The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2013
MATH1003 Calculus and Linear Algebra, 201213 Fall
Week 08 Worksheet: Derivative and Differentiation Rules
(L5L6)
ID No.:
Name:
T u t o r i a l Section:
1. (P.667, Q. 1 ) Identify the following based on the function graph:
(a) the intervals on which f l
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
HKUST
MATH1003 Calculus and Linear Algebra
Midterm Examination {Vernon A)
2s?h October 2012
14:0015:30
Name:
Student ID:
Lecture Section:
Directions:
0 Do NOT open the exam until instructed to do so.
0 Please turn off all phones and pagers, and remove h
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2015
Systems of Linear Equations in Two Variables
MATH 1003 Calculus and Linear Algebra
(Lecture 4)
Hai Zhang
Department of Mathematics, HKUST
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 4)
Systems of Linear Equati
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
Math1003 Algebra and Calculus, Fall 2011
Homework7 : Due 11/24/2016 at 11:55pm HKT
Name: Xiao Yu Zerlinda LI
Antiderivatives, Indefinite and Definite Integrals and Their
Applications
3. (5 pts) Note: You can get full credit for this problem by
just answe
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
Math1003 Algebra and Calculus, Fall 2011
Homework4 : Due 10/24/2016 at 11:50pm HKT
Name: Xiao Yu Zerlinda LI
x
,
y
.
SOLUTION
(a) The values of f (x) are
Evaluating Limits:
by graphs
by limit properties and algebra
Applications of Limits:
horizontal a
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
Math1003 Algebra and Calculus, Fall 2011
Homework8 : Due 11/30/2016 at 11:55pm HKT
Name: Xiao Yu Zerlinda LI
Antiderivatives, Indefinite and Definite Integrals and Their
Applications
We can estimate the integral with a left or right Riemann sum,
or with
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
Math1003 Algebra and Calculus, Fall 2011
Homework3 : Due 10/05/2016 at 11:55pm HKT
Name: Xiao Yu Zerlinda LI
Augmented Matrices and GaussJordan Elimination
Express systems of linear equations in terms of augmented matrices.
Perform row operations to f
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
Math1003 Algebra and Calculus, Fall 2011
Homework5 : Due 10/31/2016 at 11:50pm HKT
Name: Xiao Yu Zerlinda LI
Derivatives and Differentiation Rules
Derivatives of power functions, exponential functions and logarithmic functions
dxn
dex
d ln x
1
= nxn1 ,
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
Math1003 Algebra and Calculus, Fall 2011
Homework1 : Due 09/19/2016 at 11:55pm HKT
Name: Xiao Yu Zerlinda LI
This is a set of homework questions to let you get familiar with the basic
types of questions that WeBWorK can ask. Here is how to proceed in gen
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
Math1003 Algebra and Calculus, Fall 2011
Homework2 : Due 09/19/2016 at 11:55pm HKT
Name: Xiao Yu Zerlinda LI
The three fundamental formulas you need for solving the problems in this
homework set are the following:
The Compound Interest Formula:
A = P(1 +
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
Quiz 2
Please write down your name, ID, and Tutorial Section number (or
date & time)
Questions:
1 (a) Find the inverse of the following
2 1
1 2
0 1
matrix.
0
1
1
(b) Solve the following system of linear equation.
=1
2x1 + x2
x1 + 2x2 + x3 = 1
x2 + x3 = 1
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
Quiz 3
Please write down your name, ID, and Tutorial Section number (or
date & time)
Questions:
Find the derivative of the following functions
3x 2
7
1. f (x) =
2
2
5x
3
2. g (x) = ln x + 2e x
3. h(x) = x 6 ln x
Solutions of Quiz 2
Solutions:
1. f 0 (x)
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
Quiz 4
Please write down your name, ID, and Tutorial Section number (or
date & time)
Questions:
1. A point is moving on the graph of x 3 + y 2 = 1 in such a way
that its y coordinate is always increasing at rate of 2 units per
second. How fast is the x co
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
HKUST
MATH1003 Calculus and Linear Algebra
Midterm Exam (Version C) Name:
8th October 2016 Student ID:
10:3012:00 Lecture Section:
Directions:
0 Do NOT open the exam until instructed to do so.
Please turn off all phones and pagers, and remove headphone
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
HKUST
MATH1003 Calculus and Linear Algebra
Midterm Exam (Version A)
Name:
8th October 2016
10:3012:00
Student ID:
Lecture Section:
Directions:
Do NOT open the exam until instructed to do so.
Please turn off all phones and pagers, and remove headphones.
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
MATH 1003 Calculus and Linear Algebra
(Lecture 12)
Hai Zhang
Department of Mathematics, HKUST
Sep 30, Wednesday, 2015
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 12)
General TwoIndustry Model
Suppose that we
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
MATH 1003 Calculus and Linear Algebra
(Lecture 19)
Hai Zhang
Department of Mathematics, HKUST
Oct 19, 2015, Monday
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 19)
Implicit Functions
Draw the curve in xy plane
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2015
Present Value of an Annuity
Amortization
MATH 1003 Calculus and Linear Algebra
(Lecture 3)
Hai Zhang
Department of Mathematics, HKUST
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 3)
Present Value of an Annuity
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2015
Examples
MATH 1003 Calculus and Linear Algebra
(Lecture 6)
Hai Zhang
Department of Mathematics, HKUST
Sep 14, Monday, 2015
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 6)
Examples
GaussJordan Elimination
In th
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2015
Compound Interest
Annual Percentage Yield
Future Value of an Annuity
Sinking Fund
MATH 1003 Calculus and Linear Algebra
(Lecture 2)
Hai Zhang
Department of Mathematics, HKUST
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2015
About MATH 1003
Simple Interest
Compound interest
MATH 1003 Calculus and Linear Algebra
(Lecture 1)
Hai Zhang
Department of Mathematics, HKUST
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 1)
About MATH 1003
Sim
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Summer 2015
BEng (Hons) in Mechanical Engineering (43478)
Combustion & Pollution Control (ME44003)
2015/16 S1
Homework assignment # 2 for Chapter 2
Combustion of Gaseous and Vaporised Fuels
Due Date: Oct 15, 2015 (Thursday)
(Compulsory Textbook: Turns S.R., An Intro
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
MATH 1003 Calculus and Linear Algebra
(Lecture 22)
Hai Zhang
Department of Mathematics, HKUST
Oct 28, 2015, Wednesday
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 22)
Concavity
Hai Zhang Department of Mathemati
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
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)
Limit of a function
Example
x2 1
. Then find
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
MATH 1003 Calculus and Linear Algebra
(Lecture 21)
Hai Zhang
Department of Mathematics, HKUST
Oct 26, 2015, Monday
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 21)
Increasing and Decreasing Functions
Definition
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
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 InputOutput Analysis
Wassily Leontie
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
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
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
MATH 1003 Calculus and Linear Algebra
(Lecture 26)
Hai Zhang
Department of Mathematics, HKUST
Nov 6, 2015, Friday
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 26)
Local Extrema and Absolute Extrema
Definition
I
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
MATH 1003 Calculus and Linear Algebra
(Lecture 20)
Hai Zhang
Department of Mathematics, HKUST
Oct 23, 2015, Friday
Hai Zhang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 20)
Related Rates
Given two variables x and y , wh
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2014
(MATH1003)[2013](f)midterm~vrzhao^_30074.pdf downloaded by twjlau from http:/petergao.net/ustpastpaper/down.php?course=MATH1003&id=2 at 20160919 00:51:56. Academic use within HKUST only.
HKUST
MATH1003 Calculus and Linear Algebra
Midterm Examination (Ve
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2013
MATH 1003 Review: Part 4. Integration
MATH 1003 Review: Part 4. Integration
Big Picture
I
I
F (x) is an antiderivative of f (x), if F 0 (x) = f (x).
Indefinite integral
Z
f (x)
dx
C .
=
F (x) + cfw_z
cfw_z
cfw_z
 cfw_z
integrand differential
I
Defin
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2013
MATH 1003 Review: Finance and Linear Algebra
Ke Wang
Department of Mathematics, HKUST
Ke Wang Department of Mathematics, HKUST
MATH 1003 Review: Finance and Linear Algebra
Mathematics of Finance (Ch. 3)
(a) Simple interest rate (Ch3.1)
A = P(1 + rt)
(b) C
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2013
MATH1003 Calculus and Linear Algebra, Tutorial
Week 02 Worksheet: Mathematics of Finance II
1. (Demonstration, Amortization ) (p. 162, Q 32) (A) A car costs $80,000. You pay 10% down and
amortize the rest with equal monthly payments over a 7year period
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2013
MATH 1003 Calculus and Linear Algebra
(Lecture 08)
Ke Wang
Department of Mathematics, HKUST
Ke Wang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 08)
Leontief InputOutput Analysis
Wassily Leontief was a RussianAmerican
The Hong Kong University of Science and Technology
Calculus I
MATH 1003

Fall 2013
MATH 1003 Calculus and Linear Algebra
(Lecture 07)
Ke Wang
Department of Mathematics, HKUST
Ke Wang Department of Mathematics, HKUST
MATH 1003 Calculus and Linear Algebra (Lecture 07)
Properties for Matrix Operation
Addition (A, B and C of same size)
I
As