CITY UNI V ERSITY OF HONG KONG
nd title : MA] 201 Calculus and Basic Linear Algebra II
Semester A, 20 1 4/20 1 5
Two hours
is TIiREE pages (including, this cover 'page 811(1 the attaciled
7 candidates:
LII SIX questions in this paper.
a question} on a n
MA1201 Calcuius and Basic Linear Algebra (C01 and GED
Tutorial Worksheet (Week 3)
Integration Technique: Method of Substitution
Instruction: Try to complete the problems as much as you can in the first 25 minutes and the
TA will briey go through the solut
MAIZBI Calculus and Basic Linear Algebra (CCl and CE!)
Tutorial Worksheet (Week 4)
Integration Technique: Integration by parts
Instruction: Try to complete the problems as much as you can in the first 25 minutes and the
TA will briefly go through the solu
Brief solution to Tutorial Worksheet 5
Problem 1
(a) Use method of substitution y = 3x + 1 to transform the integral into
1 3e +1
( y 1) 2 ln ydy . Then perform the integration by parts with u = ln y
27 4
and dv = ( y 1) 2 dy . The final answer is given b
MA1261 Calculus and Basic Linear Algebra (C01 and (3131)
Tutorial Worksheet (Week 2)
Indenite integral and Denite integral
instruction: Try to complete the probiems as much as you can in the first 25 minutes and the
TA will briey go through the solution i
Version 1 (labFAY) (D
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MA1201 Calculus and Basic Algebra II (Section: C(21)
Quiz 2: Vector, Complex Number and Matrix
Version 1
Name: SED: Score:
Time allowed: 50 minutes
Instruction:
Write all your answer in the sp
MA1201 Calculus and Basic Algebra II (Section: CE1)
Quiz 1: Integration
Name:
SID:
Score:
Time allowed: 25 minutes
Instruction: Write all your answer in the spaces provided. Show all your working steps
(including evaluation of integrals) clearly. The brie
MA1201 Calculus and Basic Algebra II (Section: CC1)
Quiz 1: Integration
Name:
SID:
Score:
Time allowed: 25 minutes
Instruction: Write all your answer in the spaces provided. Show all your working steps
(including evaluation of integrals) clearly. The brie
MA1201 Calculus and Basic Algebra 1! (Section: CC1)
Quiz 1: Integration
Name: SID: Score:
Time allowed: 25 minutes
Instruction: Write all your answer in the spaces provided. Show all your working steps
(including evaluation of integrals) clearly. The brie
MA1201 Calculus and Basic Linear Algebra II
Solution of Problem Set 2
Integration Technique (Part 1)
Problem 1
1
2
(a)
1
.
2
Then the integral becomes
1
1
1
.
2
2
2
2
1
6 .
6
Then the integral becomes
1
1
sec1 2 sec1 2 sec
6
6
1
ln|sec ta
MA1201 Calculus and Basic Linear Algebra (CC1 and CE1)
Tutorial Worksheet (Week 5)
Review on Integration
Instruction: Try to complete the problems as much as you can in the first 25 minutes and the
TA will briefly go through the solution in the last 25 mi
MA1201 Calculus and Basic Linear Algebra (CC1 and CE1)
Tutorial Worksheet (Week 7)
Application of Integration and Vectors
Instruction: Try to complete the problems as much as you can in the first 25 minutes and the
TA will briefly go through the solution
MA1201 Calculus and Basic Linear Algebra II
Problem Set 5
Complex Number
Part A: Basic Concept
Problem 1
Simplify the following expression and express your answer in the form of + .
(a) 5 7 + 10
(b) 1
3 + 2
(c) (2 + )2 (3 )
(d) (1 3)1
Problem 2
Let = + b
I was brought to attention the following typos in homework 2 solutions, which I attached
below for your refernce
Problem 10(b)
In the last line of the equations, the term (128/315) a^8 should be (128/315) a^8 x.
Problem 12(b)
After the third "=" sign in t
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MA1201 Calculus and Basic Linear Algebra II
Solution of Problem Set 4 Vector Algebra
Problem 1
(a)
The position vectors of , and are given by
= + , = 2 + 3 and = 2
(b)
= = (2 + 3) ( + ) = + + 3.
= = ( + ) (2 ) = + 2.
(c)
Note that
= = (2
MA1201 Basic Calculus and Linear Algebra II
Final Review
Part 1: Review in integration and application of integration
Integration Techniques
Standard Level
Example 1
Compute the integrals
(
)
Solution:
For the 1st integral (
, one can use method of substi
MA1201 Calculus and Basic Linear Algebra (CCl and CEI)
Tutorial Worksheet (Week 10)
Complex Numbers
Instruction: Try to complete all the problems as much as you can in the first 25 minutes and
the TA will briey go through the solution in the last 25 minut
MA1201 Calculus and Basic Linear Algebra (CC1 and CE1)
Tutorial Worksheet (Week 5)
Application of Integration
Instruction: Try to complete all the problems as much as you can in the first 25 minutes and
the TA will briefly go through the solution in the l
MA1201 Calculus and Basic Linear Algebra (CC1 and CE1)
Tutorial Worksheet (Week 8)
Scalar Product and Vector Product
Instruction: Try to complete all the problems as much as you can in the first 25 minutes and
the TA will briefly go through the solution i
MA1201 (CG1)
Calculus and Basic Linear Algebra II
Semester B, 2014-15
Additional Exercise on Chapter 4 Vector Algebra
1.
Given two points P(3, 0, 1) and Q(2, 1, 3) .
(a)
Find two unit vectors which are parallel to PQ .
(b)
Given that the point M divides t
MA1201 Calculus and Basic Linear Algebra II
Problem Set 4
Application of Integration
Area of the region
Problem 1
(a) Find the area of the region bounded by the curve
(b) Find the area of the region bounded by
,
(c) Find the area of the region bounded by
MA1201 Calculus and Basic Linear Algebra II
Problem Set 2
Problem 1 (Method of substitution)
Compute the following integral using method of substitution:
(a)
(b)
(c)
(e)
(g)
(d)
(f)
(h)
(i)
(j)
(k)
(l)
(n)
(o)
(p)
(q)
(r)
(m)
Problem 2 (Integration by par
MA1201 Calculus and Basic Linear Algebra II
Problem Set 5
Part A: Basic Concept
Problem 1
Simplify the following expression and express your answer in the form of
(a)
(b)
(c)
(
) (
)
(
(d)
Complex Number
.
)
Problem 2
Let
be a complex numbers satisfying
.