# Gwybodaeth Modiwlau

Module Identifier
MP11010
Module Title
Further Algebra and Calculus
2025/2026
Co-ordinator
Semester
Semester 2
Pre-Requisite
Pre-Requisite
Other Staff

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Assessment Coursework  Mark based on attendance at lectures and tutorials and submitted assignments  20%
Semester Exam 2 Hours   (Written Examination)  80%
Supplementary Exam 2 Hours   (Written Examination)  100%

### Learning Outcomes

On successful completion of this module students should be able to:

1. solve systems of linear equations,
2. manipulate matrices according to the laws of matrix algebra,
3. evaluate determinants of square matrices,
4. determine partial derivatives of functions of several variables and establish identities involving them,
5. obtain the critical points of functions of several variables,
6. evaluate multiple integrals in rectangular coordinates,
7. evaluate multiple integrals using change of variables.

### Brief description

The aim of this module is to study situations in which functions of several variables arise naturally in Mathematics. Linear functions lead to techniques for the solution of linear equations and elementary matrix theory. Non-linear functions lead to a study of partial derivatives and multiple integrals.

### Aims

To establish a clear understanding of the techniques for studying functions of several variables and a facility for recognising when these techniques may be profitably employed.

### Content

1. MATRIX ALGEBRA: Matrix operations (addition, scalar multiplication, matrix multiplication, transposition, inversion). Special types of matrices (zero, identity, diagonal, triangular, symmetric, skew-symmetric, orthogonal). Row equivalence.
2. LINEAR EQUATIONS: Systems of linear equations. Coefficient matrix, augmented matrix. Elementary row operations. Gaussian and Gauss-Jordan elimination.
3. DETERMINANTS: Properties of determinants. Computation of determinants. Eigenvalues and eigenvectors.
4. PARTIAL DERIVATIVES: Functions of several variables. Partial Derivatives. Differentiability and linearisation. The chain rule. Critical points. Change of variables - the Jacobian.
5. MULTIPLE INTEGRALS: Riemann sums and definite integrals. Double integrals in rectangular coordinates; areas. Substitution in multiple integrals.

### Module Skills

Skills Type Skills details