Numerical Methods Course Notes Version 0.1 (UCSD Math 174, Fall ...

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158 APPENDIX B. GNU FREE DOCUMENTATION LICENSE A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution medium, is called an ”aggregate” if the copyright resulting from the compilation is not used to limit the legal rights of the compilation’s users beyond what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document. If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire aggregate, the Document’s Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate. 8. TRANSLATION Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document, and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will prevail. If a section in the Document is Entitled ”Acknowledgements”, ”Dedications”, or ”History”, the requirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title. 9. TERMINATION You may not copy, modify, sublicense, or distribute the Document except as expressly provided for under this License. Any other attempt to copy, modify, sublicense or distribute the Document is void, and will automatically terminate your rights under this License. However, parties who have received copies, or rights, from you under this License will not have their licenses terminated so long as such parties remain in full compliance. 10. FUTURE REVISIONS OF THIS LICENSE The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See http://www.gnu.org/copyleft/. Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License ”or any later version” applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation. ADDENDUM: How to use this License for your documents To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page: Copyright c○YEAR YOUR NAME. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled ”GNU Free Documentation License”. If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the ”with...Texts.” line with this: with the Invariant Sections being LIST THEIR TITLES, with the Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST. If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation. If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.
Bibliography [1] Guillaume Bal. Lecture notes, course on numerical analysis, 2002. URL http://www.columbia.edu/~gb2030/COURSES/E6302/NumAnal.ps. [2] Samuel Daniel Conte and Carl de Boor. Elementary Numerical Analysis; An Algorithmic Approach. McGraw-Hill, New York, third edition, 1980. ISBN 0070124477. [3] James F. Epperson. An Introduction to Numerical Methods and Analysis. Wiley, 2001. ISBN 0-471-31647-4. [4] Richard Hamming. Numerical Methods for Scientists and Engineers. Dover, New York, 1987. ISBN 0486652416. [5] Eugene Isaacson and Herbert Bishop Keller. Analysis of Numerical Methods. Dover, New York, 1966. ISBN 0486680290. [6] David Kincaid and Ward Cheney. Numerical analysis. Brooks/Cole Publishing Co., Pacific Grove, CA, second edition, 1996. ISBN 0-534-33892-5. Mathematics of scientific computing. [7] David Kincaid and Ward Cheney. Numerical Mathematics and Computing. Brooks/Cole Publishing Co., Pacific Grove, CA, fourth edition, 1999. ISBN 0-534-35184-0. [8] James Stewart. Calculus, Early Transcendentals. Brooks/Cole-Thomson Learning, Belmont, CA, fifth edition, 2003. ISBN 0-534-39330-6. 159
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Numerical Methods Course Notes Vers
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Contents Acknowledgments i 1 Introd
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CONTENTS v 8 Integrals and Quadratu
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Chapter 1 Introduction 1.1 Taylor
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1.1. TAYLOR’S THEOREM 3 with the
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1.3. EIGENVALUES 5 To correct this
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1.3. EIGENVALUES 7 Example Problem
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1.3. EIGENVALUES 9 for all vectors
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Chapter 2 A “Crash” Course in o
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2.1. GETTING STARTED 13 77 22 333 o
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2.2. USEFUL COMMANDS 15 octave:22>
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2.3. PROGRAMMING AND CONTROL 17 x1
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2.4. PLOTTING 19 %just plot Y plot(
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2.4. PLOTTING 21 Exercises (2.1) Wh
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Chapter 3 Solving Linear Systems A
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3.1. GAUSSIAN ELIMINATION WITH NAÏ
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3.2. PIVOTING STRATEGIES FOR GAUSSI
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3.2. PIVOTING STRATEGIES FOR GAUSSI
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3.3. LU FACTORIZATION 31 appropriat
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3.3. LU FACTORIZATION 33 We pivot o
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3.4. ITERATIVE SOLUTIONS 35 3.3.3 S
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3.4. ITERATIVE SOLUTIONS 37 3.4.2 D
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3.4. ITERATIVE SOLUTIONS 39 We star
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3.4. ITERATIVE SOLUTIONS 41 Now not
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3.4. ITERATIVE SOLUTIONS 43 Remembe
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3.4. ITERATIVE SOLUTIONS 45 is the
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Chapter 4 Finding Roots 4.1 Bisecti
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4.2. NEWTON’S METHOD 49 Algorithm
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4.2. NEWTON’S METHOD 51 4.2.2 Pro
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4.3. SECANT METHOD 53 The following
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4.3. SECANT METHOD 55 Since the roo
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4.3. SECANT METHOD 57 relation betw
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4.3. SECANT METHOD 59 (b) f(x) = x
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Chapter 5 Interpolation 5.1 Polynom
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5.1. POLYNOMIAL INTERPOLATION 63 2
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5.1. POLYNOMIAL INTERPOLATION 65 Su
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5.2. ERRORS IN POLYNOMIAL INTERPOLA
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Chapter 6 Spline Interpolation Spli
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frag replacements 6.1. FIRST AND SE
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6.2. (NATURAL) CUBIC SPLINES 81 pro
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6.3. B SPLINES 83 The zero degree B
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6.3. B SPLINES 85 Exercises (6.1) I
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Chapter 7 Approximating Derivatives
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7.2. RICHARDSON EXTRAPOLATION 89 7.
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7.2. RICHARDSON EXTRAPOLATION 91 7.
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7.2. RICHARDSON EXTRAPOLATION 93 Ex
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Chapter 8 Integrals and Quadrature
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8.1. THE DEFINITE INTEGRAL 97 Examp
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8.2. TRAPEZOIDAL RULE 99 The compos
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frag replacements 8.2. TRAPEZOIDAL
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8.3. ROMBERG ALGORITHM 103 then def
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8.4. GAUSSIAN QUADRATURE 105 8.4 Ga
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Page 139 and 140: 10.2. RUNGE-KUTTA METHODS 131 Examp
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Page 153 and 154: Appendix A Old Exams A.1 First Midt
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Page 163 and 164: Appendix B GNU Free Documentation L
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