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Module MA1S12: Mathematics for Scientists (second semester)

Credit weighting (ECTS)
10 credits
Semester/term taught
Hilary term 2015-16
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
  • Apply definite integrals to various geometric problems;
  • Apply 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
  • Cross products, determinants, evalustion by row operations and cofactor expansion, properties.
  • Bases, coordinate systems, and matrices of various linear maps.
  • Least squared error estimations.
  • Eigenvectors and eighenvalues with applications to system of first-order linear differential equations.
    Module Content - Probability and Statistics.
  • Basic concepts of probability.
  • Conditional probability.
  • Expectation and standard deviation for discrete random variables; continuous random variables.
  • Sample mean and standard deviation.
  • Examples of common probability distributions (such as binomial, Poisson, normal, Student's t-distribution, chi-squared distribution).

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%.