# Module MA1123: Analysis on the Real Line I

**Credit weighting (ECTS)**- 10 credits
**Semester/term taught**- Michaelmas term 2012-13
**Contact Hours**- 11 weeks, 5 lectures and 1 tutorial per week
**Lecturer**- Prof. Donal O'Donovan
**Learning Outcomes**-
On successful completion of this module students will be able to
- Determine whether a given relation is a function or not, and whether an inverse function exists.
- Find limits and determine whether given functions are continuous or not
- Differentiate functions and use derivatives to graph functions, solve extremal problems and related rates problems.
- Integrate functions using substitution, integration by parts, partial fractions and reduction formulae.
- Find areas, volumes, length of curves, averages and work done.
- Solve simple first order differential equations and higher order linear homogeneous differential equations.
- Determine whether a given sequence or series converges or not.
- Determine where a given power series converges absolutely, converges conditionally or diverges.

**Module Content**-
This course is mainly the study of the theory and practical uses of the
Differential and Integral Calculus. Topics covered include
- Functions
- Limits and Continuity
- Derivatives: Theory and Applications
- Integration: Theory and Applications
- Transcendental Functions
- Modelling and Differential Equations
- Sequences and Series

**Textbook:**The textbook that will be followed is

Calculus, by Anton, Bivens, Davis

Publisher, Wiley and Son **Module Prerequisite**- None for students admitted to the Mathematics, Theoretical Physics or Two-subject Moderatorships.
**Assessment Detail**-
This module will be examined in a 3 hour
**examination**in Trinity term.**Continuous assessment**will contribute 15% to the final grade for the module at the annual examination session. Supplemental examination will consist of 100% examination.