This course is intended for honors students and it is open to freshman.
This course is the second semester of the Calculus Honors sequence developed by the Mathematics Department at the UW. The goal of the sequence is to provide highly motivated and well-prepared students with an opportunity to go beyond the traditional approach to the subject to develop a deeper understanding of this fundamental area of mathematics and to appreciate its power and beauty. The material covers essentially the same topics as the standard second semester calculus course, but the material is discussed in greater depth, and with much more emphasis on mathematical ideas. The course will be challenging, and the student might find it surprisingly different at the beginning. But it is also meant to be a lot of fun and to provide the students with the kind of clear and precise thinking that is characteristic of mathematics and that will be useful for them in almost any subject they pursue.
- Examples of proofs: direct deduction, proof by contradiction, proof by mathematical induction
- Applications: binomial coefficients, arithmetical progressions, some inequalities
- Sequences and series
- Polynomial approximation: Taylor polynomials, applications to indeterminate forms and de l'Hopital's rule, infinite limits
- Sequences and series of functions: uniform convergence, power series, Taylor series, convergence of special series
- Introduction to differential equations