MATH2014/201617/2nd
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2014 Multivariable calculus and linear algebra
Tutorial 7
Date : Mar 27, 2017 Mar 31, 2017
MATH2014/201617/2nd
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2014 Multivariable calculus and linear algebra
Solution to Tutorial 10
Date : Apr 17, 2017 Apr 21, 2017
1. (a) S1 is line
MATH2014/201617/2nd
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2014 Multivariable calculus and linear algebra
Solution to Tutorial 11
Date : Apr 24, 2017 Apr 28, 2017
1 0
1
0 0
2 2 4 1
MATH2014/201617/2nd
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2014 Multivariable calculus and linear algebra
Solution to Tutorial 9
Date : Apr 10, 2017 Apr 14, 2017
3 2
2
4
1. The aug
MATH2014/201617/2nd
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2014 Multivariable calculus and linear algebra
Solution to Tutorial 8
Date : Apr 3, 2017 Apr 7, 2017
1. None of them
2.
1
SCNC1112
Fundamental Forces of Nature
From the previous lecture
Newtons laws of motion form a comprehensive
description of all possible motions, as well as the
forces that lead to them.
However, the
YEAR

OF
 C H E M I S T R Y  C E L E B R AT I O N 
Philip Ball has a Ph.D. in physics from the University of Bristol in
England and was an editor at Nature for more than 20 years. He
is the award
MATH2014 Multivariable Calculus and Linear Algebra
Class Exercise 6
1. In Exercises (i)  (iv), describe the given region in polar coordinates.
Solution.
(i) For /2 2, 0 r 9.
(ii) For /2 /2, 1 r 4.
(i
Math2014 Assignment
Instructions:
1. You should always give precise and adequate explanations to support your conclusions.
Clarity of presentation of your argument counts. So think carefully before yo
MATH2014 Multivariable Calculus and Linear Algebra
Solution to Assignment 3
1. Note that R = cfw_(x, y) 3 y x 2, 0 y 8 = cfw_(x, y)0 y x3 , 0 x 2. By
interchanging the order of integration, it yield
MATH2014 Multivariable Calculus and Linear Algebra
Class Exercise 11
1. Let
3
2 4
A = 1 2 3 .
2
3 2
(a) Find the values of det(M21 ), det(M22 ) and det(M23 ).
(b) Find the values of A21 , A22 and A23
MATH2014 Multivariable Calculus and Linear Algebra
Class Exercise 9
1. Use back substitution to solve each of the system
x1 +
x2 +
2x2 +
x3 = 8
x3 = 5 .
3x3 = 9
2. Write out the system of equations th
MATH2014 Multivariable Calculus and Linear Algebra
Class Exercise 10
1. Consider a linear system whose augmented matrix is of the form
1 2 1 0
2 5 3 0 .
1 1 0
(a) Is it possible for the system to be
MATH2014 Multivariable Calculus and Linear Algebra
Assignment 3
1. Show that the only possible maxima and minima of z on the surface z = x3 + y 3 9xy + 27
occur at (0, 0) and (3, 3). Show that neither
Proof of Lagrange Multipliers
Here we will give two arguments, one geometric and one analytic for why Lagrange multi
pliers work.
Critical points
For the function w = f (x, y, z) constrained by g(x, y
MATH 2014
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2014 Multivariable calculus and linear algebra
Tutorial 4
1. Find the rectangle with largest area that can be inscribed in the ellip
MATH 2014
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2014 Multivariable calculus and linear algebra
Tutorial 1 and 2
Exercise 1.1
1. Let f (x, y) =
2x 3y
, where x + y 6= 0. Show that
x
THE UNIVERSITY OF HONG KONG
DEPARTMENT OF MATHEMATICS
MATH2014 Multivariable calculus and linear algebra
Tutorial 3
1. Use total differential to approximate
3
1
.
(1.9)2 +(2.04)2
2. Approximate w by
MATH2014 Multivariable Calculus and Linear Algebra
Class Exercise 3
1. Let T = f (x, y) be the temperature at the point (x, y) on the circle x = cos t, y = sin t, 0
t 2 and suppose that
T
= 8x 4y,
x
MATH2014 Multivariable Calculus and Linear Algebra
Class Exercise 5
!
1. In Exercises (i)  (iv), write an iterated integral for R dA over the described region R
using (a) vertical crosssections, (b)
MATH2014 Multivariable Calculus and Linear Algebra
Assignment 4
Instructions
 Due date: 5:00 p.m., 15 April, 2016
 Write on white A4 paper. Staple multipage assignments in the top left corner only.
Math2014 Chapter 3
Linear Algebra
1
2
3
4
Example 1
5
6
7
8
9
10
Row Reduction and Echelon Forms
A rectangular matrix is in echelon form (or row
echelon form) if it has the following three
properties: