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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.