Longo: Math 20C - Winter 2017
Lecture Notes
Date: January 11, 2017
Section:
1.1 (cont.)
1.2
Topics Covered:
Special vectors
Equations of lines in 3-space
Dot product of vectors (also called inner product)
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Math 20C: Calculus for Science and Engineering III
Multivariable Calculus
Course Website
www.math.ucsd.edu/abowers/20c
Instructor
Adam Bowers ([email protected])
Office: AP&M 5230
Office Hours: (see class website)
Course Description
Vector geometry, vector
Fall 2016
Math 20C
Exam 1vA
Name:
PID:
Section:
Question
Points
1
10
2
5
3
21
4
4
Total:
40
Score
1. Write your Name, PID, and Section on the front of your Blue Book.
2. Write the Version of your exam on the front of your Blue Book.
3. Hand in the first p
Fall 2016
Name:
Math 20C
Exam 2vA
Solution
PID:
Section:
Question
Points
1
10
2
12
3
6
4
12
Total:
40
Score
1. Write your Name, PID, and Section on the front of your Blue Book.
2. Write the Version of your exam on the front of your Blue Book.
3. Hand in t
Math 20C Final Exam
June 11, 2014
Version A
Instructions
(1) No calculators or other electronic devices are allowed during this exam.
(2) You may use one page of notes, but no books or other assistance during
this exam.
(3) Write your Name, PID, and Secti
Math 20C, section D Fall 2016
MWF 3:00-3:50pm Peter 108
Instructor: Jim Conant ([email protected])
Office Hours: AP&M 6210, MW 11am-12pm. Check with your TA for additional office hours.
Textbook: Vector Calculus (Sixth Edition) Jerrold E. Marsden and A
Section 10.1: Curves Defined by Parametric Equations
In the next four sections, we consider new ways to describe curves. We
have seen that integration and differentiation can become very complicated when considering x as a function of y or y as a function
DERIVATIVES AS MATRICES; CHAIN RULE
1. Derivatives of Real-valued Functions
Lets first consider functions f : R2 R. Recall that if the partial derivatives of f exist at
the point (x0 , y0 ), then we can write down the candidate for the tangent plane:
z z0
14 DIFFERENTIATION
IN SEVERAL VARIABLES
14.1 Functions of Two or More Variables (LT Section 15.1)
Preliminary Questions
1. What is the difference between a horizontal trace and a level curve? How are they related?
solution A horizontal trace at height c c
13 CALCULUS OF
VECTOR-VALUED
FUNCTIONS
13.1 Vector-Valued Functions (LT Section 14.1)
Preliminary Questions
1.
(a)
(b)
(c)
Which one of the following does not parametrize a line?
r1 (t) = 8 t, 2t, 3t
r2 (t) = t 3 i 7t 3 j + t 3 k
r3 (t) = 8 4t 3 , 2 + 5t
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20C Practice Midterm 1
Place all books and papers under your desk. Write your name, section
number and time , and student ID # on the front of your blue book. In a
column , number 1 to 7. Show all your work and box your answers.
1.
(a) 5 pts
Let r( t) = (
Homework 4
Required: Read Sections 14.114.2, complete the preliminary questions
for each section (not to be handed in), and check your answers.
Complete and hand in the following problems:
Section 14.1: 8, 16, 20, 24, 28, 32, 44
Section 14.2: 4, 8, 14,
Homework 5
Required: Read Sections 14.314.5, complete the preliminary questions
for each section (not to be handed in), and check your answers.
Complete and hand in the following problems:
Section 14.2: 26, 32, 41
Section 14.3: 16, 24, 30, 42, 48, 58, 7
Homework 6
Required: Read Sections 14.6-14.8, complete the preliminary questions
for each section (not to be handed in), and check your answers.
Complete and hand in the following problems:
Section 14.6: 2, 4, 8, 10, 12, 16
Section 14.7: 2, 8, 14, 20, 2
Homework 7
Required: Read Sections 15.115.2, complete the preliminary questions
for each section (not to be handed in), and check your answers.
Complete and hand in the following problems:
Section 15.1: 20, 22, 26, 30, 36, 38, 42, 44
Section 15.2: 3, 8,