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).
- 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):
- 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%.