Module MA1S12: Mathematics for Scientists (second semester)
- Credit weighting (ECTS)
- 10 credits
- Semester/term taught
- Hilary term 2012-13
- Contact Hours
- 11 weeks, 6 lectures including 2 tutorials per week
- Lecturers
- Prof. Sergey Mozgovoy, Prof. Colm Ó Dúnlaing
- Learning Outcomes
Module Content
-
Calculus with Applications for Scientists
The lecturer for this part will be Prof Sergey Mozgovoy.
The main textbook will be (Anton) and the syllabus will be approximately Chapters 5, 7-10 of (Anton) plus a brief introduction to partial derivatives (sections 13.1, 13.3 of (Anton).
Chapter headings are;
- Applications of the Definite Integral in Geometry, Science and Engineering;
- Principles of Integral Evaluation;
- Mathematical Modelling with Differential Equations;
- Infinite Series;
- Parametric and Polar Curves;
Discrete Mathematics for Scientists
The lecturer for this part will be Prof. Colm Ó Dúnlaing
Module Content:
- Linear Algebra - This reference for this part of the course will be (AntonRorres). The syllabus will be approximately chapters 2, 5, section 4.2 and a selection of application topics from chapter 11 of (AntonRorres).
- Determinants, Evaluation by Row Operations and Laplace Expansion, Properties, Vector Cross Products, Eigenvalues and Eigenvectors;
- Introduction to Vector Spaces and Linear Transformations. Least Squares Fit via Linear Algebra;
- Differential Equations, System of First Order Linear Equations;
- Selected Application in Different Branches of Science;
- Probability - Basic Concepts of Probability; Sample Means; Expectation and Standard Deviation for Discrete Random Variables; Continuous Random Variables; Examples of Common Probability Distributions (binomial, Poisson, normal) (sections 24.1 - 24.3, 24.5 - 24.8 of (Kreyszig).
Essential References:
(Anton)
- Combined edition:
- Calculus: late transcendentals: Howard Anton, Irl Bivens, Stephen Davis. Combined 9th ed; Publisher New York: Wiley, c2010. (Hamilton 515P23*8;2) Or
- Calculus: single variable / Howard A.Anton, Irl Bivens, Stephen Davis. 9th ed. 2009 (Hamilton 515 P2*8;4, S-LEN 515 P2*8)
(AntonRorres)
- Howard Anton & Chris Rorres, Elementary Linear Algebra with supplementary applications. International Student Version (10th edition). Publisher Wiley, c2011. (Hamilton 512.5L32*9; - 5, S-LEN 512.5 L32*9;6-15):
Recommended References:
(Kreyszig)
- Erwin Kreyszig, Advanced Engineering Mathematics (9th edition), Wiley, 2006 (Hamilton 510.24 L21*8, S-LEN 510.24 L21*8)
(Thomas)
- Thomas' Calculus, Author Weir, Maurice D. Edition 11th ed/based on the original work by George B. Thomas, Jr., as revised by Maurice D. Weir, Joel Hass, Frank R. Giordano, Publisher Boston, Mass., London: Pearson/Addison Wesley, c2005. (Hamilton 515.1 K82*10;*)
Module Prerequisite:
MA1S11 - Mathematics for Scientists (First Semester)
- Assessment Detail
- This module will be examined in a 3 hour examination in Trinity term. Continuous assessment will contribute 10% to the final grade for the module at the annual examination session and at supplementals where applicable.