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MA 425-002

Mathematical Analysis I

Mathematics

### Reviewing for the Final Exam

The final exam is Wednesday, May 3, 8:00 - 11:00 a.m., in the usual room. The test will cover material from Chapters 3 to 9.

**Chapters 3--6**

Use the review sheets for Tests 1 and 2. However, in using the review sheet for Test 1, note that Chapter 2 will not be explicitly covered on the final. It is, of course, used as background in the remaining chapters.

**Chapter 7**

Secs. 7.1 and 7.2 only. Important notions:

- Definition of Riemann integral (7.1)
- Showing simple functions are Riemann integrable from the definition (7.1)
- Properties of the integral (7.1)
- Boundedness theorem (7.1)
- Squeeze theorem (7.2)

Important homework problems: all assigned in Secs. 7.1 and 7.2.

**Chapter 8**

Secs 8.1 and 8.2 only. Important notions: pointwise and uniform convergence. Important homework problems: all assigned.

**Infinite series (secs. 3.7, 9.1 - 9.3)**

Important notions:

- Convergence (3.7)
- Geometric series (3.7)
- nth term test (3.7)
- Comparison test (3.7)
- Absolute convergence (9.1)
- Ratio test (9.2)
- Integral test (9.2)
- Alternating series test (9.3)

Important homework problems: all assigned.

MA 425-002 home page

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Last modified Mon Apr 24 2006

Send questions or comments to schecter@math.ncsu.edu