MA12003: Applied mathematics 1B
[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: |
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| Assessment Summary: | CWRI 20%, CWSI 12%, EXCB 68% |
| Assessment Detail: |
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| Supplementary Assessment: |
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| Requisites: | Before taking this module you must take MA12002 |
| Learning Outcomes: |
By the end of the unit, you will be able to:
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| Synopsis: | Study further techniques in applied mathematics, including statistics and computer programming. You will study probability theory for continuous random variables and explore statistical modelling and parameter estimation. You'll learn about vectors, vector algebra and basic vector calculus in two- and three-dimensions, developing algebraic competency and geometric intuition. You will further your skills in Python programming and object-oriented design for the solution of mathematical problems.
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| Content: | Programming:
Representing numbers on a computer; systematic debugging; object-oriented programming and design: encapsulation and interfaces, operator overloading, inheritance, and abstract classes; sustainable software engineering: program design and modularisation; advanced data types, containers, and algorithms; libraries for solving mathematical problems and for manipulating and visualising data.
Probability & Statistics:
Properties of continuous random variables, common continuous distributions including the uniform, exponential, normal and gamma distributions. Transformations of random variables (RVs). Proof of the law of the unconscious statistician for a continuous RV. Joint probability density function (PDF). Marginal and conditional distributions of continuous RVs. Independence: factorisation of joint PDF as a product of marginals. Properties of covariance and correlation. Distribution of a sum of continuous RVs, including normal and exponential examples. Statement and application of the central limit theorem. Introduction to model fitting. Exploratory data analysis and model formulation.
Parameter estimation by the method of moments and maximum likelihood. Estimators as random variables. Sampling distributions of estimators. Bias, variance and mean-square error of an estimator. Graphical assessment of goodness of fit.
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. |
| Course availability: |
MA12003 is Compulsory on the following courses:Department of Mathematical Sciences
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Notes:
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