MA 425-002

Mathematical Analysis I

Mathematics

Reviewing for the Final Exam

The final exam is Wednesday, Dec. 7, 8:00 - 11:00 a.m., in the usual room. The test will cover material from Chapters 3 to 9.

Chapters 3 to 5

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 6

Secs. 6.1 and 6.2 only. Important notions:


• The derivative (6.1.1)
• Differentiable implies continuous (6.1.2)
• Derivatives of algebraic combinations of functions (6.1.3)
• Chain rule (6.1.6)
• Mean Value Theorem (6.2.4)

Important homework problems: 6.1 #1b, 1c, 2, 4; 6.2#6, 13, 15; 6.4 #15.

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.

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.

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