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/ma121/ 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

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

Mar 27, 2007