# Jor-el Briones

### Homework

#### Homework 1 (Due 7/10/2017 at 5PM):

Textbook Section 1.1: Exercises 4, 5, 16, 18, 26, 27
Textbook Section 1.2: Exercises 6, 7, 16, 17, 23

Read section 1.1, up to example 16 (you can skip example 17)

#### Homework 2 (due 7/17/2017 at 5PM):

Textbook Section 1.2: Exercises 13, 18, 20, 27
Textbook Section 1.3: Exercises 13, 16b, 20, 29, 31, 32
Textbook Section 2.4: Exercises 2, 8, 18, 22, 24
Textbook Section 4.1: Exercises 2, 11, 14, 18, 20, 25ab
Textbook Section 4.2: Exercises 6, 13, 16

Read section 1.3; you can skip the history section
Read section 2.4; Skip example 4; you don't need to know what an epicycle, epicycloid, or hypocycloid are; Skip historical notes
Read section 4.1; You don't need to know what Newton's law of gravitation is, or what Kepler's law is. You can skip everything from Kepler's law to the end of "Real life trajectories"
Read Section 4.2; You can skip the differential of arc length section up to the end of example 5.

Note: Not covered in lecture, but two planes are parallel if they have the same normal vector. A plane is parallel to a line if the line's direction vector lies on the plane, or if the line never intersects the plane. Also, a path is considered regular if none of its velocity vectors are (0,0,0), or (0,0), depending on whether the path is in the plane or in space. NOTE: For 7/15/2017 update, I'm just adding that 4.1 #14 has a typo. The particle's trajectory intersects the xz-plane twice, not the yz-plane.

#### Homework 3 (due 7/24/2017 at 5PM):

Textbook Section 2.1: Exercises 2, 3, 15, 20, 35
Textbook Section 2.2: Exercises 4, 6, 9, 11
Textbook Section 2.3: Exercises 3, 5, 6, 18, 19, 23
Textbook Section 2.3: Exercises 12, 16bc (added on 7/20)
Textbook Section 2.5: Exercises 10, 33
Textbook Section 2.6: Exercises 17, 18, 22, 26

Read Section 2.2; skip Limits in terms of epsilons and deltas up to example 15
Read Section 2.3; skip Differentiability: The general case up to the end of example 6.
Read Section 2.3; INCLUDING what I told you to skip before
Read Section 2.5; skip second special case of the chain rule up to end of example 6 (for now)
Read Section 2.6; skip gradient vector field (midterm will cover only up to end of example 5)

#### Homework 4 (due 7/31/2017 at 5PM):

Textbook Section 2.6: Exercises 5, 8, 20
Textbook Section 3.1: Exercises 7, 15, 25 (Note: For #15, they use a different notation for partial derivatives, explained at the bottom of page 152)
Textbook Section 3.3: 6, 28 (you may use section 3.4 for this), 41
Textbook Section 3.4: 3, 13, 17, 25

Read Section 2.6; skip gradient vector field; if you didn't get #5 on the midterm, read this section again, then do #22 in section 2.6 again on your own time; 2.6 #22 won't be graded on HW 4, and you don't have to do it, but really, you should.
Read Section 3.1; Skip Historical Notes, and Example 5.
Read Section 3.3; Skip Second Derivative Test for Local Extrema on pg 171 up to end of example 5, skip Determinant Test for Positive Definiteness, skip General Second Derivative Test (n-variables).
Read Section 3.4; Skip Existence of Solutions, skip Several Constraints, skip Second Derivative Test for Constrained Extrema.

#### Homework 5 (due 8/5/2017 at 5PM)

Textbook Section 5.1: Exercises 1, 11
Textbook Section 5.2: Exercises 1, 4
Textbook Section 5.3: Exercises 1, 3
Textbook Section 5.4: Exercises 1, 2, 5, 7, 12, 16, 17

Read Section 5.1; Skip Historical Note
Read Section 5.2; Skip Historical Note

### "Problems I Like" (likely to be assigned in the future):

Textbook Section 2.4: Exercises 2, 8, 9, 13, 16, 17, 18, 22, 24
Textbook Section 4.1: Exercises 2, 11, 12, 13, 14, 18, 19, 20, 25
Textbook Section 4.2: Exercises 1, 3, 6, 10, 11, 12, 13, 16
Textbook Section 2.1: Exercises 2, 3, 16, 20, 27, 31
Textbook Section 2.2: Exercises 4, 6, 9, 11
Textbook Section 2.3: Exercises 1, 3, 5, 6, 9, 12, 16, 17, 18, 19, 23, 24
Textbook Section 2.5: Exercises 6, 10, 15, 16, 33, 35
Textbook Section 2.6: Exercises 1, 2, 3, 4, 6, 7, 8, 10, 17, 18, 20, 22, 24, 26
Textbook Section 3.1: Exercises
Textbook Section 3.3: Exercises
Textbook Section 3.4: Exercises
Textbook Section 5.1: Exercises
Textbook Section 5.2: Exercises
Textbook Section 5.3: Exercises
Textbook Section 5.4: Exercises
(More to be added)

### Turning in Homework

Homework may be turned in during section, or into the drop boxes at the basement level of the Applied Physics and Mathematics building (AP&M) in Muir. The drop boxes should be to the left as you exit the elevators or stairs taken from the main entrance to AP&M. Be sure to drop your homework into the box labelled with your course and section number, or we will almost certainly never find your homework. The homework dropboxes for this class will be in main dropbox #1. Our dropboxes are the ones labeled with the orange labels. Please place your homework in the correct section box.