# Module MA1S12: Mathematics for Scientists (second semester)

Credit weighting (ECTS)
10 credits
Semester/term taught
Hilary term 2012-13
Contact Hours
11 weeks, 6 lectures including 2 tutorials per week
Lecturers
Prof. Sergey Mozgovoy, Prof. Colm Ó Dúnlaing

Learning Outcomes

Module Content

### Calculus with Applications for Scientists

The lecturer for this part will be Prof Sergey Mozgovoy.

The main textbook will be (Anton) and the syllabus will be approximately Chapters 5, 7-10 of (Anton) plus a brief introduction to partial derivatives (sections 13.1, 13.3 of (Anton).

• Applications of the Definite Integral in Geometry, Science and Engineering;
• Principles of Integral Evaluation;
• Mathematical Modelling with Differential Equations;
• Infinite Series;
• Parametric and Polar Curves;

### Discrete Mathematics 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. Combined 9th ed; Publisher New York: Wiley, c2010. (Hamilton 515P23*8;2)
• Or
• Calculus: single variable / Howard A.Anton, Irl Bivens, Stephen Davis. 9th ed. 2009 (Hamilton 515 P2*8;4, S-LEN 515 P2*8)

(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)

• Erwin Kreyszig, Advanced Engineering Mathematics (9th edition), Wiley, 2006 (Hamilton 510.24 L21*8, S-LEN 510.24 L21*8)

(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, Mass., London: Pearson/Addison Wesley, c2005. (Hamilton 515.1 K82*10;*)

Module Prerequisite:

MA1S11 - Mathematics for Scientists (First Semester)

Assessment Detail
This module will be examined in a 3 hour examination in Trinity term. Continuous assessment will contribute 10% to the final grade for the module at the annual examination session and at supplementals where applicable.