**Duration:** Full year

**Number of lectures per week:** 4 + 1 tutorial

**Assessment:**
Homework Homework assignments every other week.
Exams at the end of the Michaelmas term and at the end of
Hilary term.

**End-of-year Examination:** A 3-hour paper.

**Description: **
See `http://www.maths.tcd.ie/~pete/maths121/` for more complete
information.

The course will cover the following topics, yet not necessarily in the order listed.

- A short introduction to mathematical logic and proofs
- Definition of the real numbers (using Dedekind cuts)
- Definition and properties of min/max/inf/sup
- Logarithms, powers and roots
- Definition and properties of limits; limits at infinity
- Definition and properties of derivatives
- Definition of continuity; continuous and discontinuous functions
- Intermediate value and Mean value theorems
- Applications of derivatives in optimization problems
- Definition and properties of (in)definite integrals
- Techniques of integration; the Fundamental Theorem of Calculus
- Infinite and power series; tests for convergence
- Taylor's Theorem; binomial and exponential series
- Applications of integrals in computations of area
- Surfaces of revolution and their volumes
- Double integrals and polar coordinates
- Fubini's Theorem
- Basic Theory for ordinary differential equations (ODE)
- Separable and 1st-order linear ODE
- 2nd-order ODE with constant coefficients
- Homogeneous and non-homogeneous ODE

- Calculus by Michael Spivak,
- Principles of mathematical analysis by Walter Rudin,
- Differential and integral calculus by Edmund Landau.

Feb 1, 2008

File translated from T

On 1 Feb 2008, 16:31.