{"id":9649960,"date":"2019-06-01T00:20:00","date_gmt":"2019-05-31T21:20:00","guid":{"rendered":"http:\/\/iee.it.teithe.gr\/course\/%ce%b1%cf%81%ce%b9%ce%b8%ce%bc%ce%b7%cf%84%ce%b9%ce%ba%ce%ad%cf%82-%ce%bc%ce%ad%ce%b8%ce%bf%ce%b4%ce%bf%ce%b9\/"},"modified":"2025-02-09T23:44:49","modified_gmt":"2025-02-09T20:44:49","slug":"1641","status":"publish","type":"course","link":"https:\/\/www.iee.ihu.gr\/en\/course\/1641\/","title":{"rendered":"Numerical Methods"},"content":{"rendered":"<p>\u2022 Error Theory: Errors, Floating Arithmetic, Error Transfer.<br \/>\n\u2022 Calculation of Series of Mathematical Functions: Series Calculation, Clipping Error, Correction.<br \/>\n\u2022 Numerical Solution of Equations: Isolation of Roots of Nonlinear Equations, Value Calculation, Polynomial Derivatives (Horner Scheme), Methods of Solving Nonlinear Equations (Convergence, Convergence Speed), Partitioning Method, Misfit, New, Sequential<br \/>\n\u2022 Solving Linear Equation Systems: Direct Methods (Diagonal Solution, Upper-Lower Triangular System, Gauss Deletion), Repetitive Methods (Gauss-Seidel, Jacobi Method).<br \/>\n\u2022 Ascending Differences: Forward, Backward, Central Differences, Error Transfer, Difference Rulers.<br \/>\n\u2022 Linear Interpolation: Newton-Gregory Interpolation types, Lagrange Interpolation types, correction to Interpolation types.<br \/>\n\u2022 Numerical Integration: Tables Method, Newton-Cotes Method, Simpson Method, Gauss Method<\/p>","protected":false},"author":1,"template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-9649960","course","type-course","status-publish","hentry"],"acf":[],"aioseo_notices":[],"post-meta-fields":{"course-semester":["6"],"_course-semester":["field_5d132f2c14d55"],"course-id":["1641"],"_course-id":["field_5d132b9c78b6e"],"course-group":["\u03a0\u0394\u03a4\u039d"],"_course-group":["field_5d14e905fe59a"],"course-type":["\u0395\u039e"],"_course-type":["field_5d133c6ba1599"],"course-compulsory":["\u03a5\u03a0-\u0395\u03a0"],"_course-compulsory":["field_5d146d39805a6"],"course-field":["\u03a0\u0391"],"_course-field":["field_5d146e248f2b3"],"course-ects":["6"],"_course-ects":["field_5d13518794761"],"course-hours-theory":["4"],"_course-hours-theory":["field_5d13521894762"],"course-hours-lab":[""],"_course-hours-lab":["field_5d1468d18a11f"],"_edit_lock":["1739133747:1"],"_edit_last":["1"],"course-school":["School of Engineering"],"_course-school":["field_5d132bf078b70"],"course-dept":["Department of Information and Electronic Engineering"],"_course-dept":["field_5d132c3a78b71"],"course-level":["1"],"_course-level":["field_5d132c5878b72"],"course-lang":["a:2:{i:0;s:2:\"el\";i:1;s:2:\"en\";}"],"_course-lang":["field_5d133e246f04b"],"course-erasmus":["1"],"_course-erasmus":["field_5d133e8e6f04c"],"course-url":["https:\/\/exams-iee.the.ihu.gr\/course\/view.php?id=113"],"_course-url":["field_5d133f9b5c292"],"course-prerequisites":["a:2:{i:0;s:7:\"9649930\";i:1;s:7:\"9649931\";}"],"_course-prerequisites":["field_5d13405189c17"],"course-aim":["The purpose of the course is for students to acquire basic knowledge of Numerical Analysis. The main objectives of the course are:\r\n\r\na) Introduction to error theory by presenting the definitions of rounding and clipping errors, the errors of converting real decimal numbers into floating point numbers on the PC and transmitting these errors into operations between floating point numbers.\r\nb) The approximate calculation of mathematical series and the simulation of the mathematical functions in the mathematical libraries of the programming languages.\r\nc) The presentation and study of approximate methods of finding the roots of nonlinear equations and polynomials and the creation of corresponding algorithms for their implementation on PC.\r\nd) The presentation and study of direct and approximate methods for solving linear equation systems.\r\ne) The study and presentation of methods for finding polynomial interpolations from a table of values \u200b\u200bof an unknown function.\r\ng) The presentation of approximate methods for finding some integrals and the development of corresponding algorithms for implementing illustrative examples of the above methods and their programming on a computer.\r\n\r\nUpon successful completion of the course the student will be able to:"],"_course-aim":["field_5d1353f985af8"],"course-goal-1":["Understand how errors affect storage, computation, and operations between real numbers on the PC."],"_course-goal-1":["field_5d13546e85af9"],"course-goal-2":["Apply the Mac Laurin expansions to simulate the mathematical functions that exist in the mathematical libraries of the programming languages and understand the resulting clipping errors."],"_course-goal-2":["field_5d1354f885afa"],"course-goal-3":["Apply the methods of finding root equations and polynomials and distinguish the advantages of each method in terms of speed and approximation of solutions."],"_course-goal-3":["field_5d13550085afb"],"course-goal-4":["Apply linear system solving methods and distinguish the advantages of each method in terms of speed and computational cost of the operations required to approximate the solutions."],"_course-goal-4":["field_5d13550e85afc"],"course-goal-5":["Apply the interpolation methods and estimate the error transmission in the difference tables."],"_course-goal-5":["field_5d13551485afd"],"course-goal-6":["Apply Numerical Integration methods and distinguish the advantages of each method in terms of speed and approximation of solutions."],"_course-goal-6":["field_5d13551b85afe"],"course-goal-7":[""],"_course-goal-7":["field_5d13552385aff"],"course-skills":[""],"_course-skills":["field_5d1355c25aeb4"],"course-teaching-method":["Person-to-person theoretical teaching (delivery, discussion, problem solving)"],"_course-teaching-method":["field_5d1383ec75a23"],"course-it-methods":["Using the moodle platform"],"_course-it-methods":["field_5d1384b975a24"],"course-activity-1":["Lectures"],"_course-activity-1":["field_5d1387d7cba43"],"course-activity-workload-1":["52"],"_course-activity-workload-1":["field_5d1388b2cba46"],"course-activity-2":["Writing and presenting compulsory work"],"_course-activity-2":["field_5d13886ccba44"],"course-activity-workload-2":[""],"_course-activity-workload-2":["field_5d1388e9cba47"],"course-activity-3":["Individual study and analysis of literature"],"_course-activity-3":["field_5d138878cba45"],"course-activity-workload-3":["128"],"_course-activity-workload-3":["field_5d13890dcba49"],"course-activity-4":[""],"_course-activity-4":["field_5d138947cba4b"],"course-activity-workload-4":[""],"_course-activity-workload-4":["field_5d13891dcba4a"],"course-activity-5":[""],"_course-activity-5":["field_5d14ed2508982"],"course-activity-workload-5":[""],"_course-activity-workload-5":["field_5d14ed3708983"],"course-student-evaluation":["Written project\r\nWritten examination\r\nLaboratory Exercises"],"_course-student-evaluation":["field_5d1389cff8c01"],"course-eudoxus-bib":["(\u0395\u03bb\u03bb\u03b7\u03bd\u03b9\u03ba\u03ac) \"\u0391\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03ae \u03b1\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7\", \u0396\u03ae\u03c4\u03b7 \u03a0\u03b5\u03bb\u03b1\u03b3\u03af\u03b1 &amp; \u03a3\u03b9\u03b1 \u0399.\u039a.\u0395., 1\u03b7 \u03ad\u03ba\u03b4., 2008, ISBN: 978-960-456-084-4, \u039a\u03c9\u03b4\u03b9\u03ba\u03cc\u03c2 \u0392\u03b9\u03b2\u03bb\u03af\u03bf\u03c5 \u03c3\u03c4\u03bf\u03bd \u0395\u03cd\u03b4\u03bf\u03be\u03bf: 10987\r\n\"\u0391\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03ad\u03c2 \u039c\u03ad\u03b8\u03bf\u03b4\u03bf\u03b9 \u03b3\u03b9\u03b1 \u039c\u03b7\u03c7\u03b1\u03bd\u03b9\u03ba\u03bf\u03cd\u03c2\", \u0395\u039a\u0394\u039f\u03a3\u0395\u0399\u03a3 \u0391. \u03a4\u0396\u0399\u039f\u039b\u0391 &amp; \u03a5\u0399\u039f\u0399 \u0391.\u0395., 7\u03b7 \u0388\u03ba\u03b4\u03bf\u03c3\u03b7 \u0392\u03b5\u03bb\u03c4\u03b9\u03c9\u03bc\u03ad\u03bd\u03b7, 2018, ISBN: 978-960-418-763-8, \u039a\u03c9\u03b4\u03b9\u03ba\u03cc\u03c2 \u0392\u03b9\u03b2\u03bb\u03af\u03bf\u03c5 \u03c3\u03c4\u03bf\u03bd \u0395\u03cd\u03b4\u03bf\u03be\u03bf: 77106818\r\n\"\u0395\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae \u03c3\u03c4\u03b7\u03bd \u0391\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03ae \u0391\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7\",  \u0395\u039a\u0394\u039f\u03a3\u0395\u0399\u03a3 \u0391. \u03a4\u0396\u0399\u039f\u039b\u0391 &amp; \u03a5\u0399\u039f\u0399 \u0391.\u0395., 2\u03b7 \u0388\u03ba\u03b4\u03bf\u03c3\u03b7, 2015, ISBN: 978-960-418-572-6, \u039a\u03c9\u03b4\u03b9\u03ba\u03cc\u03c2 \u0392\u03b9\u03b2\u03bb\u03af\u03bf\u03c5 \u03c3\u03c4\u03bf\u03bd \u0395\u03cd\u03b4\u03bf\u03be\u03bf: 50657724"],"_course-eudoxus-bib":["field_5d138e0af441c"],"course-greek-bib":["(\u0395\u03bb\u03bb\u03b7\u03bd\u03b9\u03ba\u03ac) \u03a3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03bf \u0398\u03b5\u03c9\u03c1\u03b7\u03c4\u03b9\u03ba\u03cc \u03bc\u03ad\u03c1\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u00ab\u0391\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03ae \u0391\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7 &amp; \u03a0\u03c1\u03bf\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03cc\u03c2 \u0395\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03bf\u03bd\u03b9\u03ba\u03ce\u03bd \u0395\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ce\u03bd \u2013 \u0398\u03b5\u03c9\u03c1\u03af\u03b1, \u03a0\u03b1\u03c1\u03b1\u03b4\u03b5\u03af\u03b3\u03bc\u03b1\u03c4\u03b1 \u03ba\u03b1\u03b9 \u0386\u03bb\u03c5\u03c4\u03b5\u03c2 \u0391\u03c3\u03ba\u03ae\u03c3\u03b5\u03b9\u03c2\u00bb. \u0393\u03bf\u03c5\u03bb\u03b9\u03ac\u03bd\u03b1\u03c2 \u039a\u03c9\u03bd\u03c3\u03c4\u03b1\u03bd\u03c4\u03af\u03bd\u03bf\u03c2, \u03a4\u03bc\u03ae\u03bc\u03b1 \u03a0\u03bb\u03b7\u03c1\u03bf\u03c6\u03bf\u03c1\u03b9\u03ba\u03ae\u03c2, \u0391\u03a4\u0395\u0399-\u0398, 2011.\r\n\u03a3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2 \u03b3\u03b9\u03b1 \u03c4\u03bf \u0395\u03c1\u03b3\u03b1\u03c3\u03c4\u03b7\u03c1\u03b9\u03b1\u03ba\u03cc \u03bc\u03ad\u03c1\u03bf\u03c2 \u03c4\u03bf\u03c5 \u03bc\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03bf\u03c2 \u00ab\u0395\u03c1\u03b3\u03b1\u03c3\u03c4\u03b7\u03c1\u03b9\u03b1\u03ba\u03ad\u03c2 \u0391\u03c3\u03ba\u03ae\u03c3\u03b5\u03b9\u03c2 \u0391\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03ae\u03c2 \u0391\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7\u03c2 \u03c3\u03c4\u03b7 \u0393\u03bb\u03ce\u03c3\u03c3\u03b1 \u03a0\u03c1\u03bf\u03b3\u03c1\u03b1\u03bc\u03bc\u03b1\u03c4\u03b9\u03c3\u03bc\u03bf\u03cd C\u00bb. \u0393\u03bf\u03c5\u03bb\u03b9\u03ac\u03bd\u03b1\u03c2 \u039a\u03c9\u03bd\u03c3\u03c4\u03b1\u03bd\u03c4\u03af\u03bd\u03bf\u03c2, \u03a4\u03bc\u03ae\u03bc\u03b1 \u03a0\u03bb\u03b7\u03c1\u03bf\u03c6\u03bf\u03c1\u03b9\u03ba\u03ae\u03c2, \u0391\u03a4\u0395\u0399-\u0398, 2007.\r\n\u039a\u03c5\u03c4\u03ac\u03b3\u03b9\u03b1\u03c2 \u0394\u03b7\u03bc\u03ae\u03c4\u03c1\u03b7\u03c2, \u0392\u03c1\u03c5\u03b6\u03af\u03b4\u03b7\u03c2 \u039b\u03ac\u03b6\u03b1\u03c1\u03bf\u03c2, \u201c\u0391\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03ae \u0391\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7\/\u0391\u03bb\u03b3\u03bf\u03c1\u03b9\u03b8\u03bc\u03b9\u03ba\u03ae \u03a0\u03c1\u03bf\u03c3\u03ad\u03b3\u03b3\u03b9\u03c3\u03b7\u201d: \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u038a\u03c9\u03bd, 1991.\r\n\u03a7\u03b1\u03c4\u03b6\u03b7\u03b4\u03ae\u03bc\u03bf\u03c2 \u0391\u03c0\u03cc\u03c3\u03c4\u03bf\u03bb\u03bf\u03c2, \u201c\u0395\u03b9\u03c3\u03b1\u03b3\u03c9\u03b3\u03ae \u03c3\u03c4\u03b7\u03bd \u0391\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03ae \u0391\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7\u201d: \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03b9\u03b1\u03ba\u03ad\u03c2 \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u0399\u03c9\u03b1\u03bd\u03bd\u03af\u03bd\u03c9\u03bd, 1977.\r\n\u03a7\u03b1\u03c4\u03b6\u03b7\u03b4\u03ae\u03bc\u03bf\u03c2 \u0391\u03c0\u03cc\u03c3\u03c4\u03bf\u03bb\u03bf\u03c2, \u201c\u0391\u03c1\u03b9\u03b8\u03bc\u03b7\u03c4\u03b9\u03ba\u03ae \u0391\u03bd\u03ac\u03bb\u03c5\u03c3\u03b7 \u0399 \u03ba\u03b1\u03b9 \u0399\u0399\u201d: \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03b9\u03b1\u03ba\u03ad\u03c2 \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u0399\u03c9\u03b1\u03bd\u03bd\u03af\u03bd\u03c9\u03bd, 1979."],"_course-greek-bib":["field_5d138e3cf441d"],"course-intl-bib":["Stoer, Josef, Bulirsch, R., Introduction to Numerical Analysis, Springer-Verlag New York, 3, 2002, 978-0-387-21738-3"],"_course-intl-bib":["field_5d138e74f441e"],"course-rel-journals":[""],"_course-rel-journals":["field_5d138ec4f441f"],"course-teachers":["a:1:{i:0;s:7:\"9651016\";}"],"_course-teachers":["field_5d3aa2923f803"],"_wp_old_slug":["%ce%b1%cf%81%ce%b9%ce%b8%ce%bc%ce%b7%cf%84%ce%b9%ce%ba%ce%ad%cf%82-%ce%bc%ce%ad%ce%b8%ce%bf%ce%b4%ce%bf%ce%b9"],"course-coordinator":["a:1:{i:0;s:7:\"9651016\";}"],"_course-coordinator":["field_5faa4466f1b87"],"_aioseo_title":[null],"_aioseo_description":[null],"_aioseo_keywords":["a:0:{}"],"_aioseo_og_title":[null],"_aioseo_og_description":[null],"_aioseo_og_article_section":[""],"_aioseo_og_article_tags":["a:0:{}"],"_aioseo_twitter_title":[null],"_aioseo_twitter_description":[null]},"_links":{"self":[{"href":"https:\/\/www.iee.ihu.gr\/en\/wp-json\/wp\/v2\/course\/9649960","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.iee.ihu.gr\/en\/wp-json\/wp\/v2\/course"}],"about":[{"href":"https:\/\/www.iee.ihu.gr\/en\/wp-json\/wp\/v2\/types\/course"}],"author":[{"embeddable":true,"href":"https:\/\/www.iee.ihu.gr\/en\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":5,"href":"https:\/\/www.iee.ihu.gr\/en\/wp-json\/wp\/v2\/course\/9649960\/revisions"}],"predecessor-version":[{"id":9673183,"href":"https:\/\/www.iee.ihu.gr\/en\/wp-json\/wp\/v2\/course\/9649960\/revisions\/9673183"}],"wp:attachment":[{"href":"https:\/\/www.iee.ihu.gr\/en\/wp-json\/wp\/v2\/media?parent=9649960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}