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Fall 2008 *** MTH 427/527 – Advanced Calculus I ** Course Syllabus ** Dr. Ari Aluthge (A-lut-gay) Course Numbers: MTH 427 – Sec. 101 (CRN 3399), MTH 527 – Sec. 101 (CRN 3409), Course Title: Advanced Calculus I – Three credit hours. Textbooks: An Introduction to Analysis, 3rd Edition by William R. Wade Prerequisites: MTH 231 + MTH 300, Recommended: MTH330 Class Meeting Times: TR: 2:00 – 3:15 Classroom: Smith 513 Instructor: Dr. Ari Aluthge (A-lut-gay) Office: ML 106 (Morrow Library – First Floor) Office Hours: M - F: 8:45 – 10:00 Phone: 696 3050 Email: [email protected] Course Objectives: To provide a rigorous treatment of the real number system, continuity and differentiability of functions of a single variable, integration of functions of a single variable, infinite series of real numbers, and infinite series of functions. Course Contents: ● The Real Number System: Field Axioms, Well-ordering principle, Completeness axiom, Functions, etc. Sequences of Real Numbers: Limit theorems, Bolzano-Weierstrass theorem, Cauchy sequences, Limit supremum/infimum, etc. Continuity of Functions of a Single Variable: One- and Two-sided limits, Continuity, Uniform continuity, etc. Differentiability of Functions of a Single Variable: The derivative, Differentiability theorems, Mean Value Theorem, Inverse Function theorem, etc. Integrability of Functions of a Single Variable: Riemann integral, Fundamental Theorem of Calculus, Improper integrals, etc. Infinite Series of Real Numbers: Series with nonnegative terms, Convergence, Alternating series, estimation of series, etc. Expected Coverage of the Material: Chapters 1 - 6 in the textbook. Learner Outcomes: Upon completion of this course, students will have a clear understanding of major concepts of calculus of functions of a single variable. They will be able provide logical and valid proofs of mathematical statements and results in real analysis and related fields. They will be able to read and understand advanced books and research articles in real analysis and related topics. This course will also prepare students for further studies courses in real analysis and related subjects. Your Grade: Two tests (200 points total), weekly homework assignments (200 points total), and a comprehensive final exam (100 points total) will be given. Maximum possible total points = 500 A = [450, 500], B = [400, 450), F = [0, 300) or missing the final exam. C = [350, 400), D = [300, 350) Make-up Exams and Missing Assignments: Make-up tests will be given for excused absences only. Students must verify their absences with the dean of students. No make-up quizzes will be given (more than 15 quizzes will be given and the best 15 quizzes will be counted). Assignments must be turned in on time (no exceptions) Important Days: Test 1: Tuesday, October 14 Test 2: Tuesday, December 2 Final Exam: Thursday, December 11 – (12:45 – 2:45) Class Attendance and Excused Absences: Students are required to attend the class every day with their textbook. They must come to class on time and stay in the class for the entire period. Students are responsible for the material discussed in the class on each day even if they miss the class on that day. Please refer to page 121 of the Undergraduate Catalog (http://www.marshall.edu/ucomm/catalog/interim.htm ) for details regarding the university excused absence policy. Any excused absence must be verified by the Dean of Students. Student must also notify the instructor of any absence at the earliest convenient time. Daily attendance will be taken. Academic Honesty: I expect my students to be honest and hard working individuals. Students should not attempt to cheat on exams or on assignments. It is not difficult to catch cheating and cheaters will be dealt seriously. Please read pages 101 – 107 of the undergraduate catalog for more details. Students are allowed and encouraged to study and do homework with other students in the class. Cell Phones: Please turn of cell phones before entering the classroom. This will not be tolerated. Free Tutoring: Free tutoring will be available in Smith 526 starting August 28, 2006. Tentative Weekly Schedule Week Coverage of material and other assignments Week #1 (8/25 – 8/29) Sections 1.1 – 1.2 Week #2 (9/1 – 9/5) Sections 1.3 – 1.4 Week #3 (9/8 – 9/12) Sections 2.1 – 2.2 Week #4 (9/15 – 9/19) Sections 2.3 – 2.4 Week #5 (9/22 – 9/26) Sections 2.5 – 3.1 Week #6 (9/29 – 10/3) Sections 3.2 – 3.3 Week #7 (10/6 – 10/10) Sections 3.4, Catch-up and review Week #8 (10/13 – 10/17) Test #1, Section 4.1 Week #9 (10/20 – 10/24) Sections 4.2 – 4.3 Week #10 (10/27 – 10/31) Sections 4.4 – 5.1 Week #11 (11/3 – 11/7) Sections 5.2 – 5.3 Week #12 (11/10 – 11/14)) Sections 5.4 – 6.1 (skip 5.5 and 5.6) Week #13 (11/17 – 11/21) Sections 6.2 – 6.3, Catch-up and review Week #14 (11/24 – 11/28) Thanksgiving Holiday – No classes Week #15 (12/1 – 12/5) Test #2, Section 6.4 Week #16 (12/8 – 12/9) Finish Chapter 6 and Review for the final