Test and Final Pages

There are three midterm tests. Each test is worth 100 pointse. The tests will be held in class and the dates announced one week in advance.

Test 1

There are four questions.

(1) Definitions. (30%) You will be asked to give the definition for five items. Absolute accuracy is required. The five items are taken from the following list:

p.8  Upper bound and supremum (count as one item)
p.10  Lower bound and infimum (count as one item)
p.25  Convergence of a sequence
p.34  Monotonically increasing sequences, monotonically decreasing sequences, monotone sequences (count as one item)
p.37  Subsequences
p.43  Continuity at a point, and on a set (count as one item)
p.58  Uniformly continuous functions
p.61  Limit point
p.62  Limit of a function
p.193  Cauchy sequences

(2) and (3) Proofs of Theorems. (20% each) You will be asked to give the proof for two theorems taken from this list:

p.9  Proposition 1.3
p.15  Theorem 1.11
p.35  Theorem 2.10
p.37  Theorem 2.11
p.44-45  Theorem 3.1 and Theorem 3.3 (count as one theorem)
p.49  Theorem 3.7
p.59  Theorem 3.14

(4) Problem solving. (30%) This is a question that can be done by using what has been discussed in the course.

Test 2

(1) Statements of Theorems. (30%) You will be asked to give the statements of four theorems. Absolute accuracy (version as given in the textbook)  is required. They are taken from the following list:

p.82    Rolle's Theorem
p.83    The Lagrange Mean Value Theorem
p.90    The Cauchy Mean Value Theorem
p.94    Darboux's Theorem
p.118    The Integrability Criterion
p.127    The First Fundamental Theorem of Calculus
p.132    The Darboux Sum Convergence Criterion
p.134    The Riemann Sum Convergence Criterion

(2) Proof of One Theorem. (20%) You will be asked to give the proof for one theorem taken from this list:

p.118    Theorem 6.4
p.120    Theorem 6.5
p.121    Theorem 6.6
p.127    Theorem 6.9

(3) and (4) Problem solving. (25% each) These are questions that can be done by using what has been discussed in the course.

Final Examination

There is a final examination.

Date: May 9, 2005
Time: 8:00 - 10:10

The Final Examination is 2 hours and is worth 200 points of the course.

However, you need to pass the final examination to pass the course.

Here is the information about the syllabus for the final exam:

There are eight questions. 

(1)  Definitions. (15%)  You will be asked to give the exact definitions for five items. Absolute accurary is required. These items are taken from the following list:

Upper bounds and supremum (counted as one) (p.8), lower bounds and infimum (counted as one) (p.10)
Convergent sequences (p.25), Cauchy sequences (p.193), Monotone sequence (p34), Subsequences (p.37)
Continuity at a point (p.43), Uniformly continuous functions (p.58), Limit of a function at a point (p.62)
Derivative (p.69-70)
Riemann integrable functions (p.116)

The Archimedean Property (p.14)
The Monotone Convergence Theorem (p.35)
The Bolzano-Weierstrass Theorem (p.38)
The Extreme Value Theorem (p.47)
The Intermediate Value Theorem (p.51)
The Lagrange Mean Value Theorem (p.83)
Darboux's Theorem (p.94)
The Lagrange Remainder Theorem (p.169)
The Cauchy Integral Remainder Formula (p.180)
The Weierestrass Approximation Theorem (p.188)

Theorem 1.9:  The Archimedean Property (p.14)
Theorem 1.11:  The Density of the rationals and of the irrationals (p.15)
Theorem 2.10:  The Monotone Convergence Theorem (p.35)
Theorem 9.4:  The Cauchy Convergence Criterion for sequences (p.194)
Theorem 3.7: A version of the Intermediate Value Theorem (p.49-50)
Theorem 3.13 An alternative formulation of continuity (p.57-58)
Theorem 4.13 and Theorem 4.14:  The Rolle's Theorem and The Lagrange Mean Value Theorem (counted as one  p.82-84)
Theorem 8.6 and Proposition 8.7: The irrationality of e (counted as one  p.170-171)