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HP HP-15C Advanced Functions Handbook
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2
0
Sectio
n
1
:
Usin
g
[SOLVE
|
Effectivel
y
Th
e
relativ
e
fiel
d
intensit
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i
s
mos
t
negativ
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a
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a
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o
f
28.0680
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a
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Approximat
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Slop
e
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e
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als
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f(
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21
23
Table of Contents
Table of Contents
4
Contents
5
Introduction
7
Section 1: Using
8
Finding Roots
8
How SOLVE Samples
9
Handling Troublesome Situations
11
Easy Versus Hard Equations
11
Inaccurate Equations
12
Equations with Several Roots
12
Using | SOLVE | with Polynomials
12
Solving a System of Equations
17
Finding Local Extremes of a Function
19
Using the Derivative
19
Using an Approximate Slope
22
Using Repeated Estimation
25
Applications
28
Annuities and Compound Amounts
28
Discounted Cash Flow Analysis
41
Section 2: Working with
47
Numerical Integration Using |7T
47
Accuracy of the Function to be Integrated
49
Functions Related to Physical Situations
49
Round-Off Error in Internal Calculations
51
Shortening Calculation Time
51
Subdividing the Interval of Integration
52
Transformation of Variables
56
Calculating Difficult Integrals
57
Application
62
Section 3: Calculating in Complex Mode
67
Using Complex Mode
67
Trignomometric Modes
70
Definitions of Math Functions
70
Arithmetic Operations
71
Single-Valued Functions
71
Multivalued Functions
71
Using | SOLVE | and |7T| in Complex Mode
75
Acuracy in Complex Mode
75
Applications
78
Storing and Recalling Complex Numbers Using a Matrix
78
Calculating the /?Th Roots of a Complex Number
80
Solving an Equation for Its Complex Roots
82
Contour Integrals
87
Complex Potentials
91
Section 4: Using Matrix Operations
98
Understanding the LU Decomposition
98
Ill-Conditioned Matrices and the Condition Number
100
The Accuracy of Numerical Solutions to Linear Systems
105
Making Difficult Equations Easier
106
Scaling
106
Preconditioning 1
109
Least-Squares Calculations
112
Normal Equations
112
Orthogonal Factorization
115
Singular and Nearly Singular Matrices
119
Applications
121
Constructing an Identity Matrix
121
One-Step Residual Correction
121
Solving a System of Nonlinear Equations
124
Solving a Large System of Complex Equations
130
Least-Squares Using Normal Equations
133
Least-Squares Using Successive Rows
142
Eigenvalues of a Symmetric Real Matrix
150
Eigenvectors of a Symmetric Real Matrix
156
Optimization 1
162
Appendix: Accuracy of Numerical Calculations
174
Misconceptions about Errors
174
A Hierarchy of Errors
180
Level 0: no Error
180
Level Oo : Overflow/Underflow
181
Level 1: Correctly Rounded, or Nearly so
181
Level 1C: Complex Level 1
185
Level 2: Correctly Rounded for Possibly Perturbed Input 1
186
Trigonometric Functions of Real Radian Angles
186
Backward Error Analysis
189
Backward Error Analysis Versus Singularities
194
Summary to here
196
Backward Error Analysis of Matrix Inversion
202
Is Backward Error Analysis a Good Idea
206
Index
214
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HP HP-15C Specifications
General
Brand
HP
Model
HP-15C
Category
Calculator
Language
English
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