Further Algebra and Calculus

Cod y Modiwl
MP11010
Teitl y Modiwl
Further Algebra and Calculus
Blwyddyn Academaidd
2027/2028
Semester
Semester 2
Cyd-gysylltydd y Modiwl
Dr Alexander Pitchford
Rhestr Ddarllen
Gweld ar Aspire
Rhagofynion
MP10610
Rhagofynion
FG16210 neu MA10510 neu MT10510
Anghymharus (Unrhyw Flwyddyn Acad)
MT11010
Staff Eraill sy'n Cyfrannu
Mrs Rosemary Rogers
Dr Alexander Pitchford
Dr Tudur Davies

Dulliau Asesu

Math o Asesiad

Manylion Asesiad

Cyfran
Asesiad Semester Coursework: Mark based on engagement, participation and submitted assignments 20%
Arholiad Semester Written Exam: 2 Awr 80%
Asesiad Ailsefyll Blackboard Test: 20%
Arholiad Ailsefyll Written Exam: 2 Awr 80%

Canlyniadau Dysgu

Wedi cwblhau'r modiwl dylai'r myfyrwyr fedru:

  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.

Disgrifiad cryno

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.

Nod

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.

Cynnwys

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.

Sgiliau Modiwl

Math o Sgiliau

Manylion Sgiliau
Addasrwydd a gwydnwch Completion of tasks (assignments) to set deadlines will aid personal development.
Cyfathrebu proffesiynol Written answers to exercises must be clear and well structured.
Datrys Problemau Creadigol The assignments will give the students opportunities to show creativity in finding solutions and develop their problem solving skills.
Gallu digidol Use of Blackboard and internet resources.
Sgiliau Pwnc-benodol Broadens exposure of students to topics in mathematics.

Nodau

Mae'r modiwl hwn yn cydymffurfio a FfCChC Lefel 4