MATH 1003 Review: Matrices
Hai Zhang
Department of Mathematics, HKUST
Sep 30, 2015, Wednesday
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Review: Matrices
Matrices (Ch.4)
(i) System of linear equations in 2 variables
Find solutions by graphing
Su
MATH 1003 Review: Interest Rates
Hai Zhang
Department of Mathematics, HKUST
Oct 2, 2015, Friday
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Review: Interest Rates
Mathematics of Finance
(a) Simple interest rate
A = P(1 + rt)
(b) Compound interest
HKUST
MATH1003 Calculus and Linear Algebra
Midterm Examination (Version B) Name:
23nd October 2013 Student ID:
18:00-20:00 Lecture Section:
Seat Number:
Directions:
Turn off all electronic devices such as phones, pagers, laptops and remove headphones.
Thi
galmﬁlm
A
Part I: Multiple Choice Questions.
Each of the following MC questions is worth 10 points, for a total of 50 points. No partial
credit. Put your MC question answers in the following table.
‘Question5 1 2 3 l 4 5 “Total
E
(Mail [bl
Q
l
a
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HKUST
MATH1003 Calculus and Linear Algebra
Midterm Examination (Version A)
11 October 2014
11:00am-12:00pm
Name:
Student ID:
Lecture Section:
Seat Number:
Directions:
Turn o all electronic devices such as phones, pagers, laptops and remove headphones.
T
HKUST
MATH1003 Calculus and Linear Algebra
Midterm Examination (Version B)
23nd October 2013
18:00-20:00
Name:
Student ID:
Lecture Section:
Seat Number:
Directions:
Turn o all electronic devices such as phones, pagers, laptops and remove headphones.
Thi
MATH 1003 Calculus and Linear Algebra
(Lecture 17)
Hai Zhang
Department of Mathematics, HKUST
Oct 14, 2015, Wednesday
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 17)
Product Rule
Theorem
(Product Rule) If
y =
MATH 1003 Calculus and Linear Algebra
(Lecture 16)
Hai Zhang
Department of Mathematics, HKUST
Oct 12, 2015, Monday
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 16)
Re-visit to Compound Interest Rate
Example
Let
MATH 1003 Calculus and Linear Algebra
(Lecture 15)
Hai Zhang
Department of Mathematics, HKUST
Oct 9, 2015, Friday
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 15)
Finding Derivatives using Dierentiation Rules
G
MATH 1003 Calculus and Linear Algebra
(Lecture 14)
Hai Zhang
Department of Mathematics, HKUST
Oct 7, 2015, Wednesday
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 14)
Denition of the Limit of a Function
Denition
MATH 1003 Calculus and Linear Algebra
(Lecture 12)
Hai Zhang
Department of Mathematics, HKUST
Sep 25, Friday, 2015
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 12)
Leontief Input-Output Analysis
Wassily Leontie
MATH 1003 Calculus and Linear Algebra
(Lecture 10)
Hai Zhang
Department of Mathematics, HKUST
Sep 23, Wednesday, 2015
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 10)
Properties for Matrix Operation
Addition (A
MATH 1003 Calculus and Linear Algebra
(Lecture 9)
Hai Zhang
Department of Mathematics, HKUST
Sep 21, Monday, 2015
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 9)
Basic Operations Between Numbers
Given two non-z
MATH 1003 Calculus and Linear Algebra
(Lecture 8)
Hai Zhang
Department of Mathematics, HKUST
Sep 18, 2015
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 8)
Matrix
Hai Zhang Department of Mathematics, HKUST
MATH 1
Applications of Gauss-Jordan Elimination
MATH 1003 Calculus and Linear Algebra
(Lecture 7)
Hai Zhang
Department of Mathematics, HKUST
Sep 16, Wednesday, 2015
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 7)
Appl
MATH 1013
APPLIED CALCULUS I, FALL 2009
SECTIONS
NAME:
STUDENT #:
A: Professor Szeptycki
B: Professor Toms
C: Professor Szeto
SECTION:
Final Exam: Sat 12 Dec 2009, 09:00-12:00
No aid (e.g. calculator, written notes) is allowed.
ANSWER AS MANY QUESTIONS AS
1
Math1013 Calculus I
Implicit Dierentiation and Rates of Change
Working with implicit dierentiation and logarithmic dierentiation - just another usage of the chain rule.
Using derivatives as rates of change.
Related rate problems - the most important
Math1013 -L2-L3 Calculus I
Week 9-11 Summary Slides
Extrema, Graph Sketching, and Other
Applications of Derivatives
p. 1/34
Extreme Values of Functions
Recall that we could locate the maximum (largest function value) or
minimum (smallest function value)
Math1013 L2/L3 Calculus I
Week 3-4 Brief Summary Slides
Limits of Function Values and Continuity
p. 1/45
Trending Behaviour of Function Values
The fundamental idea of Calculus is to look at the trending behaviour
of function values, instead of just the s
Math1013-L2-L3 Calculus I
Week 11-13 Brief Summary Slides
Antiderivatives/Indenite Integrals, and
Denite Integrals
p. 1/?
Anitderivatives/Indenite Integrals
Differentiation :
Given a function
f
df
nd
.
dx
Reversing the process:
Given a function
f
nd a
1
Math1013 Calculus I
Implicit Dierentiation and Rates of Change
Working with implicit dierentiation and logarithmic dierentiation - just another usage of the chain rule.
Using derivatives as rates of change.
Related rate problems - the most important
Math1013 L2/L3 Calculus I
Week 6-7 Brief Summary Slides
More on Differentiation Techniques
p. 1/30
Derivative Formulas & Differentiation Rules
Differentiation of functions built by +, , , of polynomials, natural
exponential or logarithmic functions can b
Math1013 L2/L3 Calculus I
Week 5-6 Brief Summary Slides
Derivatives - Basic Computation
p. 1/26
Derivative
The derivative f (x) of a function y = f (x) is dened by
f (x + h) f (x)
h0
h
f (x) = lim
whenever the limit exists.
Geometrically, f (x) is the
Math1013-L2/L3 Calculus I
Week 2 Brief Summary Slides
Inverse Functions and Graphs
p. 1/?
Vertical Line Test
As every number x in the domain of a function f can give rise only to a
unique function value f (x), a curve is NOT the graph of any function if
Math1013-L2/L3 Calculus I
Week 1 Brief Summary Slides
Functions and Graphs
p. 1/36
Functions
Functions are useful for showing relationships between quantities.
Basic ingredients of a function:
the domain, which contains all the input values of the functi
1
Math013 Calculus I
The basics about limits, continuity, and derivatives
Basic algebraic tricks (e.g., factor cancelling, limit laws) and the Squeeze Theorem in limit calculation.
Understand the meaning of appearing in limit problems.
Understand the c
1
Math1013 Calculus I
The basics about limits, continuity, and derivatives
1. Find the limits:
3+x 3
(i) lim
x0
x
x3 + x2 sin
(ii) lim
x0
x
(iii)
lim
x
sin x
x
Solution
3+x3
1
1
3+x 3
3+x 3 3+x+ 3
= lim
= lim
= .
(i) lim
= lim
x 0 x ( 3 + x +
x 0
x 0
MATH1013-L4L5
Calculus I
Fall 2012
Practical Exercise 4 - Suggested Solution: Ch. 5 Integration
Q1. (Fundamental theorem of calculus) Evaluate the following denite integrals by the Fundamental
Theorem of Calculus.
2
Z
(a)
x2 dx =
1
3
Z
(b)
e
1
dx =
x ln x
MATH1013-L4L5
Calculus I
Fall 2012
Practical Exercise 4 : Ch. 5 Integration
Q1. (Fundamental theorem of calculus) Evaluate the following denite integrals by the Fundamental
Theorem of Calculus.
2
Z
(a)
x2 dx
=
1
3
Z
(b)
e
1
dx
x ln x
=
/2
Z
sin 2x dx
(c)
1
Math1013 Calculus I
Basic Problems on Derivatives
Get use to the limit denition of derivative: (i.e., by looking at slopes of nearby secant lines)
f (x) = lim
h0
f (x + x) f (x) or
f (t) f (x) or
y
f (x + h) f (x) or
= lim
= lim
= lim
t x
x 0
x 0 x
h