The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Qn. 1 (20 marks) Choose a correct option for each question. No justification is required. Each
correct answer is worth 4 marks (no deduction for wrong answers).
(i) Suppose that we have entered the fo
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
This note is about the claim I made in class that the recipe given in the
textbook does not work when the coecients are not real numbers, but the
recipe I gave in class always works. Here is an exampl
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
These notes serve as a summary and generalizations of what we have
learned in class. If you want, you can try to prove what has been stated
here.
1
Linear nthorder homogeneous dierential
equations
Th
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Examination Review
16/10/02
Chapter13
Mock Questions
Chapter One
Analysis:
I guess that one of the questions may
be in this section
Q1.
a)Linear First Order Equations
b)Bernoulli Equations
First
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 03 Worksheet: Inverses, rotations, projections
To receive credit, hand in as many solved practice problems as time permits. Complete all
unfinished problems at home. Solution o
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 02 Worksheet: Matrix algebra
To receive credit, hand in as many solved practice problems as time permits. Complete all
unfinished problems at home. Solution of this worksheet w
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 07 Worksheet: Separable and linear firstorder equations
To receive credit, hand in as many solved practice problems as time permits. Complete all
unfinished problems at home.
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 05 Worksheet: Determinants
To receive credit, hand in as many solved practice problems as time permits. Complete all
unfinished problems at home. Solution of this worksheet wil
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 06 Worksheet: Eigenvalues and eigenvectors
To receive credit, hand in as many solved practice problems as time permits. Complete all
unfinished problems at home. Solution of th
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 04 Worksheet: Gaussian elimination and LU decomposition
To receive credit, hand in as many solved practice problems as time permits. Complete all
unfinished problems at home. S
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 05 Worksheet: Determinants
To receive credit, hand in as many solved practice problems as time permits. Complete all
unfinished problems at home. Solution of this worksheet wil
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 04 Worksheet: Gaussian elimination and LU decomposition
To receive credit, hand in as many solved practice problems as time permits. Complete all
unfinished problems at home. S
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 08 Worksheet: Applications of firstorder odes
To receive credit, hand in as many solved practice problems as time permits. Try unfinished
problems at home. Solution of this wo
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 09 Worksheet: Secondorder homogeneous odes
To receive credit, hand in as many solved practice problems as time permits. Try unfinished
problems at home. Solution of this works
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 06 Worksheet: Eigenvalues and eigenvectors
To receive credit, hand in as many solved practice problems as time permits. Complete all
unfinished problems at home. Solution of th
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 03 Worksheet: Inverses, rotations, projections
To receive credit, hand in as many solved practice problems as time permits. Complete all
unfinished problems at home. Solution o
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 02 Worksheet: Matrix algebra
To receive credit, hand in as many solved practice problems as time permits. Complete all
unfinished problems at home. Solution of this worksheet w
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Math 2350Fall 2017
Week 01 Worksheet: Complex numbers and vector spaces
To receive credit, hand in as many solved practice problems as time permits. Complete all
unfinished problems at home. Solution
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
MATH 152
Applied Linear Algebra and Differential Equations
Syllabus  Fall 2010
Course Home Page
http:/www.math.ust.hk/~kchow/math152
Please check the course home page for news regarding the course.
I
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
More PastPaper:
http:/ihome.ust.hk/~cs_gxx
Additional Problems For Math 152
True Statements
In 17, A is a 4 6 matrix, B and C are 6 6 matrices
1) The null space of A is a subspace of R6 ;
2) If Col A
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
Solutions of Math 152 Midterm Exam
1 (30 points)
(1) Find the general solution of equation
xdx + ydy = 0.
(2) Solve the initial value problem:
y t2 y = t2 ,
y(0) = 0.
Solution:
(1) Multiply the equati
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
CIVL 102
Fall 2007
Quiz 3
Traverse Adjustment by Constrained Optimization
Question 1
Consider the closed loop traverse shown in Figure 1 below. Angles are observed with a 3
theodolite, while each leng
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
1
Matrix
Additions and scalar multiplications are easy to understand. To understand the multiplications,
note that matrices and linear maps are in onetoone correspondence:
cfw_m nmatrices cfw_linea
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
MATH2350 Applied Linear Algebra and Differential Equations
Note 8
Nonhomogeneous Linear Systems
Homogeneous Linear Systems
Linear homogeneous system with constant coefficients
The general solution of
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
MATH2350 Applied Linear Algebra and Differential Equations
Note 4
Vector Spaces and Subspaces
Def: A vector space is an nonempty set V of objects, called vectors, on which
are defined two operations,
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
MATH2350 Applied Linear Algebra and Differential Equations
Note 1
Linear Systems and Row Reduction
Elementary Row Operations
1. (Replacement) Add to one row a multiple of another row.
2. (Interchange)
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
2014DSE
BIO
PAPER 1A
HONG KONG EXAMINATIONS AND ASSESSMENT AUTHORITY
HONG KONG DIPLOMA OF SECONDARY EDUCATION EXAMINATION 2014
BIOLOGY PAPER 1
8.30 am  11.00 am (2 hours 30 minutes)
Th
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
(MATH2111)[2014](f)midterm~=w1sgpimcb^_65491.pdf downloaded by akoktavius from http:/petergao.net/ustpastpaper/down.php?course=MATH2111&id=4 at 20161018 04:47:41. Academic use within HKUST only.
Qn.
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
MATH2350: Solutions to Week 9 Tutorial (unofficial)
Wei Xu
November 3, 2016
1. Solution (You should check the orthogonality between any two vectors in the given set.)
(ii) u1 u2 = 0, u1 u3 = 0, u2 u3
The Hong Kong University of Science and Technology
MATH 2350

Fall 2012
MATH2350: Solutions to Week 13 Tutorial (unofficial)
Wei Xu
November 29, 2016
1(i). Solution
Solve the characteristic equation for eigenvalues:
4 r 1
det
= 0 r1 = 2, r2 = 3.
2
1r
For r1 = 2, solve (A