F17XF - Mathematics for Engineers and Scientists 2

Course leader(s):

Mateja Presern (Edinburgh, January)

Aims

To provide a sound basis in mathematical topics of relevance to science and engineering and other numerate disciplines.

Syllabus

1. Advanced Differentiation (1.1 Revision of differentiation; Maclaurin and Taylor series.)

2. Applications of Differentiation (2.1 Optimisation, Differential equations.)

3. Advanced Integration (3.1 Revision of integration; Integration by substitution; Integration by parts; Integration using partial fractions.)

4. Applications of Integration (4.1 Area under and between curves; Average value; Curvelength; Separation of variables for 1st order ODEs; Approximate integration Trapezoidal rule.)

5. Complex Numbers (5.1 Definition; Real and imaginary parts; Arithmetic of complex numbers;Solving quadratic equations; The Argand diagram; Modulus and argument; the polar form of a complex number; The exponential form; De Moivre’s theorem.)

6. Matrices (6.1 Definition and notation for matrices; Null zero matrix; Identity matrix; Transpose matrix; Addition and subtraction; Multiplication by a scalar; Matrix multiplication; The 2x2 and 3x3 determinant; The inverse of a 2x2 matrix; Solving systems of linear equations; formulating problems in matrix form.)

Learning outcomes

By the end of the course, students should be able to do the following:

Apply differentiation to solving maximisation or minimisation problems in science and engineering
Calculate Maclaurin and Taylor series for functions of one variable using known results for the differentiation of functions
Evaluate indefinite and definite integrals using various analytical and numerical methods
Verify solutions of first and second order differential equations and solve first order separable differential equations
Demonstrate fluency in manipulating complex numbers in cartesian, polar and exponential form
Perform accurate calculations with matrices and determinants and use them to solve systems of equations
Solve systems of linear equations using row elimination

Further details

Curriculum explorer: Click here

SCQF Level: 7

Credits: 15