{"id":2233,"date":"2023-07-24T14:38:33","date_gmt":"2023-07-24T11:38:33","guid":{"rendered":"http:\/\/www.food.ihu.gr\/?post_type=course&#038;p=2233"},"modified":"2024-09-12T12:02:48","modified_gmt":"2024-09-12T09:02:48","slug":"276-190101","status":"publish","type":"course","link":"https:\/\/www.food.ihu.gr\/en\/courses\/276-190101\/","title":{"rendered":"Mathematics I"},"author":6,"template":"","meta":[],"semester":[10],"course_type":[76],"acf":{"code":"276-190101","semester":10,"level":"1","teaching_activities":{"activity_1":{"description":"Lectures","weekly_hrs":3,"ects":6},"activity_2":{"description":"Practical Exercises","weekly_hrs":1,"ects":""},"activity_3":{"description":"","weekly_hrs":"","ects":""},"activity_4":{"description":"","weekly_hrs":"","ects":""},"activity_5":{"description":"","weekly_hrs":"","ects":""}},"type":76,"language":"Greek","erasmus":"\u038c\u03c7\u03b9","url":"https:\/\/exams-geo.the.ihu.gr\/course\/view.php?id=208","prerequisites":"","instructors":[1405],"coordinator":"","content":"<ul>\r\n \t<li>Real analysis of single-variable functions:\r\nContinuity and limits of functions. Differentiation. Extreme values of functions. Application of derivatives in engineering. Integration. Integrals of elementary functions. Numerical integration. Trapezoidal rule and Simpson's rule to approximate definite integrals. Application of integration in engineering.<\/li>\r\n \t<li>An introduction to linear programming:\r\nSimplex method for linear optimization. A geometric interpretation of linear optimization problems with two variables. Application of Simplex method in optimal design.<\/li>\r\n \t<li>Nonlinear equations:\r\nSolving exponential equations. Solving equations with complex numbers<\/li>\r\n \t<li>Basic probability theory:\r\nDefinitions of probability. Venn diagrams. Mathematical formulation of probability. Properties of probability. Conditional probability. Total probability and the Bayes\u2019 theorem. Discrete and continuous random variables. Distribution functions. Expected values. Moments of random variables and the variance. Application of probability in engineering.<\/li>\r\n<\/ul>","goals":"The course aims to achieve the following learning outcomes for students:\r\n<ul>\r\n \t<li>Acquiring knowledge in the basic Mathematics concepts and skills for food science and technology.<\/li>\r\n \t<li>Application of Mathematics in the food industry in the form of computational exercises.<\/li>\r\n<\/ul>","skills":"<ul>\r\n \t<li>Students must be capable of using mathematical methods for solving problems in food science and technology.<\/li>\r\n \t<li>Promotion of analytical, creative and inductive thinking.<\/li>\r\n \t<li>Decision-making.<\/li>\r\n \t<li>Autonomous work.<\/li>\r\n \t<li>Teamwork.<\/li>\r\n<\/ul>","teaching_methods":"Face to face:\r\n<ul>\r\n \t<li>Lectures (theory and exercises) in the classroom.<\/li>\r\n<\/ul>","ict_usage":"<ul>\r\n \t<li>Lectures with PowerPoint slides using PC and projector.<\/li>\r\n \t<li>Notes, solved and unsolved problems in electronic format. Each session involved both a faculty lecture and student participation in problem-solving exercises.<\/li>\r\n \t<li>Posting course material and communicating with students on the Moodle online platform.<\/li>\r\n<\/ul>","teaching_organization":{"activity_1":{"description":"Lectures","workload":50},"activity_2":{"description":"Independent study","workload":100},"activity_3":{"description":"","workload":""},"activity_4":{"description":"","workload":""},"activity_5":{"description":"","workload":""},"activity_6":{"description":"","workload":""}},"students_evaluation":"Evaluation methods:\r\n<ul>\r\n \t<li>Attendance at class and participation in discussions, and solving exercises in the classroom is rewarded with 20% of the final grade.<\/li>\r\n \t<li>Written final exams (80% of the final grade).<\/li>\r\n<\/ul>\r\nThe evaluation criteria are presented and analyzed to the students at the beginning of the semester and are available at the course website.","bib_textbooks":"<ol>\r\n \t<li>\u0398\u03c9\u03bc\u03ac \u039a\u03c5\u03b2\u03b5\u03bd\u03c4\u03af\u03b4\u03b7, \u0394\u03b9\u03b1\u03c6\u03bf\u03c1\u03b9\u03ba\u03ad\u03c2 \u0395\u03be\u03b9\u03c3\u03ce\u03c3\u03b5\u03b9\u03c2, \u03a4\u03cc\u03bc\u03bf\u03c2 \u03a0\u03c1\u03ce\u03c4\u03bf\u03c2, \u0398\u03b5\u03c3\u03c3\u03b1\u03bb\u03bf\u03bd\u03af\u03ba\u03b7,1982.<\/li>\r\n \t<li>R. Churchill, J. Brown, \u039c\u03b9\u03b3\u03b1\u03b4\u03b9\u03ba\u03ad\u03c2 \u03c3\u03c5\u03bd\u03b1\u03c1\u03c4\u03ae\u03c3\u03b5\u03b9\u03c2 \u03ba\u03b1\u03b9 \u03b5\u03c6\u03b1\u03c1\u03bc\u03bf\u03b3\u03ad\u03c2, 2<sup>\u03b7<\/sup> \u0388\u03ba\u03b4\u03bf\u03c3\u03b7, \u039c\u03b5\u03c4\u03ac\u03c6\u03c1\u03b1\u03c3\u03b7: \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.<\/li>\r\n \t<li>Howard E. Taylor, Thomas L. Wade, University Calculus, New York,1982.<\/li>\r\n \t<li>Frank Ayres, Schaum\u2019s outline of theory and problems of Matrices, Singapore,1983.<\/li>\r\n \t<li>Richard Bronson, Shaum\u2019s outline of Modern Introductory Differential Equations, United States, 1973.<\/li>\r\n<\/ol>","bib_journals":""},"_links":{"self":[{"href":"https:\/\/www.food.ihu.gr\/en\/wp-json\/wp\/v2\/course\/2233"}],"collection":[{"href":"https:\/\/www.food.ihu.gr\/en\/wp-json\/wp\/v2\/course"}],"about":[{"href":"https:\/\/www.food.ihu.gr\/en\/wp-json\/wp\/v2\/types\/course"}],"author":[{"embeddable":true,"href":"https:\/\/www.food.ihu.gr\/en\/wp-json\/wp\/v2\/users\/6"}],"version-history":[{"count":33,"href":"https:\/\/www.food.ihu.gr\/en\/wp-json\/wp\/v2\/course\/2233\/revisions"}],"predecessor-version":[{"id":5445,"href":"https:\/\/www.food.ihu.gr\/en\/wp-json\/wp\/v2\/course\/2233\/revisions\/5445"}],"acf:post":[{"embeddable":true,"href":"https:\/\/www.food.ihu.gr\/en\/wp-json\/wp\/v2\/staff\/1405"}],"acf:term":[{"embeddable":true,"taxonomy":"course_type","href":"https:\/\/www.food.ihu.gr\/en\/wp-json\/wp\/v2\/course_type\/76"},{"embeddable":true,"taxonomy":"semester","href":"https:\/\/www.food.ihu.gr\/en\/wp-json\/wp\/v2\/semester\/10"}],"wp:attachment":[{"href":"https:\/\/www.food.ihu.gr\/en\/wp-json\/wp\/v2\/media?parent=2233"}],"wp:term":[{"taxonomy":"semester","embeddable":true,"href":"https:\/\/www.food.ihu.gr\/en\/wp-json\/wp\/v2\/semester?post=2233"},{"taxonomy":"course_type","embeddable":true,"href":"https:\/\/www.food.ihu.gr\/en\/wp-json\/wp\/v2\/course_type?post=2233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}