ENG2005 Advanced engineering mathematics

When you finish this unit, you should be able to:

1. 1

   Use essential concepts related to mxn linear systems, including linear independence and basis, and demonstrate a broad appreciation of tensors

2. 2

   Solve systems of simple ordinary differential equations, establish and use their eigenvalues, solve simple second-order boundary-value problems

3. 3

   Represent a periodic function with a Fourier series, determine their convergence, calculate even and odd series, and apply these to solving simple periodic systems

4. 4

   Perform change of variables for multivariable functions with the chain rule, use polar coordinates, represent 2D and 3D curves parametrically and solve line integrals on these curves

5. 5

   Manipulate and evaluate double and triple integrals in Cartesian, cylindrical and spherical coordinates

6. 6

   Calculate the gradient, divergence and curl vector operations, and apply these in the evaluation of surface and volume integrals through the Gauss and Stokes theorems

7. 7

   Solve elementary partial differential equations, apply boundary and initial conditions as appropriate, and use the method of separation of variables with the wave equation, heat equation and Laplace's equation

8. 8

   Appreciate key issues related to the numerical solution of full and sparse linear systems

9. 9

   Apply a range of suitable techniques for the numerical solution of ODEs, including using discrete Fourier transforms, PS and FE methods

10. 10

    Use a range of suitable simple numerical techniques for the solution of PDEs and appreciate their advantages and disadvantages

11. 11

    Use MATLAB and other appropriate software to assist in understanding these mathematical techniques

12. 12

    Express and explain mathematical techniques and arguments clearly in words.