The first aim of Mathematics 4 is to further develop the broad range of standardmathematical techniques in linear algebra, analysis and calculus assimilated inMathematics 2. The second aim is to enable the student to apply thesemathematical techniques to the solution of bounded engineering problems.
Introduction to functions of several variables
Evaluation of functions of several variables. Plotting in MATLAB. Partial differentiation.
Vector Calculus
Scalar fields, vector fields. Calculate the gradient of a scalar field and the divergence and curl of a vector field.
Integration
Integration methods. Definite and indefinite integrals. Using substitution. Integration by Parts. Partial fractions.
Matrix Algebra
Eigenvectors and Eigenvalues. Finding using algebraic method. Approximation using the Power Method. Determinants and inverses: using cofactors to find 4 × 4 determinants and 3 × 3 inverses.
Programming Skills
Review and programming exercises to consolidate the understanding of the basic programming structures.
Solution of Non Linear Equations
Graphical exploration to locate approximate roots. Iterative point estimation and interval reduction methods. Convergence of iterative methods. Algorithms. Writing programs to solve non-linear equations.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 30 |
| Formal Examination | 70 |