Math 2374, Afternoon
Spring 2011
Midterm 1
February 17, 2011
Time Limit: 50 minutes
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This exam contains 6 pages (including this cover page) and 5 problems. Check to see if any pages
a
Test 3 Solutions
Math 2374
April 22, 2015
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Instructions: This test has 5 questions for a total of 100 points. Enter all requested
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Math 2374: Lecture 3
January 28, 2015
Math 2374: Lecture 3
Overview of today
n-dimensional Euclidean space
standard basis vectors
inner product, length, norm
Cauchy-Schwarz, triangle inequality
Matrices
Matrix algebra
Properties of matrices
Inverses and d
Math 2374: Lecture 26
April 24, 2015
Math 2374: Lecture 26
Overview of today
8.2 Stokes theorem :
the divergence theorem in 2D
boundaries of surfaces
Stokes theorem for graphs
Stokes theorem for parametrized surfaces
Math 2374: Lecture 26
Divergence theor
Math 2374: Lecture 2
January 23, 2015
Math 2374: Lecture 2
Overview of today
Matrix geometry
Planes in space
Cylindrical coordinate system
Spherical coordinate system
Math 2374: Lecture 2
Geometry of 3 3 matrices
The matrix
a1 a2 a3
b1 b2 b3
c1 c2 c3
de
Test 2 Solutions
Math 2374
March 11, 2015
Name (print):
Student ID number:
Section:
Teaching assistant:
Signature:
Instructions: This test has 6 questions for a total of 100 points. Enter all requested
information on the top of this page, and put your ini
Math 2374: Lecture 16
March 13, 2015
Math 2374: Lecture 16
Overview of today
Changing the order of integration when the region is not a
rectangle (5.4)
Triple integrals (5.5)
Math 2374: Lecture 16
Integration over simple regions
If a region D is simple, t
Math 2374: Lecture 24
April 17, 2015
Math 2374: Lecture 24
Overview of today
Surface integrals of vector-valued functions (Section 7.6): the
definition and plenty of examples
Math 2374: Lecture 24
Integrals of vector functions on surfaces
Let F (x, y , z)
Math 2374: Lecture 17
March 25, 2015
Math 2374: Lecture 17
Overview of today
Motivation for studying maps
The geometry of maps from R2 R2 (6.1)
Change of variables for double integrals (6.2, the beginning of
it)
Math 2374: Lecture 17
Change of variables (
Math 2374: Lecture 5
February 4, 2015
Math 2374: Lecture 5
Overview of today
Partial derivatives
Differentiability
Linear approximations
Tangent planes
Theorems on differentiability
Math 2374: Lecture 5
Review of Calc I
Continuity: no jumps
Differentiabil
Math 2374: Lecture 8
February 13, 2015
Math 2374: Lecture 8
Overview of today
Mixed partial derivatives
Taylors theorem
Math 2374: Lecture 8
C 1 functions
Recall: we say that f : R3 R, f (x, y , z), is C 1 if
f
,
x
f
,
y
f
z
are all continuous functions.
Math 2374: Lecture 11
February 25, 2015
Math 2374: Lecture 11
Overview of today
Vector-valued functions: differentiation rules, velocity,
acceleration, regular points and paths (section 4.1)
Arc length: definition, arc length differential, and the arc
len
Math 2374 Spring 2008 Exam 2 solutions 1. (30 points) (a) (3 points each) curl( f ) YES curl(div F) NO; div F is a real-valued function, and curl applies to vector elds. div(curl F) YES ( ( F) YES F) NO; as above.
d d (b) (15) Since |c(t)|2 = c(t) c(t) =
Math 2374 Spring 2007
Midterm 1 Solutions - Page 1 of 3
February 21, 2007 1 1 and
1. (25 points) Let g(x, y) = ex+y and r : R R2 be a function where r(0) = r (0) = 1 . Find F (0) where F (t) = g(r(t). 2
We use the special case of the chain rule: F (0) = F
Math 2374 Spring 2007
Midterm 3 Solutions - Page 1 of 6
April 25, 2007
1. (30 points) Consider the surface parametrized by (x, y, z) = (x, y) = (x, y, 4(x2 +y 2 ) between the planes z = 1 and z = 3. (i) (15 points) Set up the integral to nd the surface ar
Math 2374 Practice final exam answers and hints Email corrections to [email protected] Spring 2007 1. Four critical points: (0, 0) max (D = 8 and fxx = -4), (0, 2) saddle (D = -8), (4, 0) saddle (D = -8), and (4, 2) min (D = 8 and fxx = 4). 2. -2. (A potenti
Math 2374 Practice nal exam answers and hints Email corrections to [email protected] Spring 2006 1.
513 135 .
2. (8, 6, 6) (x 2, y 3, z 1) = 0. 3. 8.
1 4. (a) 3 + 2 (3(x 2)2 2(y 8)2 + 2(x 2)(y 8). (Note that f y are 0 at (2, 8) because it is a critical point
Math 2374 Spring 2008 Exam 3 solutions 1. By Stokes Theorem, the surface integral is equal to S F ds. But S lies in the three coordinate planes, where at least one of x, y, and z are 0, so F = 0 on S and hence S F ds = 0. 2. (a) Parametrize S by (u, v) =
Math 2374: Lecture 29
May 6, 2015
Math 2374: Lecture 29
Overview of today
8.3 Conservative vector fields:
When a vector field is a curl
8.4 Gauss divergence theorem:
Elementary regions in space and their boundaries
Gauss divergence theorem
Examples using
Math 2374: Lecture 21
April 8, 2015
Math 2374: Lecture 21
Overview of today
Example from 7.2 (line integrals)
Why we need parametrizations of surfaces
How to parametrize a surface
Tangent vectors to parametrized surfaces
When a surface is regular
How to w
Math 2374: Lecture 13
March 4, 2015
Math 2374: Lecture 13
Overview of today
Divergence and curl continued (the rest of section 4.4)
An introduction to double integrals (section 5.1)
Math 2374: Lecture 13
Recall.
Last time we defined the del operator:
=i
+
Math 2374: Lecture 28
May 1, 2015
Math 2374: Lecture 28
Overview of today
8.3 Conservative vector fields:
How to find f such that f = F: two different ways
When a vector field is conservative in the plane, R2
Math 2374: Lecture 28
Example 1: Determine whe
Math 2374: Lecture 25
April 22, 2015
Math 2374: Lecture 25
Overview of today
8.1 Greens theorem :
simple closed curves as boundaries
orientation of curves
the statement of Greens theorem
area formula
vector form of Greens theorem
the divergence theorem in
Math 2374: Lecture 12
February 27, 2015
Math 2374: Lecture 12
Overview of today
Vector fields: what they are, how to draw them, what a flow
line is (section 4.3)
Divergence and curl: definitions and examples (section 4.4)
well do more on this next week
M
Study guide for the rst exam
Math 2374, Fall 2006
1. Basic vector material (Chapter 1)
(a) Comments: the initial sections of this course are background material for the rest
of the course. The following may help you organize your studying of the diverse
t
Study guide for the second exam
Math 2374, Fall 2006
1. Higher order partial derivative (section 3.1)
(a) Be able to compute all secord-order partial derivatives
(b) Clairauts Theorem: mixed partials are equal for twice continuously dierentiable
functions
Math 2374 Fall Semester 2014
CSE Multivariable Calculus and Vector Analysis
INSTRUCTOR: Adrian Diaconu
OFFICE: Vincent Hall 357; tel. (612) 625-6380;
EMAIL: [email protected]
OFFICE HOURS: WF 10:00 AM - 11:00 AM, Vincent Hall 357
Text: Marsden and Tromba,
Math 2374, Syllabus, Spring 2017
Required text: Vector Calculus, 6th edition, by Marsen and Tromba.
1. It is assumed that you are familiar with the material of sections 1.1 and 1.2.
2. Sections 2.2, 3.4, 3.5, 6.3, 6.4, 7.7, 8.5, and 8.6 will not be covere