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Module MA1S12: Mathematics for Scientists (second semester)

Credit weighting (ECTS)
10 credits
Semester/term taught
Hilary term 2014-15
Contact Hours
11 weeks, 6 lectures including tutorials per week
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:


  • Combined edition:
  • Calculus: late transcendentals: Howard Anton, Irl Bivens, Stephen Davis 10th edition (2013) (Hamilton Library 515P23*9)
  • Or
  • Single variable edition.


  • 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:


  • 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' 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%.