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MATH 227 : Calculus 3 for Honours Physics
Fall 2016 - Assignment #1
Instructions:
The problems on this assignment cover lines and planes in <3 , and an introduction
to vector curves and motion in <3
MATH 227: CALCULUS 3 for HONOURS PHYSICS
FALL 2016
Lectures: 10:30 - 11:20 a.m. MWF in MC 4021
Tutorial: 5:30 a.m. - 6:20 p.m. in MC 4020
Instructor: B. J. Marshman
Email: [email protected]
Phone:
Math 228: Assignment 1
due Friday, September 25, 2015 at 1:30pm
1. Sketch the direction eld of the dierential equation
y0 =
for t
y(y
2)
0 and y 2 [ 2, 5]. What are the equilibrium solutions?
2. Sketc
Math 228: Assignment 2
due Friday, October 2, 2015 at 1:30pm
1. Solve the following rst-order linear dierential equations (or IVP, as it may be).
(a) y 0 = t + 5y
(b) 2xy 0 + y = 6x, with the conditio
Math 228: Assignment 3
due Friday, October 9, 2015 at 1:30pm
Note: For exact equations, solve means solve implicitly.
1. Determine whether the equation is exact. If so, solve it.
(a) (2x + 3) + (2y 2)
Math 228: Assignment 4
due Friday, October 16, 2015 at 1:30pm
1. For each of the functions f (t, y) identify regions in the (t, y)-plane where the initial value
problem y 0 = f (t, y), y(t0 ) = y0 has
Math 228: Assignment 1 Solutions
due Friday, September 25, 2015 at 1:30pm
1. Sketch the direction eld of the dierential equation
y0 =
for t
y(y
2)
0 and y 2 [ 2, 5]. What are the equilibrium solutions
Math 228: Assignment 2
due Friday, October 2, 2015 at 1:30pm
1. Solve the following rst-order linear dierential equations (or IVP, as it may be).
(a) y = t + 5y
(b) 2xy + y = 6x, with the conditions x
MATH 228: Dierential Equations for Physics and Chemistry
Fall 2015 - LEC 001
MWF 11:30-12:20 in MC 2017
Instructor: Andrew Beltaos
Email: [email protected]
Phone: 519-888-4567, ext. 33508
Oce:
MC
MATH 227: CALCULUS 3 for HONOURS PHYSICS
FALL 2014
Lectures: 10:30 - 11:20 a.m. MWF in MC 4021
Tutorial: 5:30 a.m. - 6:20 p.m. M in RCH 301
Instructor: B. J. Marshman
Email: [email protected]
Phon
1
MATH 227 : Calculus 3 for Honours Physics
Fall 2015 - Assignment #1
Instructions:
The problems on this assignment cover lines and planes in 3 , and an introduction
to vector curves in 3 , as discus
1
MATH 227 : Calculus 3 for Honours Physics
Fall 2015 - Assignment #2
Instructions:
The problems on this assignment cover further work on vector curves in 3 , motion,
and line integrals of scalar and
1
MATH 227 : Calculus 3 for Honours Physics
Fall 2015 - Assignment #4
Instructions:
The problems on this assignment cover double integrals in Cartesian and polar
coordinates, as discussed in Sections
1
MATH 227 : Calculus 3 for Honours Physics
Fall 2015 - Assignment #5
Instructions:
The problems on this assignment cover triple integrals in Cartesian, cylindrical
polar, and spherical polar coordin
1
MATH 227 : Calculus 3 for Honours Physics
Fall 2014 - Assignment #3
Instructions:
The problems on this assignment cover surfaces in <3 , expressed in Cartesian,
cylindrical polar, and spherical pol
Lecture 4
Level Sets/Contours
(Relevant section from Stewart, Calculus, Early Transcendentals, Sixth Edition: 14.1)
You are no doubt familiar with the idea of contour plots from geography topographic
Lecture 18
Double Integrals (contd)
Electrostatic eld near an innite at charged plate
Consider a thin, at plate of innite size that is charged, with constant charge density (in appropriate
units of ch
Lecture 7
Gradient and directional derivative (contd)
In the previous lecture, we showed that the rate of change of a function f (x, y) in the direction of a
vector u, called the directional derivativ
THE MOBIUS STRIP AND STOKES' THEOREM
1. Stokes' Theorem Let us recall Stokes' Theorem: Theorem 1.1. Let M be an oriented surface in R3 with boundary given by the closed curve , with orientation induc
LINES AND PLANES IN R3
In this handout we will summarize the properties of the dot product and cross
product and use them to present various descriptions of lines and planes in three
dimensional space
KEPLERS LAWS OF PLANETARY MOTION
1. Introduction
We are now in a position to apply what we have learned about the cross product
and vector valued functions to derive Keplers Laws of planetary motion.
PHYSICAL INTERPRETATIONS OF CURL AND DIVERGENCE
1. Physical Interpretation of the Curl
Let F(x, y, z) = (P (x, y, z), Q(x, y, z), R(x, y, z) be a vector eld. We can think
of F as representing the velo
THE VOLUME OF AN n-DIMENSIONAL SPHERE IN Rn+1
1. Introduction
A circle of radius R can be thought of as the set of points (x, y) in R2 that are
a distance R from the origin. The equation is written x2
THE DIFFERENT KINDS OF INTEGRALS
We have seen many dierent kinds of integrals in this course. Let us review them
and the relations between them. All of them involve integrating functions or vector
eld
INTEGRATION AND DENSITIES
1. Introduction
In this course we study many dierent kinds of integrals. However, all of them
share something in common: All integrals are computed to measure some quantity
w
CURVES AND SURFACES IN R3
Let us intuitively dene a curve as a geometric object which, on a very small
scale, looks like a straight line. We need to make this more precise. The simplest
example of a c
Lecture 15
Multiple Integration
(Relevant section from Stewart, Section 15.1)
We now turn to the integration of scalar-valued functions f : Rn R, i.e., f (x1 , x2 , , cn ), over
regions in Rn . The ne
Lecture 27
Line integrals: Integration along curves in Rn
(Relevant section from Stewart, Calculus, Early Transcendentals, Sixth Edition: 16.2, pp. 1034-1041)
In this section, we shall be integrating