MATH19731
Mathematics 1G1
10
Semester 1
Undergraduate
Level 1
Gabor Megyesi
Unit coordinator
Department of Mathematics
1
FHEQ level (Framework for Higher Education Qualifications) ' First part HE study/Bachelors '
European Credit Transfer & Accumulation System Rating : 5.0
<p>This unit covers the topics in applied mathematics required to provide the necessary tools to study materials science at an undergraduate level.</p><p> </p><p>The lectures cover:</p><p> </p><p>Elementary functions: linear functions, powers, polynomials, fractions, exponentials, logarithms,</p><p> </p><p>Basic differential calculus: differentials and derivatives, main properties, differentiation of elementary functions. Chain, Product and Quotient Rules. Differentiation of functions of several variables, partial derivatives </p><p> </p><p>Integral calculus: definite and indefinite integrals, relation with differentiation, tables of integrals, methods of integration. Error function.</p><p> </p><p>Application of differential calculus to functions: Taylor formula, approximate calculations, maxima / minima. </p>
<p>This unit covers the topics in applied mathematics required to provide the necessary tools to study materials science at an undergraduate level.</p><p> </p><p>The lectures cover:</p><p> </p><p>Elementary functions: linear functions, powers, polynomials, fractions, exponentials, logarithms,</p><p> </p><p>Basic differential calculus: differentials and derivatives, main properties, differentiation of elementary functions. Chain, Product and Quotient Rules. Differentiation of functions of several variables, partial derivatives </p><p> </p><p>Integral calculus: definite and indefinite integrals, relation with differentiation, tables of integrals, methods of integration. Error function.</p><p> </p><p>Application of differential calculus to functions: Taylor formula, approximate calculations, maxima / minima. </p>
<p>The unit aims to:</p><p>Introduce the mathematical tools for symbolic and numerical manipulation and analysis required to study materials science at an undergraduate level. </p>
<p><i>On the successful completion of the course, students will be able to: </i></p><p>ILO 1</p><p>Use properties of elementary functions, solve simple equations, use the binomial formula, and express an arbitrary rational function as the sum of its whole part and partial fractions;</p><p>ILO 2</p><p>Differentiate (find differentials and derivatives of) all elementary functions and apply properties of differentiation to differentiate their arbitrary combinations; find differentials and partial derivatives for functions of several variables, including higher partial derivatives; apply differentials to approximate calculations and estimation of errors;</p><p>ILO 3</p><p>Recognize standard indefinite integrals; express definite integrals using the fundamental theorem of calculus, in particular, calculate areas under graphs; find antiderivatives satisfying initial value condition;</p><p>ILO 4</p><p>Apply integration methods such as integration by parts and substitution; solve integrals of rational functions by using partial fraction decomposition;</p><p>ILO 5</p><p>State the Taylor formula for the standard list of functions; find Taylor expansion with a small number of terms for a given function; apply Taylor expansions to finding limits and approximate calculations.</p>
<p>1 review session and 1 tutorial per week, 4 hours of private study including watching the videos, reading the notes and doing the quizzes in the VLE. </p>
0
Other
10%
1
Written exam
70%
2
Written assignment (inc essay)
10%
3
Report
10%
<p><strong>Coursework - 1-2 hours, 30% weighting</strong></p><p><strong>Final exam - 2 hours, 70% weighting</strong></p>
N
<p>“Mathematical techniques: An introduction for the engineering, physical and mathematical sciences” D.W. Jordan and P. Smith, 2008, 4th ed, Oxford University Press: Oxford.</p><p> “Engineering mathematics” K.A. Stroud and D.J. Booth, 2013, 7th ed, Palgrave Macmillan: Basingstoke. (available as an e-book from the library)</p><p>HELM (Helping Engineers Learn Mathematics), available at http://www.maths.manchester.ac.uk/study/undergraduate/information-for-current-students/service-teaching/helm/ </p>
Assessment written exam
3
Lectures
11
Tutorials
11
0
75