Term: Fall 2012
Course: MATH 2004
Instructor: Minyi Huang
1
Chapter 14. Partial Derivatives
1 Notes
First version: 2012-10-23
1.1 A function f of two variables
A function f of two variables is a rule that assigns to each ordered pair of
two numbers (x, y)
Term: Fall 2012
Course: MATH 2004
Instructor: Minyi Huang
1
Chapter 12. Vectors and the Geometry of Space
1 Notes
First version: 2012-10-02
1.1 The three dimensional coordinate system.
i) Three perpendicular axes:
x-axis,
y-axis,
z-axis.
ii) A point P
Term: Fall 2012
Course: MATH 2004
Instructor: Minyi Huang
1
Chapter 13. Vector Functions
1 Notes
First version: 2012-10-16
1.1 Vector functions
The vector function r is dened as
r(t ) =< f (t ), g(t ), h(t ) >= f (t )i + g(t )j + h(t )k,
where t is the in
MATH 2004 A Fall 2012
Tutorial 4
Please reserve 10 minutes for the quiz; if really necessary, you may switch to the quiz without nishing the
tutorial problems.
Problem 1: Given two planes L1 : x + y + z = 1 and L2 : x 2y + 3z = 1, nd the equation of the l
MATH 2004 A Fall 2012
Tutorial 3
Please reserve 10 minutes for the quiz; if necessary, you may switch to the quiz without nishing the problems.
Problem 1: Find the area bounded by r = , and = /2.
Solution:
A = (1/2)
/2
0
r2 d = (1/2)(1/3)( /2)3 = 3 /48.
MATH 2004 A Fall 2012
Tutorial 2
Problem 1. Let
f (x) =
1, 0 x < 1,
0, 1 x < 2.
Find the Fourier cosine series of f .
Solution: In order to nd the Fourier cosine series, we need to make an even extension and next a
periodic extension.
We extend f (x) to a
MATH 2004 Fall 2012
Tutorial 1
1. Suppose f1 (x) and f2 (x) are even functions, g1 (x) and g2 (x) are odd functions.
Then
(1) f1 (x)f2 (x) and g1 (x)g2 (x) are even, i.e., even even is even; odd odd is even.
(2) f1 (x)g1 (x) are odd, i.e., even odd is odd
Term: Fall 2012
Course: MATH 2004
Instructor: Minyi Huang
1
Chapter 10. Parametric Equations and Polar Coordinates
1 Notes
First version: 2012-09-13
1.1 Parametric equations
Given a function, for example y = sin x, where 0 x 2 , a curve can be
generated.
MATH2004
Notes on Fourier Series
Notes on Fourier Series
For MATH2004B, Fall 2009
1. Definition
A function f (x) is piecewise continuous in interval (a, b) if we have a = t0 < t1 < < tm =
b, such that f (x) is continuous in each interval (t i, t i+1) and
Multivariable Calculus
Math 2004
Instructor: Minyi Huang
School of Mathematics & Statistics
Carleton University
Ottawa
Contents
A piecewise continuous function
Calculate Fourier Series
Check convergence
The Function
The (2)-periodic function is given
MATH2004
Fourier Series Practice Problems
Winter 2008
Practice Problems for Fourier Series
MATH2004, Winter 2008
1,
1. Find the Fourier series of the function f (x) =
0
< x < .
0 < x < ,
< x < 0,
f (x + 2) = f (x),
2. Find the limit of the right-hand s
Course: MATH 2004
1
Fourier Series (solutions to selected problems)
(Note: The notes are subject to possible revision for improving readability; please constantly check WebCT for possible update.)
Problem 1. Solution:
a0 = (1/L)
For n = 1, 2, . . .,
an =
MATH 2004A Multivariable Calculus for Engineering or Physics
Fall 2012, Carleton University
Instructor:
Dr. Minyi Huang
Oce: 5269 HP
School of Mathematics and Statistics
Phone: 613-520-2600 ext. 8022
E-mail:
[email protected]
Webpage:
http:/www.math