M 408S - Spring 2012
Preparatory Assignments
Calculus, Early Transcendentals, 7th
Edition, Stewart
Choose the section:
5.4
5.5
6.1
6.2
7.1
7.2
7.3
7.4
7.5
7.8
9.3/9.4
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
11.10
11.11
5.4 ********************************
Read through section 5.4 and write down all definitions, theorems, and anything else that seems pertinent.
**Look through examples 1- 5 to see how we use the table of integrals to solve them.
**Be able to answer the following questions:
1. What are the differences between the definite and indefinite integrals?
2. What is a great strategy to use when checking for correct antidifferentiation?
3. What is the difference between displacement of a particle and distance travelled by a particle?
** Look carefully at example 6
4. Can you give a practical illustration of the Net Change Theorem? (See problems 51-58)
**Complete the Quest Prep 5.4
5.5 **********************************
Read through section 5.5 and write down all definitions, theorems, and anything else that seems pertinent.
**Be able to answer the following questions:
1. What is the main idea behind the substitution rule?
2. What is the main challenge of the substitution rule?
3. When using the substitution rule with a definite integral what happens to the limits of the integration?
4. Can you sketch an even function and see how the Integrals of Symmetric functions work?
5. Can you sketch an odd function and see how the Integrals of Symmetric functions work?
**Be able to explain the solutions to problems 1-6 on page 413.
**Complete the Quest Prep 5.5
6.1 *********************************
Read through section 6.1 and write down all definitions, theorems, and anything else that seems pertinent.
**Be able to answer the following questions:
1. When finding the area between functions f and go on [a,b], how do you know which to subtract from which?
2. How do you adjust the integrals if on [a,b] when sometimes f > g and sometimes g > f ?
3. How do you find the bounds of integration when finding the area between two curves?
4. Does the formula still apply when both f and g are negative valued functions?
**Complete the Quest Prep 6.1
6.2 *************************************
Read through section 6.2 and write down all definitions, theorems, and anything else that seems pertinent.
**Be able to answer the following questions:
1. In the integral to determine the volume of a solid, what does A(x) represent?
2. When finding the volume of a solid of revolution, what geometric shape does A(x) represent?
3. How do we find the radius of this shape?
4. How do you adjust your integral if the rotation occurs around the y-axis?
**Some Videos that may be useful
http://www.youtube.com/watch?v=-CPUdbjpnno
http://www.youtube.com/watch?v=E5OOMbz5jZk
**Complete the Quest Prep 6.2
7.1 *************************************
Read through section 7.1 and write down all definitions, theorems, and anything else that seems pertinent.
**Be able to answer the following questions:
1. As you read through the development of the rule for integration by parts, make sure you understand each line. The first line is just the statement of the product rule. The second line is obtained by integrating the first line. Distributing the integral and re-arranging gives us the formula. Could you describe this proof to the class?
2. Can you work problems 1-2 on page 468
3. What is special about example 3?
4. What is special about example 4?
5. How do you apply the rule of integration by parts to a definite integral?
**Complete the Quest Prep 7.1
7.2 *************************************
Read through section 7.2 and write down all definitions, theorems, and anything else that seems pertinent.
**Be able to answer the following questions:
1. If you have an integral containing only powers of sine and cosine, what do you do if the power of sine is odd?
2. If you have an integral containing only powers of sine and cosine, what do you do if the power of cosine is odd?
3. If you have an integral containing only powers of sine and cosine, what do you do if both of the powers of sine and cosine are odd?
4. If you have an integral containing only powers of sine and cosine, what do you do if both of the powers of sine and cosine are even?
5. What is the antiderivative of tan(x)? of sec(x)?
**Complete the Quest Prep 7.2
7.3 *************************************
Read through section 7.3 and write down all definitions, theorems, and anything else that seems pertinent.
**Be able to answer the following questions:
1. Can you summarize the table of trigonometric substitutions?
2. Why is this type of substitution called inverse substitution?
3. Why do we restrict the domains when making trig substitutions?
4. Be able to work for the class exercises 1-3, page 483.
**Complete the Quest Prep 7.3
7.4 *************************************
Read through section 7.4 and write down all definitions, theorems, and anything else that seems pertinent.
**Be able to answer the following questions:
1. What are the different cases we need to consider in this method of integration?
2. How do we find the values of our A, B, C… variables?
3. What do we do first if our rational function is improper?
4. Be able to work for the class exercises 1-6, page 492.
**Complete the Quest Prep 7.4
7.5 *************************************
Read through section 7.5 and write down all definitions, theorems, and anything else that seems pertinent.
**Be able to answer the following questions:
1. What are the four methods suggested in tackling integrals?
2. Can we integrate all continuous functions?
3. What are the elementary functions?
**Complete the Quest Prep 7.5
7.8 *************************************
Read through section 7.8 and write down all definitions, theorems, and anything else that seems pertinent.
**Be able to answer the following questions:
**Complete the Quest Prep 7.8
9.3/9.4 **********************************
Read through sections 9.3/9.4 and write down all definitions, theorems, and anything else that seems pertinent.
**Be able to answer the following questions:
1. What does it mean for a differential equation to be separable?
2. What is the law of natural growth?
3. What is the carrying capacity in a logistics model?
4. What is the logistic differential equation?
5. Are the law of natural growth and the logistic model the only equations that model population growth?
**Complete the Quest Prep 9.3/9.4
11.1 *************************************
Read through sections 11.1 and write down all definitions, theorems, and anything else that seems pertinent.
**Be able to answer the following questions:
**Complete the Quest Prep 11.1
11.2 *************************************
Read through 11.2 and
write down all definitions, theorems and other pertinent information
You should know the following:
1) The definition of a series (and how it is different than a sequence).
2) What is partial sum? What is the sequence generated by partial sums? What does the sequence of partial sums have to do with whether a series converges or diverges?
3) What is a geometric series and when does it converge?
4) What is a telescoping series? (Think partial fraction decomposition)
5) What is the famous harmonic series? Does it converge?
6) If a series converges, what is true about the limit of the sequence of terms? Is the converse true?
7) What is the test for Divergence?
8) What are some rules for convergent series?
** Complete the Quest Prep 11.2
11.3 *************************************
Read through sections 11.3 and write down all definitions, theorems, and anything else that seems pertinent.
You should know the following:
1) What is the integral test?
2) You must test to see if the hypothesis of the Integral test are satisfied before using the test. AND – you need to show me that part.
3) Does this test tell us what a series converges to?
4) Know the p-series. It comes up often!
** You do not need to know how to estimate the error – BUT it is interesting indeed.
** Complete the Quest Prep 11.3
11.4
*************************************
Read through sections 11.4 and write down all definitions, theorems, and anything else that seems pertinent.
I will ask the following questions at the beginning of class:
1. Can you fully state the Comparison Test?
2. Can you fully state the Limit Comparison Test?
3. We reach for these tests when we think our series should act like a series we know something about. What are the likely candidates (LOST) to use to compare?
4. If we suspect that our series converges, what must be true about the series we use to compare? (Hint: It is more than the series we use converges)
5. If we suspect that our series diverges, what must be true about the series we use to compare?
(Hint: It is more than the series we use diverges)
Looking at the examples is the key to the prep.
**
Complete the Quest Prep 11.4
11.5 *************************************
Read through sections 11.5 and write down all definitions, theorems, and anything else that seems pertinent.
I will ask the following questions at the beginning of class:
1. Can you fully state the Alternating Series Test?
2. What are two techniques to show the a sequence is decreasing?
3. Do you have to show the sequence is decreasing (yes) or can you just state that it does (no)?
4. Can you use this test on any series?
** Complete the Quest Prep 11.5
11.6 *************************************
Read through sections 11.6 and write down all definitions, theorems, and anything else that seems pertinent.
I will ask the following questions at the beginning of class:
1. What does it mean for a series to be absolutely convergent?
2. What does it mean for a series to be conditionally convergent?
3. If a series is absolutely convergent is it necessarily conditionally convergent?
4. If a series is conditionally convergent is it necessarily absolutely convergent?
5. What is the ratio test?
6. What do we conclude if the third limit is true in the ratio test?
7. What is the root test?
8. What do we conclude if the third limit is true in the root test?
** Complete the Quest Prep 11.6
11.7 *************************************
Read through sections 11.7 and write down all definitions, theorems, and anything else that seems pertinent.
I will ask the following questions at the beginning of class:
1. What is your detailed strategy you will employ when asked if a particular series converges or diverges?
**
Complete the Quest Prep 11.7
11.8 *************************************
Read through sections 11.8 and write down all definitions, theorems, and anything else that seems pertinent.
I will ask the following questions at the beginning of class:
1. What do the c values represent in a power series?
2. What does it mean for a series to be centered at x = a?
3. What are the only three possibilities of convergence for a power series?
4. What is the radius of convergence?
** Complete the Quest Prep 11.8
11.9 *************************************
Read through sections 11.9 and write down all definitions, theorems, and anything else that seems pertinent.
I will ask the following questions at the beginning of class:
1. What is the power series expansion for 1/(1-x) and what is its radius of convergence? What does that mean?
2. How do we differentiate and integrate power series?
3. What is the power series representation for arctan(x)?
4. Why do we want to be able to express a function as a power series?
5. Can all functions be expressed as a power series?
6. What does where the power series is centered have to do with anything?
** Complete the Quest Prep 11.9
11.10 *************************************
Read through sections 11.10 and write down all definitions, theorems, and anything else that seems pertinent.
I will ask the following questions at the beginning of class:
1. What is a Maclaurin series? What is a Taylor series? How are they different?
2. What is the Maclaurin series representation for e^x?
3. Why do we want to be able to express sine and cosine as a Maclaurin series?
**
Complete the Quest Prep 11.10
11.11 *************************************
Read through sections 11.11 and write down all definitions, theorems, and anything else that seems pertinent.
I will ask the following questions at the beginning of class:
1. Why would we want to approximate a function with a Taylor series?
2. What are the three possibilities for estimating the error on a Taylor polynomial approximation?
** Complete the Quest Prep 11.11