Hi all,

I have noticed some interesting questions you guys had from quiz 1. Here is a brief sum up. The goal is to help you understand the big picture of what we have learned so far.

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# Math taught and learned

## Yajun An

# Month: September 2015

# Sum up of Quiz 1

# Practice test 1: Math 152

# Review of week three and preview of week four

# Review of week three and preview of week four

# Change of office hours

# Practice quiz and hints

# MATH152-03 20140 Fall2015: Review of week two and preview of week three

# Week 2 plan

# Week 2 plan

# Lecture notes for Integral calculus

Hi all,

I have noticed some interesting questions you guys had from quiz 1. Here is a brief sum up. The goal is to help you understand the big picture of what we have learned so far.

Here you go: prac_test_1

There is a typo in the instructions: for our class, NO CALCULATORS are allowed.

Same deal: Feel free to show me your work and check your work with me!

Hi all,

Last week we have finished talking about polynomials, and rational expressions. We will continue with radicals on Tuesday and introduce functions. On Thursday, we will review for the upcoming test the Tuesday after next.

In Polynomials, we talked about factoring and multiplying polynomials. If you want to check your answer to one of them, use the fact that they are inverse process of each other. Make sure you are familiar with the quadratic formula, it is the most reliable way of factoring degree two polynomials (and finding their zeros!)

Rational expressions (the fraction of two polynomials) are really very similar to rational numbers (the fraction of two integers). For example, to add/subtract two rational expressions, you need to find the common denominator then add/subtract the numerators; to divide a rational expression, you multiple by its reciprocal. The only thing different (and important, and easy to forget) is the domain of a rational expression. Make sure* all* your rational expressions have non-zero denominators!

We will talk about functions next Tuesday, from section 3.1 of the book, read ahead and ask me if you have any questions!

Assignment:

Reading: 0.5,0.6,3.1 and notes! Review for test 1.

0.6: 3,4,5,15,29,32,43,45,64,74

3.1: 1,3,12,19,28,29,36,37,47,64

Practice Test (to upload)

Hi all,

Last week we finished 5.3: the Fundamental theorem of calculus (FTC), 5.4: indefinite integrals and 5.5: Substitution method.

The FTC has two parts: part one about the *derivative* of a special type of functions; part two gives you *the third way *of computing a definite integrals. (the other two ways being the limit of Riemann sum and net area under curves). Check out problem 68 of section 5.3 for the most general formula for derivatives. This is a good time to review derivatives you learned in 151!

Indefinite integral of a function f(x) is another function. It is the most general antiderivative of f(x). Make sure you review the tables on page 341 and 392. Also review section 4.9! Now to compute a definite integral with the* third *method (FTC, 2), you first compute the indefinite integral, then evaluate and subtract.

For u-substitution, follow the general tips we summed in class, and whenever you try to make a u-substitution, take its derivative!! That is the best way to tell if you did the right substitution.

Next week, we will finish 5.5: the Substitution method, learn 7.1: integration by parts, then we will review for our first test. I have finished grading your quizzes and will hand them back to you on Tuesday/Wednesday. Remember to regrade if you like some extra points!

Alright, see you on Tuesday!

Assignment:

Reading: 5.5, 7.1 and review

5.5: Read problems 1-6 (no need to write up!); 7,18,27,35,43,46,52,73,75,77

7.1: Read problems 1 and 2 (no need to write up!); 3,5,9,10,23,32,33,37,63,65

Practice tests (to upload)

Hi all,

This is to announce a permanent change in the time schedule of Wednesday’s homework session: the new time is

10.20-12.20

For temporary changes, make sure to check your emails.

Here is the practice quiz and some hints: quiz1_practice

Hi all,

Last week we covered 5.1-5.3. The definite integral is a generalization of area under curve, therefore, the computations, definitions, etc. are all quite similar. Make sure to compare them to gain a deep understanding of the concept.

The fundamental theorem of calculus allows us to compute the net area under continuous curve using antiderivatives. Use the properties of definite integral to simplify your computations!

Next week, we will finish 5.3, talk about 5.4 (indefinite integral, actually a review of antiderivative), and introduce the first integration technique-substitution in section 5.5.

There will be a quiz on *Thursday* (instead of Tuesday!!), it should cover everything we have done up to 5.3.

Finally, Office hours on Wednesday is *only* 11.00-13.00. But as long as my door is open, you are welcome to come in!

We will cover 5.2-5.3

Reading: 5.2,5.3,5.4

Problems:

5.2: 44,49,56

5.3: 3(a,b),5(don’t draw anything),11,14,24,28,35,39,42,53

5.4: 2,18,27,41,52,57,60

We will cover: 0.2-0.4

Homework:

Reading: 0.2,0.3,0.4

Problems:

0.3: 9,15,20,24,36,43,76

0.4: 1,2,11,14,17,20,99

0.5: 7,9,33,56,70,95

Here are some notes that will get updated regularly: Notes