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Module MA1S12: Mathematics for Scientists (second semester)

Credit weighting (ECTS)
10 credits
Semester/term taught
Hilary term 2013-14
Contact Hours
11 weeks, 6 lectures including tutorials per week
Prof. Sergey Mozgovoy, Prof. Richard Timoney

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. Richard Timoney

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%.