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
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) S
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 suc
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.
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 su
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
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 (
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 (Lec
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 (Lect
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 (L
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 (Lec
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 (
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 (Lect
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)
M
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 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,
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
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 (larges
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 trend
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
n
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
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 polynomi
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
w
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 va
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 do
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 me
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
=
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
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
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