SECTION 2.1 (PAGE 98)
CHAPTER 2.
DIFFERENTIATION
R. A. ADAMS: CALCULUS
7. Slope of y =
x + 1 at x = 3 is
Section 2.1
(page 98)
4+h 2
4+h +2
h0
h
4+h +2
4+h4
= lim
h0 h
h+h+2
1
1
= lim
= .
h0
4
4+h +2
m = lim
Tangent Lines and Their Slopes
1. Slope of y =
MATH 3620 Assignment
Chapter 1:
1. (Do not use MATLAB) Compute the least-square polynomials of degree one and two for the
following data:
xi 0.0 0.25 0.5
0.75 1.0
yi 1.0 1.284 1.6487 2.117 2.7183
2. (MATLAB, polyt) Find the least-square polynomials of deg
MATH 3620 Assignment
Chapter 3:
1. (Do not use MATLAB) Let
f (x) = x4 3x3 + 3x2 3x + 2
use Fibonacci Method to nd the minimum of f (x) in the interval [1, 2], nd x5 .
Answer:
x1 = 1.375, x2 = 1.625, x3 = 1.750, x4 = 1.500, x5 = 1.625
2. (Do not use MATLAB
MATH 3620 Assignment
Chapter 1: (solution)
1. (Do not use MATLAB) Compute the least-square polynomials of degree one and two for the following data:
xi
yi
0.0
1.0
0.25
1.284
0.5
1.6487
0.75
2.117
1.0
2.7183
Solution:
Degree one: Let
5
[yi (axi + b)]2
E=
i
MATH 3620 Assignment
Chapter 2:
(Solution)
1. Consider the nonlinear system
3x2 x2 = 0;
1
2
3x1 x2 x3 1 = 0;
2
1
a)
Verify that this system can be changed to the xed point problem
x
p2 ;
x1 = g1 (x1 ; x2 ) =
3
q
x2 + x11
1
p
x2 = g2 (x1 ; x2 ) =
b)
3
:
Sh
MATH 3620 Assignment
Chapter 2: (due Wed, Mar. 1)
1. Consider the nonlinear system
3x2 x2 = 0;
1
2
3x1 x2 x3 1 = 0;
2
1
a)
Verify that this system can be changed to the xed point problem
x1
x2
b)
= g1 (x1 ; x2 ) =
p2
x
q3
= g2 (x1 ; x2 ) =
;
2
+ x11
p
x1
MATH 1005(2)
Course Overview
MATH 1005 Calculus
Course Information
Instructor: Dr. Felix KWOK
Lecture times and Venue:
Monday 14:30-15:20 @ LT2
Thursday 11:30-13:20 @ LT2
Tutorials (two sections):
Wednesday 13:30-14:20 @ CEC 801
Wednesday 14:30-15:
Chapter P: Preliminaries
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Hong Kong Baptist University
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Preliminaries
The preliminary chapter reviews the most important things
that you should know before beginning calculus.
Depending on your pre-calculus backg
Chapter P: Preliminaries
Fall 2014
Department of Mathematics
Hong Kong Baptist University
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History
Calculus was developed in the 17th century to study important
scientic and mathematical problems raised in physical science.
For instance, it can be u
Chapter 5: Integration
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Hong Kong Baptist University
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5.1 Sums and Sigma Notation
Denition (Sigma Notation)
If m and n are integers with m n, and if f is a function dened
at the integers m, m + 1, . . . , n, the sy
Chapter 7: Applications of Integration
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Hong Kong Baptist University
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7.1 Volumes by Slicing Solids of Revolution
In this section, we show how volumes of certain
three-dimensional regions (or solids) can be express
Chapter 4: More Applications of Dierentiation
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In the fall of 1972, President Nixon announced that,
the rate of increase of ination was decreasing.
This was the rst time a sitting pres
Chapter 2: Dierentiation
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2.1 Tangent Lines and Their Slopes
This section deals with the problem of nding a straight line L
that is tangent to a curve C at a point P.
Let C be the grap
Chapter 1: Limits and Continuity
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1.1 Examples where limits arise
Calculus has two basic procedures: dierentiation and
integration. Both of the procedures are based on the
fundamental
Chapter 6: Techniques of Integration
Fall 2014
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Hong Kong Baptist University
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6.1 Integration by Parts
In 5.6, we have introduced the method of substitution.
Recall that the method of substitution can be regarded as
inverse
Chapter 3: Transcendental Functions
Fall 2014
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Hong Kong Baptist University
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Except for the power functions, the other basic elementary
functions are also called the transcendental functions.
Transcendental functions cannot
MATH 3620 Assignment
Chapter 3:
1. (Do not use MATLAB) Let
( ) = x4 3 x3 + 3 x2 3 x + 2
f x
use Fibonacci Method to nd the minimum of f (x) in the interval [1; 2], nd
x5
.
2. (Do not use MATLAB) Let
( ) = x4 3 x3 + 3 x2 3 x + 2
f x
use Golden Section Meth
MATH 3620 Assignment
Chapter 4:
1. (Do not use MATLAB) Use Euler's method with h = 0:2 to approximate the solution of the
following initial-value problems:
yH = sin t + et ; 0
Solution.
Use Euler's method
we have
t
1; y (0) = 0:
wi+1 = wi + hf (ti ; wi )
MATH 3620 Assignment
Chapter 5:
1. (MATLAB) Use the nonlinear shooting with secant method to solve the boundary value
problem
y HH = y H + 2(y ln x)3 x1 ;
1
x
2;
y (1) = 1;
y (2) = 1=2 + ln 2;
(Take h = 0:1 and tol = 104 . Exact: y = x1 + ln x)
Solution.
Chapter 1. Approximations
Section 1. Discrete Least-Square Approximation
Polynomial approximations. Given a set of discrete points
i = 0, 1, , M,
(xi , yi ),
then a polynomial of degree n can be obtained which ts the set of points by use of
interpolation.
Chapter 3. Optimization
Section 1. Introduction
This chapter is concerned with methods for nding the optimum value (maximum
or minimum) of a function f (x1 , x2 , , xn ) of n real variables. If the function refers to
the prot obtained by producing quantit
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SEMESTER 2 EXAMINATION, 1996-97
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SEMESTER 2 EXAMINATION, 2000-2001
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SEMESTER 2 EXAMINATION, 1995-96
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2
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SEMESTER 2 EXALNIINATION, 1997-98
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Subject Title: Numerical Methods II Total Number of Pages: 2
W
INSTRUCTIONS:
i 1. Answer ALL of the follo