Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2024Year School of Science HA500000 Specialized Education 解析学I演習 カイセキガク１エンシュウ Exercises in Analysis I TAKIMOTO KAZUHIRO,KOREEDA YOSHIMUNE タキモト　カズヒロ,コレエダ　ヨシムネ Higashi-Hiroshima 1st-Year,  First Semester,  2Term (2T) Weds5-6,Fri5-6：SCI E209,SCI E211 Seminar Exercises and presentations on the blackboard 1.0 J : Japanese 1 : Undergraduate Introductory 25 : Science and Technology 01 : Mathematics/Statistics Freshman (1st year) students Continuity of real numbers, Convergence and divergence of sequences, Series, Continuity of functions, Derivative. Mathematics（Knowledge and Understanding）・Understanding classical basic theory which is a base of modern mathematics.  Being able to find and explain issues from specific events.（Abilities and Skills）・To acquire basic mathematical abilities (Ability to understand concepts, calculation ability, argumentation ability). The course, Exercises in Analysis I, is given for helping your understanding of the contents of "Analysis I". Lesson1 Continuity of real numbers, I (Supremum, Infimum, Maximum, Minimum)Lesson2 Continuity of real numbers, II (Axiom of the continutity of real numbers)Lesson3 Sequences, I (Defintion of the limit, convegence and divergence)Lesson4 Sequences, II (Elementary properties)Lesson5 Sequences, III (Cauchy sequence, Completeness of real numbers)Lesson6 Series, I (Definition of convergence and divergence)Lesson7 Series, II (Method of convergence criteria)Lesson8 Series, III (Alternating series, Absolute convergence and conditional convergence)Lesson9 ReviewLesson10 Limits of functions and continuous functions, I (Defintion and elementary properties)Lesson11 Limits of functions and continuous functions, II (Extreme value theorem, Intermediate value theorem)Lesson12 Limits of functions and continuous functions, III (Continuity of inverse function, Uniform continuity)Lesson13 Derivatives, I (Defintion and elementary properties)Lesson14 Derivatives, II (Derivative of composite function, Derivative of inverse function)Lesson15 Derivatives, III (Mean-value theorem)Some quizes and some reports may be assigned. Textbook:[1] Takeru Suzuki, Yoshio Yamada, Yoshihiro Shibata and Kazunaga Tanaka, Rikokei-no-tameno Bibunsekibun I, Uchida Rokakuho, 2007.Study-aid books:[2] Ken-Ichi Shiraiwa, Kaisekigaku-nyumon, Gakujutsu Tosho Shuppan-sha, 1981.[3] Nobuyuki Suita and Tsunehiko Shimbo, Rikokei-no-Bibunsekibun-gaku, Gakujutsu Tosho Shuppan-sha, 1987.[4] Koji Kasahara, Bibunsekibun-gaku, Saiensu-sha, 1974.[5] Kunihiko Kodaira, Kaiseki-nyumon I, Iwanami Shoten, 2003.[6] Teiji Takagi, Kaiseki-gairon, 3rd Edition, Iwanami Shoten, 1983.I strongly recommend that you have some books for exercises. I will hand out some documentations if necessary. Lesson1--Lesson15  Preparation and review are necessary. It is strongly recommended that you take the course "Analysis I". Mark given in a class (65 percents), Midterm examination and final examinations (35 percents). Please fill in the class improvement questionnaire which is carried out on all classes.Instructors will reflect on your feedback and utilize the information for improving their teaching.
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