Contents
1. Functions and Limits
1.1. Basic concepts of functions
1.2. Classification of functions
1.3. New functions from old functions
1.4. Tangent and velocity
1.5. Limit of a function with intuitive definition
1.6. The precise definition of a limit
1.
MA1300
Problem Set # 1
1. (P21, #1.1.45) Find the domain and sketch the graph of the function
3x + |x|
.
x
G(x) =
2. (P21, #1.1.49) Find the domain and sketch the graph of the function
x + 2 if x 1
f (x) =
x2
if x > 1.
3. (P22, #1.1.67) In a certain count
MA1300
Problem Set # 11
1. (P221, #3.3.11, 3.3.14) For the following two functions:
(a) Find the intervals on which f is increasing or decreasing.
(b) Find the local maximum and minimum values of f .
(c) Find the intervals of concavity and the inflection
2016 MATH1030
Lecture 3: Reduced Row Echelon Form
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
The lecture is based on
Beezer, A first course in Linear algebra. Ver 3.5
Downloadable at http:/linear.ups.e
2016 MATH1030
Lecture 3 additional note 1
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
1
Reduced Row Echelon form
Terminology:
Zero row: a row consists of 0.
Leftmost nonzero entry of a row: the first no
2016 MATH1030
Lecture 18: Determinant Part 2, Summary and more examples
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
The lecture is based on
Beezer, A first course in Linear algebra. Ver 3.5
Downloadable
2016 MATH1030
Lecture 13: Row operations and matrix multiplication
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
In this lecture, we will discuss the relation between elementary row operations and
matrix
2016 MATH1030
Lecture 5: Homogeneous Systems of Equations and non singular matrices
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
The lecture is based on
Beezer, A first course in Linear algebra. Ver 3.5
2016 MATH1030
Lecture 16: Subspace
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
1
Subspaces
A vector space V is a set with addition and scalar multiplication with properties as in
Lecture 6 Theorem 5 (or
2016 MATH1030
Lecture 9: Linear independence
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
The lecture is based on
Beezer, A first course in Linear algebra. Ver 3.5
Downloadable at http:/linear.ups.edu/do
2016 MATH1030
Lecture 8: Spanning Sets
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
The lecture is based on
Beezer, A first course in Linear algebra. Ver 3.5
Downloadable at http:/linear.ups.edu/download
2016 MATH1030
Lecture 10: Linear Dependence and Span
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
The lecture is based on
Beezer, A first course in Linear algebra. Ver 3.5
Downloadable at http:/linear.up
2016 MATH1030
Lecture 21: Inner Product
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
In below, unless otherwise stated, V is always a subspace of Rm with dim n and
hv, wi or hv, wiV is an inner product o
2016 MATH1030
Lecture 6: Vector operations
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
The lecture is based on
Beezer, A first course in Linear algebra. Ver 3.5
Downloadable at http:/linear.ups.edu/down
2016 MATH1030
Lecture 15: Four subsets
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
The lecture is based on
Beezer, A first course in Linear algebra. Ver 3.5
Downloadable at http:/linear.ups.edu/download
2016 MATH1030
Lecture 20: Properties of Eigenvalues and Eigenvectors
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
The lecture is based on
Beezer, A first course in Linear algebra. Ver 3.5
Downloadable at
2016 MATH1030
Lecture 4: Type of solution sets
Charles Li
Important announcement: Midterm II has been changed to Mar 21 (Mon) 7:30-9pm
Warning: the note is for reference only. It may contain typos. Read at your own risk.
The lecture is based on
Beezer, A
2016 MATH1030
Lecture 7: Linear Combinations
Charles Li
Warning: the note is for reference only. It may contain typos. Read at your own risk.
The lecture is based on
Beezer, A first course in Linear algebra. Ver 3.5
Downloadable at http:/linear.ups.edu/do
MA1300
Problem Set # 4
1. (P92, #1.8.46) Find the values of a and b that make f continuous everywhere.
2
x 4
if x < 2
x2
f (x) =
2
ax bx + 3 if 2 x < 3
2x a + b
if x 3.
2. (P92, #1.8.51, 1.8.53) Use the Intermediate Value Theorem to show that there is a
MA1300
Problem Set # 12
1. (P402, #6.2.49, 6.2.50; P418, #6.4.3, 6.4.12; P419, #6.4.49, 6.4.52)
(P460, #6.6.25, 6.6.26, 6.6.29; P468, #6.7.33, 6.7.35)
Find the derivative of the function.
1 e2x
(a). y = cos
,
1 + e2x
2
(b). f (t) = sin2 esin t ,
(c). f
MA1300
Problem Set # 7
1. (P156, #2.5.85)
a If n is a positive integer, prove that
d
(sinn x cos nx) = n sinn1 x cos(n + 1)x.
dx
b Find a formula for the derivative of y = cosn x cos nx that is similar to the on in part a.
2. (P156, #2.5.88)
a Write |x| =
Contents
3. Applications of Differentiation
3.1. Maximum/Minimum
3.2. The Mean Value Theorem
3.3. From derivatives to properties of graph
3.4. Limits at infinity: Horizontal asymptotes
3.5. Curve sketching
3.6. Optimization
1
1
2
3
4
6
6
3. Applications o
Contents
2. Derivatives
2.1. Derivatives at a point
2.2. The derivative on an interval
2.3. Differentiation formulas
2.4. Derivatives of trigonometric functions
2.5. Chain rule
2.6. Implicit differentiation
2.7. Rates of change and applications
2.8. Relat
Contents
5. Infinite sequences and series
5.1. Sequences
5.2. Series
5.3. The comparison tests and p-series test
5.4. Alternating series
5.5. Absolute convergence and the ratio and root tests
5.6. Strategy for testing series
5.7. Power series
5.8. Represe
MA1301 Quiz II, 12 April, 2014
IHINamlez' g I Student ID:
I Class: MAl301A/MA1301B (please delete one as appropriate)
1.( ) [5 marks] Find all cube roots of \/ z'x/.
$~15=2 .2 (Q- 51") 2132P1
+La Hale im din-e, 359C + EM #0252,
if 71r~ 5
1/59. 958?
(-b )
MA1300B Enhanced Calculus and Linear Algebra I
Autumn 2014
Instructor:
Min Huang
E-mail:
[email protected]
Office:
AC1 Y6626
Tutor:
Yifeng Hou, [email protected]
Textbook:
James Stewart, Single Variable Calculus, 7th Ed, International (Chapters
MA1300
Problem Set # 13
1. (P724, #11.1.25, 11.1.30) Determine whether the sequence converges or diverges. If it converges,
find the limit.
3 + 5n2
,
n + n2
r
n+1
.
(b). an =
9n + 1
(a). an =
2. (P725, #11.1.80) A sequence cfw_an is given by a1 =
2 and a
MA1300
Problem Set # 10
1. Suppose that a function f is continuous on [a, b] and f (x) exists for every x (a, b). If f (a) = f (b) = 0
and f (c) < 0 for some point c (a, b), prove that there exists some (a, b) such that f () > 0.
2. Suppose that a functio
MA1300
1. (P70, #1.6.15) Evaluate the limit
2. (P70, #1.6.19) Evaluate the limit
3. (P70, #1.6.26) Evaluate the limit
Problem Set # 2
t2 9
t3 2t2 + 7t + 3
lim
x+2
x2 x3 + 8
1
1
lim
2
t0 t
t +t
lim
4. (P70, #1.6.36) Use the Squeeze Theorem to show that
li
Department of Mathematics
City University of Hong Kong
MA1300A Enhanced Calculus and Linear Algebra I
Instructor: Dr. Andrea CAPONNETTO,
Office: Y65342, Phone: 3442-6466,
E-mail: [email protected]
Tutor: WANG Jilu,
E-mail: [email protected]
MA1300
1 of 3
https:/eportal.cityu.edu.hk/bbcswebdav/institution/APP.
MA1300 Enhanced Calculus and Linear Algebra I
Part I
Course Duration: One semester
Credit Units: 3
Level: B1
Medium of Instruction: English
Prerequisites:
(i) HKDSE Mathematics Compulso
MA1300
Problem Set # 14
1. (P750, #11.4.5, 11.4.12, 11.4.15) Determine whether the series converges or diverges.
(a).
X
X
X
(2k 1)(k2 1)
4n+1
n+1
, (b).
.
,
(c).
n n
(k + 1)(k2 + 4)2
3n 2
n=1
n=1
k=1
2. (P755, #11.5.7, 11.5.11, 11.5.19, 11.5.20) Test the
MA1300
Problem Set # 6
1. (P138, #2.3.81) Find an equation of the normal line to the parabola y = x2 5x + 4 that is parallel
to the line x 3y = 5.
2. (P138, #2.3.82) Where does the normal line to the parabola y = x x2 at the point (1, 0) intersect
the par