# 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
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
• 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:

(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-LEN 512.5 L32*9;6-15):

Recommended References:

(Kreyszig)