Category: Archive: Math 253: Calculus 3_Fall2017

Math 253: last hwk(DUE 12/8)

yajunanLeave a comment

Hi all,

Please start reviewing for the final exam. Each problem is one type of problems we did, so please use this set of homework as a guideline for your customized review material (i.e. find more problems of the same type you want more practice on).

Exercise from pg 690: 4, 5, 18, 22

Exercise from pg 842: 4: (a), (c), (d), (e), (j)

Exercise from pg 882: 1, 2, 5, 17, 19

Exercise from pg 982: 16, 20, 25, 27, 33, 43, 44, 46, 48, 55, 59

Exercise from pg 1062: 5, 6, 8, 9, 10, 22, 23, 29

Exercise from pg 1084: 1, 3

Math 253 Hwk(Due 11/17)

yajunanLeave a comment

Please review 152 content: integration requires a lot of techniques and those come from familiarity!

These homework problems are from section 15.1: 

Only set up and don’t evaluate: 

1(a), 2, 7(a)

Compute: 

9, 10, 12, 13, 14, 20, 23, 27, 28, 29, 37, 40, 50

Math 253 Hwk(due 11/3)

yajunanLeave a comment

Hi all,

Test 2 is coming up, please start reviewing chapter 14, functions of several variables. Also start making your sheet. 

Here are problems to turn in: 

14.7: 1, 8, 14, 31, 33, 42

14.8: 5, 14

Chapter 14 review: 

Look thru concept check (no need to turn in)

Exercises: 2 (no need to graph), 9 and 10 (change the problems into: both limits exist, find them), 15, 16, 20, 21, 23, 28 (normal line on Pg 954), 32, 35, 37, 45, 47

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

yajunanLeave a comment

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

 

Summary of vectors

yajunanLeave a comment

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.