{"id":1437,"date":"2024-07-25T18:37:09","date_gmt":"2024-07-25T15:37:09","guid":{"rendered":"https:\/\/www.iem.ihu.gr\/?post_type=course&p=1437"},"modified":"2025-05-28T20:01:09","modified_gmt":"2025-05-28T17:01:09","slug":"16","status":"publish","type":"course","link":"https:\/\/www.iem.ihu.gr\/en\/courses\/16\/","title":{"rendered":"Calculus"},"author":5,"template":"","meta":{"_acf_changed":false},"semester":[10],"course_type":[58],"class_list":["post-1437","course","type-course","status-publish","hentry","semester-10","course_type-core"],"acf":{"code":"16","semester":10,"level":"1","teaching_activities":{"activity_1":{"description":"Theory","weekly_hrs":4,"ects":6},"activity_2":{"description":"Exercises","weekly_hrs":1,"ects":""},"activity_3":{"description":"","weekly_hrs":"","ects":""},"activity_4":{"description":"","weekly_hrs":"","ects":""},"activity_5":{"description":"","weekly_hrs":"","ects":""}},"type":58,"language":"\u0395\u03bb\u03bb\u03b7\u03bd\u03b9\u03ba\u03ac","erasmus":"\u038c\u03c7\u03b9","url":"https:\/\/exams-sm.the.ihu.gr\/enrol\/index.php?id=98","prerequisites":"","instructors":"","coordinator":"","content":"\u2022 Foundation of the real number system. Field and order axioms, the least upper bound axiom and the Archimedean principle.\r\n\u2022 Monotone and bounded real-valued functions, continuation of a real-valued function, Bolzano theorem, and intermediate value theorem, extreme value theorem, uniform continuity.\r\n\u2022 Elements of set theory, the system of real numbers.\r\n\u2022 Function derivative, derivative calculus and higher order derivatives, Rolle, Mean Value, and L\u2019Hospital theorems, local extrema.\r\n\u2022 The Riemann integral, integral properties (sum-difference rule, triangular inequality, linearity), differentiability and continuity, integral at points of discontinuity of the integrable function, integrability of continuous functions, mean value theorem, indefinite integral, fundamental theorem of integral calculus.\r\n\u2022 Integration techniques (variable change, integration by parts, etc.), logarithm and exponential function, generalized integrals, examples and applications.\r\n\u2022 Subsets of R, accumulation points, sequences of real numbers, monotonic sequences, subsequences and Cauchy\u2019s convergence criterion, Bolzano-Weierstrass theorem, convergence theorems for sequences.\r\n\u2022 Series of real numbers, series with positive terms, convergence and absolute convergence tests of series. Taylor's theorem and Taylor series.","goals":"The course is designed to provide the basic tools of advanced mathematics, including mainly elements of differential and integral calculus of functions of one variable. In particular, it focuses on the detailed presentation of mathematical concepts, theorems and propositions but also on problem-solving techniques related to them. For this purpose, extensive use is made of examples that find use in practical applications from the field of engineering.\r\nAs a background course, it offers the engineer the mathematical knowledge and the way of thinking in order to develop his \/ her ability to express mathematically and to face methodological practical problems.\r\nConsistent and successful course attendance has as expected learning outcomes for the student:\r\nto achieve the gradual theoretical logical subtraction from the real numbers, in the sense of the variable, in the definition of a function, in the sense of the differential of a function,\r\nto connect and be able to study the representations of a function (analytical form, graphical representation, verbal description),\r\nto understand theoretically and in practice the basic theorems of differential calculus,\r\nto understand the concept of the integral of a function and relate it to practical applications,\r\nto learn all the necessary techniques related to the differentiation and integration of functions,\r\nto identify and distinguish problem-solving methods related to the differentiation and integration of functions,\r\nto make him\/her capable to apply the above methods to engineering problems,\r\nto analyze and interpret the obtained results,\r\nto be able to attend, without significant learning gaps, more specialized courses of the department.","skills":"Research, analysis and synthesis of data and information, using corresponding technologies, Adaptation to new situations\r\nIndependent work, Teamwork \u2013 distribution of responsibilities, Intellectual competences, Societal competence.","teaching_methods":"Lectures, Exercises, Projected Presentations, Online Synchronous and Asynchronous Teaching Platform (moodle).","students_evaluation":"Assessment Language: Greek \/ English. Final Written Examinations. Evaluation criteria: Application of definitions, algorithms or propositions. Combination and synthesis of concepts and proof or computational procedures. Taking initiatives to implement problem-solving strategies.","bib_textbooks":"Calculus, Fourth Edition, by Michael Spivak\r\nThomas\u2019 Calculus, 14th edition, by Joel Hass, Christopher Heil, Maurice Weir\r\nCalculus, Second Edition, by William Briggs, Lyle Cochran, Bernard Gillett","bib_journals":""},"_links":{"self":[{"href":"https:\/\/www.iem.ihu.gr\/en\/wp-json\/wp\/v2\/course\/1437","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.iem.ihu.gr\/en\/wp-json\/wp\/v2\/course"}],"about":[{"href":"https:\/\/www.iem.ihu.gr\/en\/wp-json\/wp\/v2\/types\/course"}],"author":[{"embeddable":true,"href":"https:\/\/www.iem.ihu.gr\/en\/wp-json\/wp\/v2\/users\/5"}],"version-history":[{"count":12,"href":"https:\/\/www.iem.ihu.gr\/en\/wp-json\/wp\/v2\/course\/1437\/revisions"}],"predecessor-version":[{"id":4128,"href":"https:\/\/www.iem.ihu.gr\/en\/wp-json\/wp\/v2\/course\/1437\/revisions\/4128"}],"acf:term":[{"embeddable":true,"taxonomy":"course_type","href":"https:\/\/www.iem.ihu.gr\/en\/wp-json\/wp\/v2\/course_type\/58"},{"embeddable":true,"taxonomy":"semester","href":"https:\/\/www.iem.ihu.gr\/en\/wp-json\/wp\/v2\/semester\/10"}],"wp:attachment":[{"href":"https:\/\/www.iem.ihu.gr\/en\/wp-json\/wp\/v2\/media?parent=1437"}],"wp:term":[{"taxonomy":"semester","embeddable":true,"href":"https:\/\/www.iem.ihu.gr\/en\/wp-json\/wp\/v2\/semester?post=1437"},{"taxonomy":"course_type","embeddable":true,"href":"https:\/\/www.iem.ihu.gr\/en\/wp-json\/wp\/v2\/course_type?post=1437"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}