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Links
o Free PDF file of the text book If you need a printed version please check with the bookstore, if they don't have it let me know and I will ask the department/bookstore to make more copies. |
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What's new
o Oct. 1: I posted two sample midterms (see belwo). o Oct. 3: I posted the solutions to sample midterms. I also posted an info sheet for the midterm with a list of theorems/definitions you need to know. o Oct. 6: Posted solutions to HW4. o Oct. 6: There is no recitation after the test on Wednesday. o Oct. 15: I posted HW5. It is due next Wednesday Oct. 22. o Oct. 22: Posted HW6. Due next Wedneday Oct. 29. o Oct. 22: We have finished proof of Mean Value Theorem. o Oct. 27: HW 7 posted. Solutions to MT1 and HW5 posted. o Nov. 12: HW 8 and 9 plus info sheet for midterm 2 and some practice questions (with solutions) posted. o Nov. 12: Midterm 2 postponed to this coming monday. o Nov. 18: HW8 had two questions in common with HW7 (4.5.1 and 4.5.4) they were removed and instead 4.5.6 added to the homework. HW8 due date extended to next monday. o Dec. 1: HW 10 posted (last homework). It is due next Monday Dec. 8. There is no class on Monday so either slip your HWs under my office door, or email them to me. o Dec. 5: Posted info about final and a practice test with solutions. |
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Homeworks and other online material
Info sheet for final A practice test (You can ignore the problem about log-exp in the practice test, also do not expect that the final be very similar to this practice test.) Solutions for the practice test Homework 10: Due Monday Dec. 8 (slip under my office door or email me) Ex. 5.2.4, 5.2.5, 5.3.2, 5.3.7, 6.1.1, 6.1.9, 6.2.2, 6.2.4 Info sheet for midterm 2 Practice questions for midterm 2 Some more practice questions for midterm 2 Homework 9: Due Monday November 24th in class Ex. 5.1.1, 5.1.3, 5.1.5, 5.1.6, 5.1.7 Homework 8: Due Monday November 24th in class Ex. 4.5.6, 4.5.7 Also A. Compute the Taylor expansion with remainder for exp(x/a) about the point x=b to n terms and state the remainder. B. Compute the Taylor polynomial degree 2 with remainder for cos(ax) about the point x=pi/4. Solutions to midterm 1 Homework 7: Due Wednesday November 5th in class Ex. 4.3.5, 4.3.6, 4.3.7, 4.4.1, 4.4.3, 4.5.1, 4.5.4. Homework 6: Due Wednesday October 29th in class Ex. 3.5.3, 4.1.5, 4.1.9, 4.2.1, 4.2.2, 4.3.3 Homework 5: Due Wednesday October 22nd in class Ex. 3.3.1, 3.3.2, 3.3.6, 3.4.2, 3.4.3, 3.4.4 Solutions to HW5 Sample midterm 1 Sample midterm 2 Solutions to sample midterm 1 Solutions to sample midterm 2 Info sheet for midterm 1 Homework 4: Due Wednesday October 1st in class Ex. 3.2.1, 3.2.3, 3.2.9, 3.2.10 Suggested problems: Ex. 3.2.2, 3.2.4, 3.2.5, 3.2.11, 3.2.12 Solutions to HW4 Homework 3: Due Wednesday Sep. 24 in class Ex. 3.1.1 a,c,e; 3.1.2, 3.1.4, 3.1.5 Suggested problems: Ex. 3.1.7, 3.1.8, 3.1.9, 3.1.10 Solutions to HW3 Homework 2: Due Wednesday Sep. 17 in class Ex. 2.3.5 (prove your answers), Ex. 2.3.12. Ex. 2.5.3, Ex. 2.5.8, Ex. 2.5.9. Suggested problems: Ex. 2.3.1, Ex. 2.3.9. Ex. 2.5.5, Ex. 2.5.7. Solutions to HW2 Homework 1: Due Monday Sep. 8 in class Ex. 2.1.6, Ex. 2.1.12 Ex. 2.2.1 Ex. 2.4.1, Ex. 2.4.2 Solutions to HW1 Suggested problems: Ex. 2.1.1, Ex. 2.1.3, Ex. 2.1.10, Ex. 2.1.11, Ex. 2.1.15, Ex. 2.1.17 Ex. 2.2.4 (check Sec. 2.2.3), Ex. 2.2.5, Ex. 2.2.9 Ex. 2.4.5 |
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Course information
Text: Basic Analysis (with Pitt supplement) by Jiri Lebi Time of lectures: MW 4PM-5:15PM Location of lectures: Thackeray Hall 627 Important date: Midterm 1: October 8 Midterm 2: November 17 Last class: December 3 Grading scheme: 10% Homework and quizzes + 25% mideterm 1 + 25% midterm 2 + 40% final Core topics: 1. The Bolzano-Weierstrass Theorem; Cauchy sequences; Cauchy completeness of the real numbers. 2. Real-valued functions on an interval: limits and continuity. 3. Intermediate Value Theorem; Max-Min Theorem. 4. Uniform continuity; continuous functions on a closed and bounded interval are uniformly continuous. 5. Differentiable functions. 6. Interior Extremum Theorem, Rolle's Theorem, Mean Value Theorem. 7. Taylor's Theorem and Taylor Series. 8. The Riemann Integral on a closed and bounded interval. Increasing functions are Riemann-integrable. Continuous functions are Riemann-integrable. 9. The Fundamental Theorem of Calculus. 10. Definition and examples of pointwise and uniformly convergent sequences of functions. 11. Continuity of uniform limits of continuous functions. 12. Interchange of uniform limits and integration. 13. Interchange of limits with differentiation. 14. The M-test for uniform convergence of series. 15. Application to power series. |
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Instructor's
Information
Email: kavehk AT pitt.edu Office: Thackeray #424 Office hours: Tuesdays and Thursdays 11:00PM-12:00PM or by appointment. You can drop by anytime, I am usually in. Office phone: 412-624-8331 |