### MATH 217 - Honors Advanced Calculus, I

### Instructor

### Office hours

### Syllabus

#### The real number system and finite dimensional Euclidean space

- axiomatic introduction of the real numbers
- the Euclidean space
*R*^{N}
- functions
- topology in
*R*^{N}

#### Limits and continuity

- limits of sequences
- limits of functions
- global properties of continuous functions
- uniform continuity

#### Differentiation in *R*^{N}

- differentiation of real valued functions of a real variable
- partial derivatives
- vector fields
- total differentiability
- Taylor's theorem
- classification of stationary points

#### Integration in *R*^{N}

- content in
*R*^{N}
- the Riemann integral in
*R*^{N}
- calculation of integrals
- Fubini's theorem
- integration in polar, spherical, and cylindrical coordinates

### Textbooks

None required, but the following are recommended.

- Robert G. Bartle,
*The Elements of Real Analysis*, Second Edition. Jossey-Bass, 1976.
- Patrick M. Fitzpatrick,
*Advanced Calculus*. PWS Publishing Company, 1996.
- James S. Muldowney,
*Advanced Calculus Lecture Notes for Mathematics 217-317*, I, Third Edition.
- William R. Wade,
*An Introduction to Analysis*, Second Edition. Prentice Hall, 2000.

I will more or less follow my notes, but I plan to revise them thoroughly during the course and make the updated version also available online.

### Grading

The grade will be based on (approximately) weekly homework assignments (30%), an in-class-midterm on October 20 (20%), and a final (50%).

Last update: 01/12/18.