{"id":1446,"date":"2023-05-12T17:28:31","date_gmt":"2023-05-12T14:28:31","guid":{"rendered":"https:\/\/www.civil.ihu.gr\/?post_type=course&#038;p=1446"},"modified":"2023-11-14T16:40:29","modified_gmt":"2023-11-14T14:40:29","slug":"%ce%b3%ce%b5%ce%bd004","status":"publish","type":"course","link":"https:\/\/www.civil.ihu.gr\/en\/courses\/%ce%b3%ce%b5%ce%bd004\/","title":{"rendered":"Differential and Integral Calculus \u0399\u0399"},"author":6,"template":"","meta":{"_acf_changed":false},"semester":[11],"course_type":[12],"class_list":["post-1446","course","type-course","status-publish","hentry","semester-11","course_type-general_background"],"acf":{"code":"\u0393\u0395\u039d004 ","semester":11,"level":"1","teaching_activities":{"activity_1":{"description":"\u0394\u03b9\u03b1\u03bb\u03ad\u03be\u03b5\u03b9\u03c2","weekly_hrs":4,"ects":5},"activity_2":{"description":"","weekly_hrs":"","ects":""},"activity_3":{"description":"","weekly_hrs":"","ects":""},"activity_4":{"description":"","weekly_hrs":"","ects":""},"activity_5":{"description":"","weekly_hrs":"","ects":""}},"type":12,"language":"\u0395\u03bb\u03bb\u03b7\u03bd\u03b9\u03ba\u03ac","erasmus":"\u039d\u03b1\u03b9","url":"","prerequisites":[1422,1417],"instructors":"","coordinator":"","content":"Course content: 1. Introduction to functions of two real variables, examples of graphical\r\nrepresentations, sphere, ellipsoid, paraboloid, cone, intersection of surfaces and planes, domain and\r\ndefinition of continuity for z=f(x, y). 2. The concept of partial derivative, physical and geometric\r\ninterpretation, types and theorems of partial derivatives. The concept of total differential, higherorder partial derivatives. 3. Study of extrema, the problem of least squares, constrained extrema 4.\r\nDouble Integrals, their physical and geometric interpretation, properties, and methods of\r\ncomputation. Types of integration domains 5. Double integrals, change of variables. Polar\r\nCoordinates. Generalization of the Change of Variables Problem, moment of Inertia of a Plane\r\nSurface. 6. Triple Integrals. Physical Interpretation. Properties and Computation Methods 7-9.\r\nFundamental knowledge of vector analysis: scalar and vector fields, vector functions. Derivative of a\r\nvector function. Angular velocity. Uniform circular motion. Arc length of a curve. Derivative of z=f(x,y)\r\nin a given direction. Integration of vector functions. Gradient of scalar fields. Divergence and curl of\r\nvector fields 10-11. Line integrals (definition, properties and calculation methods). Path-independent\r\nline integrals. Conservative vector fields. 12. Surface integrals (definition, properties and calculation\r\nmethods). 13. Stokes' theorem and Gauss's Divergence theorem","goals":"Upon completing this course students should be able to use: functions of most variables and\r\nrecognize their graphic representations 2. The concepts of partial derivative and total differential 3.\r\nThe solving of double and triple integrals 4. Basic concepts of Differential Geometry 5. Line integrals\r\nand surface integrals. 6. Implement the above in the field of Civil Engineering.","skills":"The course contributes to the following skills:\r\n- Working independently\r\n- Production of free, creative and inductive thinking","teaching_methods":"Face to face.","ict_usage":"Poweroint presentations, Excel, Matlab\/Octave, E-learning\r\nplatform for educational material.","teaching_organization":{"activity_1":{"description":"Lectures","workload":52},"activity_2":{"description":"Individual study","workload":52},"activity_3":{"description":"Practice\/exercises","workload":26},"activity_4":{"description":"TOTAL","workload":130},"activity_5":{"description":"","workload":""},"activity_6":{"description":"","workload":""}},"students_evaluation":"Final written examination\r\n- open-ended questions (30-40%)\r\n- problem - solving questions (70-60%)","bib_textbooks":"<ul>\r\n \t<li>\u03a4\u03b5\u03c1\u03b6\u03af\u03b4\u03b7\u03c2 \u03a7\u03b1\u03c1\u03ac\u03bb\u03b1\u03bc\u03c0\u03bf\u03c2, \u039b\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc\u03c2 \u03a3\u03c5\u03bd\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03c9\u03bd \u03c0\u03bf\u03bb\u03bb\u03ce\u03bd \u039c\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ce\u03bd &amp; \u0394\u03b9\u03b1\u03c6\u03bf\u03c1\u03b9\u03ba\u03ad\u03c2\r\n\u0395\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2, \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u0391\u03bd\u03b9\u03ba\u03bf\u03cd\u03bb\u03b1, \u0398\u03b5\u03c3\u03c3\u03b1\u03bb\u03bf\u03bd\u03af\u03ba\u03b7 2006 ISBN: 9789605160319<\/li>\r\n \t<li>Hass J., Heil C., Weir M.D., \u0391\u03c0\u03b5\u03b9\u03c1\u03bf\u03c3\u03c4\u03b9\u03ba\u03cc\u03c2 \u039b\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc\u03c2, \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03b9\u03b1\u03ba\u03ad\u03c2 \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u039a\u03c1\u03ae\u03c4\u03b7\u03c2,\r\n\u039a\u03c1\u03ae\u03c4\u03b7 2015, ISBN 978-960-524-515-3, \u039a\u03c9\u03b4\u03b9\u03ba\u03cc\u03c2 \u03c3\u03c4\u03bf\u03bd \u0395\u03cd\u03b4\u03bf\u03be\u03bf: 77107082<\/li>\r\n \t<li>\u039c\u03c0\u03c1\u03ac\u03c4\u03c3\u03bf\u03c2 \u0391\u03b8\u03b1\u03bd\u03ac\u03c3\u03b9\u03bf\u03c2, \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03b1 \u0391\u03bd\u03ce\u03c4\u03b5\u03c1\u03c9\u03bd \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd, ISBN 978-960-603-030-7,\r\n[\u03b7\u03bb\u03b5\u03ba\u03c4\u03c1. \u03b2\u03b9\u03b2\u03bb.] \u0391\u03b8\u03ae\u03bd\u03b1: \u03a3\u03cd\u03bd\u03b4\u03b5\u03c3\u03bc\u03bf\u03c2 \u0395\u03bb\u03bb\u03b7\u03bd\u03b9\u03ba\u03ce\u03bd \u0391\u03ba\u03b1\u03b4\u03b7\u03bc\u03b1\u03ca\u03ba\u03ce\u03bd \u0392\u03b9\u03b2\u03bb\u03b9\u03bf\u03b8\u03b7\u03ba\u03ce\u03bd, \u0397\u03bb\u03b5\u03ba\u03c4\u03c1\u03bf\u03bd\u03b9\u03ba\u03ae\r\n\u0394\u03b9\u03b5\u03cd\u03b8\u03c5\u03bd\u03c3\u03b7: https:\/\/repository.kallipos.gr\/handle\/11419\/424<\/li>\r\n \t<li>\u03a0\u03b1\u03c0\u03b1\u03ca\u03c9\u03ac\u03bd\u03bd\u03bf\u03c5 \u03a3\u03c4\u03b1\u03cd\u03c1\u03bf\u03c2, \u03a3\u03b7\u03bc\u03b5\u03b9\u03ce\u03c3\u03b5\u03b9\u03c2, \u0397\u03bb\u03b5\u03ba\u03c4\u03c1\u03bf\u03bd\u03b9\u03ba\u03ae \u0394\u03b9\u03b5\u03cd\u03b8\u03c5\u03bd\u03c3\u03b7:\r\nhttp:\/\/pde.teiser.gr\/papaioannou\/Mathimatika_2.asp<\/li>\r\n \t<li>[In Greek]. \u03a4\u03b5\u03c1\u03b6\u03af\u03b4\u03b7\u03c2 \u03a7\u03b1\u03c1\u03ac\u03bb\u03b1\u03bc\u03c0\u03bf\u03c2, \u039b\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc\u03c2 \u03c3\u03c5\u03bd\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03c9\u03bd \u03bc\u03b9\u03b1\u03c2 \u03bc\u03b5\u03c4\u03b1\u03b2\u03bb\u03b7\u03c4\u03ae\u03c2 \u03bc\u03b5 \u03c3\u03c4\u03bf\u03b9\u03c7\u03b5\u03af\u03b1 \u03b4\u03b9\u03b1\u03bd\u03c5\u03c3\u03bc\u03b1\u03c4\u03b9\u03ba\u03ae\u03c2\r\n\u03b3\u03c1\u03b1\u03bc\u03bc\u03b9\u03ba\u03ae\u03c2 \u03ac\u03bb\u03b3\u03b5\u03b2\u03c1\u03b1\u03c2, \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u03a7\u03c1\u03b9\u03c3\u03c4\u03bf\u03b4\u03bf\u03c5\u03bb\u03af\u03b4\u03b7\u03c2, \u0398\u03b5\u03c3\u03c3\u03b1\u03bb\u03bf\u03bd\u03af\u03ba\u03b7 2006\r\n[In greek]. Hass J., Heil C., Weir M.D., \u0391\u03c0\u03b5\u03b9\u03c1\u03bf\u03c3\u03c4\u03b9\u03ba\u03cc\u03c2 \u039b\u03bf\u03b3\u03b9\u03c3\u03bc\u03cc\u03c2, \u03a0\u03b1\u03bd\u03b5\u03c0\u03b9\u03c3\u03c4\u03b7\u03bc\u03b9\u03b1\u03ba\u03ad\u03c2 \u0395\u03ba\u03b4\u03cc\u03c3\u03b5\u03b9\u03c2 \u039a\u03c1\u03ae\u03c4\u03b7\u03c2,\r\n\u039a\u03c1\u03ae\u03c4\u03b7 2005, ISBN 978-960-524-515-3, \u039a\u03c9\u03b4\u03b9\u03ba\u03cc\u03c2 \u03c3\u03c4\u03bf\u03bd \u0395\u03cd\u03b4\u03bf\u03be\u03bf: 77107082\r\n[In greek]. \u039c\u03c0\u03c1\u03ac\u03c4\u03c3\u03bf\u03c2 \u0391\u03b8\u03b1\u03bd\u03ac\u03c3\u03b9\u03bf\u03c2, \u039c\u03b1\u03b8\u03ae\u03bc\u03b1\u03c4\u03b1 \u0391\u03bd\u03ce\u03c4\u03b5\u03c1\u03c9\u03bd \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ce\u03bd, ISBN 978-960-603-030-7,\r\n[\u03b7\u03bb\u03b5\u03ba\u03c4\u03c1. \u03b2\u03b9\u03b2\u03bb.] \u0391\u03b8\u03ae\u03bd\u03b1: \u03a3\u03cd\u03bd\u03b4\u03b5\u03c3\u03bc\u03bf\u03c2 \u0395\u03bb\u03bb\u03b7\u03bd\u03b9\u03ba\u03ce\u03bd \u0391\u03ba\u03b1\u03b4\u03b7\u03bc\u03b1\u03ca\u03ba\u03ce\u03bd \u0392\u03b9\u03b2\u03bb\u03b9\u03bf\u03b8\u03b7\u03ba\u03ce\u03bd, \u0397\u03bb\u03b5\u03ba\u03c4\u03c1\u03bf\u03bd\u03b9\u03ba\u03ae\r\n\u0394\u03b9\u03b5\u03cd\u03b8\u03c5\u03bd\u03c3\u03b7: https:\/\/repository.kallipos.gr\/handle\/11419\/424\r\n[In greek} \u03a0\u03b1\u03c0\u03b1\u03ca\u03c9\u03ac\u03bd\u03bd\u03bf\u03c5 \u03a3\u03c4\u03b1\u03cd\u03c1\u03bf\u03c2, \u0392\u03bf\u03b3\u03b9\u03b1\u03c4\u03b6\u03ae, \u0394\u03ad\u03c3\u03c0\u03bf\u03b9\u03bd\u03b1, \u039c\u03b1\u03b8\u03b7\u03bc\u03b1\u03c4\u03b9\u03ba\u03ac \u0399, ISBN 978-960-603-427-5,\r\n[\u03b7\u03bb\u03b5\u03ba\u03c4\u03c1. \u03b2\u03b9\u03b2\u03bb.] \u0391\u03b8\u03ae\u03bd\u03b1: \u03a3\u03cd\u03bd\u03b4\u03b5\u03c3\u03bc\u03bf\u03c2 \u0395\u03bb\u03bb\u03b7\u03bd\u03b9\u03ba\u03ce\u03bd \u0391\u03ba\u03b1\u03b4\u03b7\u03bc\u03b1\u03ca\u03ba\u03ce\u03bd \u0392\u03b9\u03b2\u03bb\u03b9\u03bf\u03b8\u03b7\u03ba\u03ce\u03bd, \u0397\u03bb\u03b5\u03ba\u03c4\u03c1\u03bf\u03bd\u03b9\u03ba\u03ae\r\n\u0394\u03b9\u03b5\u03cd\u03b8\u03c5\u03bd\u03c3\u03b7: https:\/\/repository.kallipos.gr\/handle\/11419\/4551<\/li>\r\n<\/ul>","bib_journals":""},"_links":{"self":[{"href":"https:\/\/www.civil.ihu.gr\/en\/wp-json\/wp\/v2\/course\/1446","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.civil.ihu.gr\/en\/wp-json\/wp\/v2\/course"}],"about":[{"href":"https:\/\/www.civil.ihu.gr\/en\/wp-json\/wp\/v2\/types\/course"}],"author":[{"embeddable":true,"href":"https:\/\/www.civil.ihu.gr\/en\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":4,"href":"https:\/\/www.civil.ihu.gr\/en\/wp-json\/wp\/v2\/course\/1446\/revisions"}],"predecessor-version":[{"id":1957,"href":"https:\/\/www.civil.ihu.gr\/en\/wp-json\/wp\/v2\/course\/1446\/revisions\/1957"}],"acf:post":[{"embeddable":true,"href":"https:\/\/www.civil.ihu.gr\/en\/wp-json\/wp\/v2\/course\/1417"},{"embeddable":true,"href":"https:\/\/www.civil.ihu.gr\/en\/wp-json\/wp\/v2\/course\/1422"}],"acf:term":[{"embeddable":true,"taxonomy":"course_type","href":"https:\/\/www.civil.ihu.gr\/en\/wp-json\/wp\/v2\/course_type\/12"},{"embeddable":true,"taxonomy":"semester","href":"https:\/\/www.civil.ihu.gr\/en\/wp-json\/wp\/v2\/semester\/11"}],"wp:attachment":[{"href":"https:\/\/www.civil.ihu.gr\/en\/wp-json\/wp\/v2\/media?parent=1446"}],"wp:term":[{"taxonomy":"semester","embeddable":true,"href":"https:\/\/www.civil.ihu.gr\/en\/wp-json\/wp\/v2\/semester?post=1446"},{"taxonomy":"course_type","embeddable":true,"href":"https:\/\/www.civil.ihu.gr\/en\/wp-json\/wp\/v2\/course_type?post=1446"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}