MA 426-003 - Mathematical Analysis II

MA 426-003

Mathematical Analysis II

Mathematics

MA 426-003 Home Page

Information

schecter@math.ncsu.edu

Goals of the Course

MA 426 introduces the student to the fundamental ideas of analysis -- open, closed, compact and connected sets, convergent sequences, continuous mappings, diferentiability and the inverse and implicit function theorems, integration -- in the setting of R^n. The student should develop an intuitive grasp of these ideas, as well as the ability to use them in rigorous proofs.

Text

Jerrold E. Marsden and Michael J. Hoffman, Elementary Classical Analysis, second edition, W. H. Freeman, $92.

Here is a recent lecture by Professor Marsden on designing space flights to the planets to minimize fuel use by making clever use of gravity.

Schedule

Topic

Sections of Marsden and Hoffman

Weeks

Topology of Euclidean space

1.6 - 1.7, 2.1 - 2.8

2 1/2

Compact and connected sets

3.1 - 3.5

1 1/2

Continuous mappings

4.1 - 4.6

2

Uniform convergence

5.1

1/2

Differentiable mappings

6.1 - 6.9

3

Inverse and implicit function theorems

7.1 - 7.2, 7.7

1

Integration

8.1 - 8.4

2

Fubini's theorem, change of variables

9.1 - 9.5

1 1/2

Syllabus

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Last modified Thu Nov 7 2002
Send questions or comments to schecter@math.ncsu.edu

Topic	Sections of Marsden and Hoffman	Weeks
Topology of Euclidean space	1.6 - 1.7, 2.1 - 2.8	2 1/2
Compact and connected sets	3.1 - 3.5	1 1/2
Continuous mappings	4.1 - 4.6	2
Uniform convergence	5.1	1/2
Differentiable mappings	6.1 - 6.9	3
Inverse and implicit function theorems	7.1 - 7.2, 7.7	1
Integration	8.1 - 8.4	2
Fubini's theorem, change of variables	9.1 - 9.5	1 1/2