Module MA1S12: Mathematics for Scientists (second semester)
 Credit weighting (ECTS)
 10 credits
 Semester/term taught
 Hilary term 201415
 Contact Hours
 11 weeks, 6 lectures including tutorials per week
 Lecturers
 Prof. Sergey Mozgovoy, Prof. Colm Ó Dúnlaing

Calculus with Applications for Scientists
The lecturer for this part will be Prof Sergey Mozgovoy.
 Learning Outcomes
 On successful completion of this module students will be able to
 How to apply definite integrals to various geometric problems;
 Various methods of integration;
 The concept of a differential equations and methods of their solution;
 The concept of infinite series and their convergence; Taylor series;
 The concepts of parametric curves and polar coordinates,
 Module Content

 Application of definite integrals in geometry (area between curves, volumne of a solid, length of a plane curve, area of a surface of revolution).
 Methods of integration (integration by parts, trigonometric substitutions, numberical integration, improper integrals).
 Differential equations (separable DE, first order linear DE, Euler method).
 Infinite series (convergence fo sequences, sums of infinite series, convergence tests, absolute convergence, Taylor series).
 Parametric curves and polar coordinates.
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 10th edition (2013) (Hamilton Library 515P23*9) Or
 Single variable edition.
(AntonRorres)
 Howard Anton & Chris Rorres, Elementary Linear Algebra with supplementary applications. International Student Version (10th edition). Publisher Wiley, c2011. (Hamilton 512.5L32*9;  5, SLEN 512.5 L32*9;615):
Recommended References:
(Kreyszig)
 Erwin Kreyszig, Advanced Engineerin
 Erwin Kreyszig, Advanced Engineering Mathematics (10th edition), (Erwin Kreyszig in collaboration with Herbert Kreyszig, Edward J. Normination), Wiley 2011 (Hamilton 510.24 L21*9)
(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 Scientist (First Semester)
 Assessment Detail
 This module will be examined in a 3 hour examination in Trinity term. Continuous assessment in the form of weekly tutuorial work will contribute 20% to the final grade at the annual examinations, with the examination counting for the remaining 80%. For supplementals if required, the supplemental exam will count for 100%.