Last modified: Tue 7 August 15:15:54 IST 2018

Welcome Study @ MIC St. Patrick's Campus Thurles Faculties & Departments Research & Grad School International Students
MIC > Academic Departments > Mathematics and Computer Studies > Bernd Kreussler > MH4712

MH4712 — Foundations of Analysis

This module is not taught at the moment

Contact Information

Name Dr. Bernd Kreussler
Office N29
Internal Telephone 4578
Email bernd.kreussler@mic.ul.ie
WWW www.maths.mic.ul.ie/kreussler/

Contents of the lecture delivered during the spring semester 2010

  1. Functions
    • The mathematical language we are going to use
    • Domain and range of a function, examples
    • Trigonometric functions, basic properties
  2. Differentiation and Limits
    • Lines in the plane, secants and tangents
    • The idea of the derivative of a function
    • First examples: powers
    • Limits of functions
    • Computing the derivative of sums, products and quotients
    • The chain rule
    • Implicit differentiation
  3. Applications
    • Curve sketching, minima and maxima
    • Rate of change of a physical quantity
  4. Inverse functions
    • Definition and examples
    • Derivative of the inverse
    • Logarithm and exponential function
  5. Integration
    • Indefinite integrals (antiderivatives)
    • Definite integrals
    • Measuring area
    • Techniques of Integration

Textbooks

  • BERBERIAN, S, A First Course in Real Analysis, (Springer Verlag), 1994
  • BOOTH, D.J., Foundation Mathematics, (Addison Wesley), 1991.
  • FLANDERS, H., Calculus, (Freeman), 1985.
  • HUNTER, J., Calculus, (Blackie and Chambers), 1986.
  • LANG, S., A First Course in Calculus, (Springer Verlag), 1986.
Mary Immaculate College, South Circular Road, Limerick, Ireland, Tel: +35361 204300