Math 253 HWK 4: Review for chap. 13(Due 10/13)

Hi all,

These problems are due after your test, but the content will be on your test, so I highly recommend you do them before the test.

Section 13.1: 1, 2, 3, 4, 21-26, 28, 49, 50(we did this problem in class. Notice when looking for intersections, it is convenient to give \mathbf{r}_2 a different parameter)

Section 13.2: 9, 13, 16, 17, 20, 21, 23(check out Example 3 on page 857), 36

Section 13.4: 3(no need to sketch), 6, 15(hint: integrate), 19

 

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Math 151(Practice test)

Here is a practice for the test: 151_Test_1P

 

I will be gone next week, so I will make myself as available as possible this week! Do not hesitate to make appointments with me to get help on these problems!

 

 

Math 151:HWK 3(DUE 10/3)

Please review what we have covered for upcoming test!

I will go over the two problems in section 2.6 on Tuesday before you hand in the homework.

Hand in these problems on review day:

2.2: 6,7,9,11

2.3: 2,11,14,19,24,25,35(no need to draw),37

2.5: 17,18,31,33

2.7: 5,6,11,12,13

Summary of vectors

Hi all,

This is a brief summary of vectors. We will be using these properties in the rest of chapter 12.

Vector is a quantity with both magnitude (length, norm, etc.) and direction. To completely determine a vector, you will need both magnitude and direction only. In particular, position is irrelevant for describing a vector.  Vector is a concept in any dimensions, not only 2 or 3.

We talk about vectors both with and without coordinate systems, and both ways can be useful.

If we do not introduce coordinate systems: a vector is represented by drawing a line segment with an arrow at the end. We study the addition by using the triangle law or parallelogram law. Subtraction of vector is simply adding the vector of same magnitude but opposite direction. Scalar multiplication of a vector yields either the zero vector, or a parallel vector of same or opposite direction.

Now with coordinate systems: a vector can be represented by its initial and terminal point: say vector \vec{ u} has initial point (x_1,y_1) and terminal point (x_2,y_2). Then the vector \vec{ u} can be simply represented by \vec{u}=<x_2-x_1,y_2-y_1>. Notice this is enough information to determine a vector: direction from slope of the line segment, and magnitude from distance of the two points. As the position of the vector doesn’t impact the vector, we often move vectors so that their initial point is at the origin. Studying the addition (or subtraction) of two vectors \vec{u}=<u_1,u_2> and \vec{v}=<v_1,v_2> now simply becomes the addition or subtraction of the corresponding components. \vec{u} \pm \vec{v}=<u_1\pm v_1, u_2\pm v_2>.

Finally, the standard  basis vectors are useful tools for studying ”skeletons” of all vectors on the plane or in space. We often like to write vectors as combined quantities of standard basis vectors.

 

How to study math?

According to Paul Halmos (image from here):

study_math

Don’t just read it; fight it! Ask your own questions,
look for your own examples, discover your own proofs.
Is the hypothesis necessary? Is the converse true?
What happens in the classical special case? What
about the degenerate cases? Where does the proof
use the hypothesis?

— Paul R. Halmos

Review of Pre-calculus

Hi all,

I found these two resources online for review:

This and this.

I can’t choose between the two, but they definitely have overlaps. Focus on one and see how you feel about the content. Check out review for chapter 1 on page 68 if you are done and let me know if you have any questions.