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Module MAU11S02: Mathematics for Scientists (second semester)

Credit weighting (ECTS)
10 credits
Semester/term taught
Hilary term 2021-22
Contact Hours
11 weeks, 6 lectures and two tutorials per week
 
Lecturers
Prof. Colm Ó Dúnlaing Prof Miriam Logan
 

Calculus with Applications for Scientists

The lecturer for this part will be Prof Miriam Logan

Learning Outcomes
On successful completion of this module students will be able to
  • Solve definite integrals using a variety of methods of integration;
  • Use integration to solve geometrical problems, such as finding volumes, areas and lengths;
  • Evaluate improper integrals
  • Formulate and solve first order differential equations;
  • Determine if an infinite sequence converges or not;
  • Test a series for convergence;
  • Approximate a function by polynomials using Taylor and Maclaurin series;
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, numerical 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.

    Recommended Reading:

    • Single Variable Calculus 7th ed. Early Transcendentals by James Stewart.
    • Calculus, 9th edition, Early Transcendentals by H. Anton, I. Bivens, S. Davis. 

Further linear algebra and statistics 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, S-LE N 512.5 L32*9;6-15):

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, Mas s., London: Pearson/Addison Wesley, c2005. (Hamilton 515.1 K82*10;*)
 
Module Prerequisite
MAU11S01 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 tutorial work will contribute 20% to the final grade at the ann ual examinations, with the examination counting for the remaining 80%. Re-assessments if required will consist of 100% exam.