MTWRF 9:10-10:05 at BP (Bolz Hall) 124
| Instructor: Sasha Leibman | office: MW406 office hours: Monday 12-1pm, Thursday 10:10-11am, and by appointment |
| e-mail: leibman.1@osu.edu |
Textbook: M. Spivak Calculus, 4th edition
Mentoring:
Two mentors (two experienced students) Adarsh and Levi
will be helping you with this course and grading your homework.
Meetings with them will be held
Wednesdays from 5:30 to 7:30 p.m. and Sundays from 2 to 4 p.m.
in Cockins Hall 218.
Lecture notes, version of 9/11
Homework:
| Homework 1 – | due by Tuesday, September 2. Solutions |
| Homework 2 – | due by Tuesday, September 9. Solutions |
| Homework 3 – | due by Tuesday, September 16. |
Studied topics:
| August 26: |
Logical and set-theretical notations, mappings, types of proofs (Lecture notes 0.2-0.5)
Axioms of real numbers (Lecture notes 1.1, Spivak pp.1-11 and 135) |
August 27: |
Axioms of real numbers (Lecture notes 1.1, Spivak pp.1-11 and 135)
Some elementary properties of real numbers (Lecture notes 1.2, Spivak pp.1-11) |
August 28: |
Some elementary properties of real numbers (Lecture notes 1.2, Spivak pp.1-11)
The order relation ">" on R (Lecture notes 1.3, Spivak pp.10-11) The absolute value (Lecture notes 1.4, Spivak pp.11-12) |
August 29: |
The absolute value (Lecture notes 1.4, Spivak pp.11-12)
Squares and square roots of real numbers (Lecture notes 1.5, Spivak p.12) |
September 2: |
Existence of square roots (Lecture notes 1.5)
The arithmetic–geometric mean inequality and the Cauchy-Schwarz inequality (Lecture notes 1.6, Spivak ex.7 on p.15, ex.18,19 on pp.17-18) |
September 3: |
The triangle inequality in the plane (Lecture notes 1.6)
Natural numbers and the principle of induction (Lecture notes 1.7, Spivak pp.21-26 and ex.25 on p.24) The Archimedian property of N (Lecture notes 1.7, Spivak pp.138-139) |
September 4: |
Bernoulli's inequality and its corollaries (Lecture notes 1.7, Spivak ex.19 on p.32)
Natural numbers are closed under addition and multiplication (Lecture notes 1.7) Inductive definitions, powers, finite sums and products (Lecture notes 1.7, Spivak pp.21-26) "Modified" induction principle (Lecture notes 1.7) |
September 5: |
Binomial coefficients and the binomial formula (Lecture notes 1.7, Spivak ex.3 on p.27)
Integers (Lecture notes 1.8, Spivak p.25) |
September 8: |
Divisibility of integers, coprime and prime integers
(Lecture notes 1.8, Spivak ex.17 on p.31)
The principle of complete induction (Lecture notes 1.7, Spivak p.23) |
September 9: |
The fundamental theorem of arithmetic (Lecture notes 1.8, Spivak ex.17 on p.31)
The well ordering of N (Lecture notes 1.7, Spivak p.23) |
September 10: |
Rational numbers (Lecture notes 1.10, Spivak pp.25-26)
Irrationality of √2 (Lecture notes 1.10, Spivak pp.25-26) Intervals in R, infinite points, limit points, dense sets (Lecture notes 1.9) Denseness of Q in R (Lecture notes 1.10, Spivak ex. 5 on p.140) |
September 11: |
Another proof of irrationality of √2 (Lecture notes 1.10)
The extended real line (Lecture notes 1.9) Supremum and infimum (Lecture notes 1.11, Spivak p.134) |
Plans for the nearest future:
Supremum and infimum (Lecture notes 1.11, Spivak p.134)
The nested intervals principle (Lecture notes 1.12, Spivak ex.14 on p.142)