- Academic Registry
Course & Unit Catalogues


MA12011: Core pure and applied mathematics B

[Page last updated: 23 October 2023]

Academic Year: 2023/24
Owning Department/School: Department of Mathematical Sciences
Credits: 15 [equivalent to 30 CATS credits]
Notional Study Hours: 300
Level: Certificate (FHEQ level 4)
Period:
Semester 2
Assessment Summary: EXCB 100%
Assessment Detail:
  • Algebra 1b (EXCB 40%)
  • Vectors, vector calculus and mechanics (EXCB 40%)
  • Functions exam (EXCB 20%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module you must take MA12010
Learning Outcomes: By the end of the unit, you will be able to:
  • Demonstrate understanding of linear algebra, including bases, dimension, rank, orthogonality, diagonalisation, including proofs. Perform computations with determinants, matrix inverses, orthonormal bases, eigenvalues, and eigenvectors.
  • Construct, implement, interpret, and visualise vectors, the operations of vector algebra, vector-valued functions and basic vector calculus in two- and three-dimensions. Set up, solve, and interpret models of physical phenomena involving particle motion, including Newton's second law. Use computer packages to visualise vectors and vector operators in two- and three-dimensions and develop physical intuition from equations of motion.
  • Demonstrate fluency and familiarity with scalar-valued functions, including elementary definitions and results and applying these concepts to a range of examples.



Synopsis: You will develop further skills in mathematics. You will study linear algebra, both via matrices and via vector spaces and linear maps, focussing on the most widely applicable aspects. You will examine the theory of continuity for functions of one real variable. You will learn about vectors, vector algebra and basic vector calculus in two and three dimensions, developing algebraic competency and geometric intuition. You will develop skills in mathematical modelling, through Newtonian mechanics

Content: Algebra: Vector spaces (over the rational, real, and complex numbers), linear maps, subspaces, kernel, and image. Linear independence, spans, bases, and dimension Matrix of a linear map, change of basis, linear operators, similar matrices. Rank, nullity and the Rank-Nullity theorem. Inner-product spaces: orthogonality, Cauchy-Schwarz inequality and applications. Gram-Schmidt process: orthonormal bases, orthogonal matrices and QR decomposition, orthogonal subspaces. Determinants and adjugates: properties and computation; invertibility of matrices. Eigenvalues, eigenvectors and eigenspaces; characteristic polynomial, algebraic and geometric multiplicities, diagonalisability. Self-adjoint operators, symmetric/Hermitian matrices and their orthogonal diagonalisation. Vectors, vector calculus and mechanics: Analysing spatial objects and particle motion with vectors. Vectors in two- and three-dimensions: vector algebra and vector identities; equations of lines and planes; finding angles; intersections and distances between points, lines, and planes; computing volumes. Vector calculus: vector-valued functions of one variable; differentiation; arc length; line integrals; directional derivatives and gradients. Kinematics of particles: velocity, acceleration, angular velocity. Newtonian particle dynamics: Introduction to mathematical modelling. Newton's laws of motion and associated forces. Forces and Newtons: inverse square laws; particle motion. Motion under constant gravity, friction, and pendulum motion. Motion under central forces: angular momentum, torque, orbits, conservation of energy. Key applications may include Kepler's laws of planetary motion; projectiles in non-resisting and resisting media; pendulums; chaotic double pendulum; spacecraft and celestial dynamics. Functions: Limits. Continuity. Differentiability. Real power series

Course availability:

MA12011 is Compulsory on the following courses:

Department of Mathematical Sciences
  • USMA-AFB33 : BSc(Hons) Mathematics, Statistics and Data Science (Year 1)
  • USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with professional placement (Year 1)
  • USMA-AKB33 : BSc(Hons) Mathematics, Statistics and Data Science with study abroad (Year 1)
Department of Physics
  • USPH-AFB26 : BSc(Hons) Mathematics and Physics (Year 1)
  • USPH-AKB26 : BSc(Hons) Mathematics and Physics with professional placement (Year 1)
  • USPH-AKB26 : BSc(Hons) Mathematics and Physics with study abroad (Year 1)
  • USPH-AFM26 : MSci(Hons) Mathematics and Physics (Year 1)
  • USPH-AKM26 : MSci(Hons) Mathematics and Physics with professional placement (Year 1)
  • USPH-AKM26 : MSci(Hons) Mathematics and Physics with study abroad (Year 1)

Notes:

  • This unit catalogue is applicable for the 2023/24 academic year only. Students continuing their studies into 2024/25 and beyond should not assume that this unit will be available in future years in the format displayed here for 2023/24.
  • Courses and units are subject to change in accordance with normal University procedures.
  • Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
  • Find out more about these and other important University terms and conditions here.