Schedule of lectures and homework

Week 9

Mon Mar 3. Interchange of limit operations. Read: Ch VII, section 1

Wed Mar 5. Power series. Read: Ch VII, sections 2, 3

Fri Mar 7. Trigonometric functions. Read: Ch VII, section 4

No homework this week.

Week 8

Mon Feb 24. Darboux's theorem about Riemann integrability. (No reading.)

Wed Feb 26. The fundamental theorem of calculus. Read: Ch VI.4

Fri Feb 28. The logarithm and the exponential function. Read: Ch VI.5

Homework (due Wed Mar 5; this is the last pset): Ch VI, problems 15, 17, 20, 22, 24cd

Week 7

Mon Feb 17. The Mean Value Theorem. Read: Ch V, section 3

Wed Feb 19. Taylor's theorem. Read: Ch V, section 4

Fri Feb 21. The Riemann integral. Read: Ch VI, sections 1, 2, 3

Homework (due Wed Feb 26): Ch V, problems 6, 12; Ch VI, problems 3, 8, 11

Week 6

Mon Feb 10. Function spaces. Read: Ch IV.6

Fri Feb 14. Derivatives. Read: Ch V.1 and V.2

Homework (due Wed Feb 19): Ch IV, problems 1d, 4, 14ab, 41, 42

Week 5

Mon Feb 3. Continuity and limits. Read: Ch IV, section 2

Wed Feb 5. The Intermediate Value Theorem. Read: Ch IV, sections 3 and 5

Fri Feb 7. Continuous functions and compact sets. Read: Ch IV, section 4

No homework this week.

Week 4

Mon Jan 27. Compact sets. Read: Ch III, section 6 (p. 54-56)

Wed Jan 29. The Heine-Borel theorem. Read: Ch III, section 6

Fri Jan 31. Continuous functions. Read: Ch IV, section 1

Homework (due Wed Feb 5): Ch III, problems 28, 30b, 35, 36, 37

Week3

Tue Jan 21. Convergent sequences (continued)

Wed Jan 22. Completeness. Read: Ch III, section 4

Fri Jan 24. Connectedness. Read: Ch III, section 6

Homework (due Wed Jan 29): Ch III, problems 11, 18, 24, 38

Week 2

Mon Jan 13. Metric spaces. Read: Ch III, section 1

Wed Jan 15. Open and closed sets. Read: Ch III, section 2

Fri Jan 17. Convergent sequences. Read Ch III, section 3

Homework (due Fri Jan 24): Ch III: 1ab, 3, 4, 5, 8, 10 (solutions Download solutions)

Week 1

Mon Jan 6. Introduction: Why Analysis? Read: Chapter I.

Wed Jan 8. Ordered Fields. Read: Chapter II, sections 1 and 2

Fri Jan 10. The Least Upper Bound property. Read: Chapter II, section 3

Homework (due Wed Jan 15): Ch I: 3a, 5a, 7d, 10a; Ch II: 2a, 6, 11, 13 (solutions Download solutions)