lecture note and understand the examples coved in class.
• Section 2.8 Exercises odd #21,25,27 (you don`t have to state the domains.)

• Jan. 29, Fri.
Lecture:
• Section 2.6 Computation of lim_{x -> \finity} f(x). Handout Limit when x-> infinity; Cases.
• Section 2.6 Examples 3,3'(variation of 3),4,5, Exercise #34*
• Section 2.8 The limit definition of the derivatives, started; review of some college algebra.
Homework:
• Study the lecture note and understand the examples coved in class first before start exercise problems.
• Section 2.6 Exercises #21,23,25,29,35*
Announcement: Review for the hour exam 1. A past first hour exam

• Jan. 27, Wed.
Lecture:
• Section 2.5 Continuity. Examples of what I have made up.
• Section 2.6 Computation of lim_{x -> \finity} f(x). Handout Limit when x -> infinity;Limit Laws .
• Section 2.6 Examples of my own similar to Examples 1,2,9,10
Homework:
• Study the lecture note and understand the examples coved in class first before start exercise problems.
• 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).

• Jan. 25, Mon.
Lecture:
• Section 2.3 The limit of a function & Section 3.3: Algebraic approach. Cases 5 (Squeeze theorem) and 6 (Using the result of lim_{\theta->0} sin \theta / \theta = 1).
• Section 2.3 Examples: Exercise #38 (easy level), Example 11 (intermediate level), Box 2 in p.192 Section 3.3 (hard level)
• Section 3.3 Examples: Basic/instructional examples made up by me. Example 5
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?)
• Section 3.3 Example 6. Exercises odd #39--46.
Quiz 2 this Wednesday will be based on Sections 2.3 & 3.3 The limit of a function: Algebraic approach, cases 1--6.

• Jan. 20, Wed.
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.
• Section 2.3 Examples 4,6,8
Homework:
• Study the lecture note and redo the examples done in class first before start the following examples and exercise problems.
• Section 2.3 Examples 5,6,7,9. Exercises #21,27,41,48,49

• Jan. 15, Fri.
Lecture:
• Section 2.3 The limit of a function: Algebraic approach, started. A handout distributed. We covered the case 1 from the handout.
• Section 2.3 Examples 2,3
Homework:
• Study the lecture note and redo the examples covered in class first before start the following examples and exercise problems.
• Section 2.3 Examples 5, Exercises #11,15,19
Quiz 1 Next Wednesday will be based on what we learned so far: Basic functions, Sine, Cosine, Tangent values at special angles between 0 and pi/2 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. 13, Wed.
Lecture:
• Trigonometry, reviews, and its solution (Covered only Sine, Cosine, Tangent values at special angles between 0 and pi/2; The rest will be done sometime later)..
• Section 2.2 The limit of a function: Graphical approach. Difference between f(a)=b vs. lim_x->a f(x)=b. Examples similar to Examples 8, 9 and exercise 7.
Homework:
• Study the lecture note and understand the examples coved in class first before start exercise problems.
• Section 2.2 Examples 3,7,9,10 (Refer to the graphs given in the textbook). Exercises 7,11 (Postpone #11 till after the class this Friday)

• Jan. 11, Mon
Lecture: Basic functions and their graphs and its solution .
Do the problems on the blank copies first before looking at the solutions.
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.