UNIVERSITY OF DURHAM - Department of Mathematical Sciences

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MATH 1551: MATHEMATICS FOR ENGINEERS & SCIENTISTS. Dr. J.F. Blowey/ Dr. C. Kearton ... K.A. Stroud, Engineering Mathematics, Macmillan (paperback),.
22 MATH 1551: MATHEMATICS FOR ENGINEERS & SCIENTISTS Dr. J.F. Blowey/Dr. C. Kearton Prerequisites: Grade C at A-level Mathematics. Method of Assessment: 90% for a 3-hour written examination in May/June, 10% for completion of the weekly problems. Excluded combinations of Modules: Core Mathematics A (MATH 1012), Core Mathematics B (MATH 1022), Single Mathematics A (MATH 1561), Single Mathematics B (MATH 1571) may not be taken before with or after this module. This module is intended to supply the basic mathematical needs for students in Engineering and other sciences. The module beings with a diagnostic test followed by revision classes. There are 3 lectures each week and fortnightly tutorials. Problems will be set to be handed in each week and there is a Collection examination in January. All these form an integral part of the module. Books Students should buy either the two books by Stroud or the book by Spiegel or Stephenson. M.R. Spiegel, Advanced Mathematics for Engineers and Scientists, McGraw-Hill (paperback), (ISBN 0-07-084355-4). K.A. Stroud, Engineering Mathematics, Macmillan (paperback), (ISBN 0-333-91939-4). K.A.Stroud, Further Engineering Mathematics, Macmillan (paperback), (ISBN 0-333-65741-1). G.Stephenson, Mathematical Methods for Science Students, Longman. If you are not too confident about the mathematics module then the books by Stroud will provide you with much support throughout the module. Students found these books very helpful in previous years. You will probably already know some of the material in the first book. Spiegel is a more concise text and assumes knowledge of elementary calculus from the first term. It is short on explanation but contains lots of worked examples. Stephenson is also concise. Each of the above books should prove useful for parts of the second year mathematics module for Engineering students. You may also like to refer to: (all paperbacks) A. Croft, R. Davison and M. Hargreaves, Engineering Mathematics, Addison-Wesley. M.R. Spiegel, Advanced Calculus, Schaum. M.R.Spiegel, Vector Analysis, Schaum.

23 Mathematics for Engineers & Scientists – MATH 1551 Term 1 Elementary Functions (practical) Their graphs, trigonometric identities and 2D Cartesian geometry: To include polynomials, trigonometric functions, inverse trigonometric functions, e x , !n , x , sin (x ± y ) , sine and cosine formulae. Line, circle, ellipse, parabola, hyperbola. Differentiation (Practical) Definition of the derivative of a function as slope of tangent line to graph. Local maxima, minima and stationary points. Differentiation of elementary functions. Rules for differentiation of sums, products, quotients and function of a function. Integration (Practical) Definition of integration as reverse of differentiation and as area under a graph. Integration by partial fractions, substitution and parts. Reduction formula for ∫ sin n x dx . Complex Numbers (9) Addition, subtraction, multiplication, division, complex conjugate. Argand diagram, modulus, argument. Complex exponential, trigonometric and hyperbolic functions. Polar coordinates. de Moivre's theorem. Positive integer powers of sin u, cos u in terms of multiple angles. Differentiation (9) Limits: Continuity, l'Hopital's rule. Leibniz rule. Tangents, normals. Newton Raphson method for roots of f (x ) = 0 . Power series, Taylor's and Maclaurin's theorem, and applications. Vectors (9) Addition, subtraction and multiplication by a scalar. Applications in mechanics. Direction cosines. Lines and planes. Distance apart of skew lines. Scalar and vector products. Triple scalar product, determinant notation. Moments about point and line. Differentiation with respect to a scalar. Velocity and acceleration. Terms 2 and 3 Partial Differentiation (6) Functions of several variables. Chain rule. Level curves and surfaces. Gradient of a scalar function. Normal lines and tangent planes to surfaces. Local maxima, minima, and saddle points. Integration (9) Areas, volumes, length of arc, area of a surface of revolution, centre of gravity, second moments of area, moments of inertia. Cylindrical and spherical coordinates. Numerical Integration Rectangular, trapezoidal and Simpson's rules. Ordinary Differential Equations (18) First order differential equations: Separable, homogeneous, exact, linear. Second order linear equations: Superposition principle. Complementary function and particular integral for equations with constant coefficients. Fitting initial conditions. Application to circuit theory and mechanical vibrations. Laplace transform and inverse Laplace transform: Basic properties and theorems concerning derivatives, integrals, shifts, transforms of elementary functions. Tables. Application to the solution of ordinary differential equations. Dirac delta function. Convolution theorem. Final value theorem. Transients in electrical circuits. Linear systems and transfer functions. Visit this module’s web page for more info and links