Mathematics 1

PHYS10071 Mathematics 1 10 Semester 1 Undergraduate Level 1 Robert Appleby Unit coordinator Justin Evans Unit coordinator Department of Physics & Astronomy 1 FHEQ level (Framework for Higher Education Qualifications) ' First part HE study/Bachelors ' European Credit Transfer & Accumulation System Rating : 5.0 Mathematics 1 Mathematics 1 To allow students to develop their mathematical competence with functions, calculus, complex numbers, power series, linear algebra and differential equations to a level where they can cope with the demands of the first year of the physics course and beyond. On completion successful students will be able to:<ol><li>Describe the properties of different types of functions and be able to sketch them in both Cartesian and polar coordinates </li><li>Integrate and differentiate functions of one variable using a range of techniques and be able to apply integration and differentiation to a range of physical problems. </li><li>Show how smooth functions can be expressed in terms of power series.</li><li>Explain the properties of complex numbers and construct some basic complex functions.</li><li>Solve first and second order ordinary differential equations using a range of techniques.</li><li>Calculate surface and volume integrals in various coordinate systems</li></ol>    1. Functions, 2D coordinates, and the basics of vectors<o:p></o:p>Properties of functions. 2D and 3D coordinate systems. Sketching functions. Exponential and logarithmic functions. Vectors.<o:p></o:p>2. Polar coordinates and differential calculus<o:p></o:p>Sketching and expressing functions in polar coordinates.  The differential; differentiation of products and functions of functions; maxima, minima and inflexion points. Partial differentiation; relationship between partial and total derivative; multivariate maxima, minima and saddle points; examples and applications from physics.<o:p></o:p>3. Complex numbers<o:p></o:p>Definition, modulus and argument; multiplication and division. Complex roots of quadratic equations. Complex numbers in polar and exponential form. Examples of applications from physics. De Moivre’s theorem.  Hyperbolic functions. <o:p></o:p>4. Power series<o:p></o:p>Series. Limits of series. Binomial expansion. Taylor and Maclaurin series expansions. Taylor’s theorem for multivariate functions.<o:p></o:p>5. Integral calculus<o:p></o:p>Common and standard integral Assessment - ExamWorkshopLectureTutorial  0 Other 20% 1 Written exam 80% * Other10% Online Test 10% Tutorial Exercise   Online quizzes will also be incorporated into the weekly learning material to give students instant feedback on their understanding and ability to apply their knowledge and skills. N Recommended texts:Our recommended text: Mathematics for Physicists by Martin and Shaw (Manchester Physics Series)Mathematics for Physicists - Martin, Brian R. Shaw, Graham – Wiley – 2015 - ISBN: 0470660228<o:p></o:p>Mathematical techniques: an introduction for the engineering, physical, and mathematical sciences - Jordan, D. W.; Smith, Peter - Oxford University Press – 2008 - ISBN: 0199282013<o:p></o:p>Online Resource Centre for Jordan & Smith: Mathematical Techniques (4th edition) - web site: www.oup.com - URL: Web site: www.oup.com…<o:p></o:p>Further mathematics for the physical sciences - Tinker, Michael; Lambourne, Robert - John Wiley – 2000 -ISBN: 0471866911<o:p></o:p>Mathematical methods in the physical sciences - Boas, Mary L. – Wiley – 2006 - ISBN: 0471198269<o:p></o:p>Basic mathematics for the physical sciences - Lambourne, Robert; Tinker, Michael - Wiley – 2000 - ISBN: 0471852066<o:p></o:p>  Assessment written exam 1.5 Lectures 22 Tutorials 10 0 66.5