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. (
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, x
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
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 ;
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
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)
Chapter P: Preliminaries
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Preliminaries
The preliminary chapter reviews the most important things
that you should know before b
Chapter P: Preliminaries
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History
Calculus was developed in the 17th century to study important
scientic and mathematical problem
Chapter 5: Integration
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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 fun
Chapter 7: Applications of Integration
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7.1 Volumes by Slicing Solids of Revolution
In this section, we show how volumes of certa
Chapter 4: More Applications of Dierentiation
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In the fall of 1972, President Nixon announced that,
the rate of increase of inati
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
Chapter 1: Limits and Continuity
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1.1 Examples where limits arise
Calculus has two basic procedures: dierentiation and
integratio
Chapter 6: Techniques of Integration
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6.1 Integration by Parts
In 5.6, we have introduced the method of substitution.
Recall that
Chapter 3: Transcendental Functions
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Except for the power functions, the other basic elementary
functions are also called the tra
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
(
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 me
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
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 obtai
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 fu
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