The first aim of Mathematics 4 is to further develop the broad range of standard mathematical techniques in linear algebra, analysis and calculus assimilated in Mathematics 2. The second aim is to enable the student to apply these mathematical 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.
