MA10236: Vectors, vector calculus and mechanics
[Page last updated: 20 April 2021]
Academic Year:  2021/2 
Owning Department/School:  Department of Mathematical Sciences 
Credits:  6 [equivalent to 12 CATS credits] 
Notional Study Hours:  120 
Level:  Certificate (FHEQ level 4) 
Period: 

Assessment Summary:  EX 100% 
Supplementary Assessment: 

Requisites:  Before taking this module you must take MA10230 
Aims:  Introduce vectors, vector algebra and basic vector calculus in two and three dimensions, developing algebraic competency and geometric intuition. Demonstrate the application of these techniques in kinematics. Develop an understanding of the process of mathematical modelling, and technical competency in vectorbased approaches to mathematical modelling through Newtonian mechanics applied to a selection of problems in classic particle dynamics. Develop the ability to identify and solve second order differential equations that occur in diverse contexts. Develop the ability to make geometric and physical interpretations of mathematical formulations. Motivate mathematical methods with a broad range of practical applications. 
Learning Outcomes:  After taking this unit students should be able to: construct, implement, interpret and visualise vectors, the operations of vector algebra, vector valued functions and basic vector calculus in two and three dimensions. Use vectors, vector algebra and basic vector calculus to set up, solve and interpret models of physical phenomena involving particle motion. Use vectors, vector algebra and basic vector calculus with Newton's Second Law to set up, solve and interpret models of physical phenomena involving particle dynamics. Use computer packages to visualise vectors and vector operators in two and threedimensions, and develop physical intuition from equations of motion. 
Skills:  Numeracy T/F A
Problem Solving T/F A Information Technology T/F Written and Spoken Communication F (in tutorials) 
Content:  Part 1 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: vectorvalued functions of one variable; differentiation; arc length; line integrals; directional derivatives and gradients. Kinematics of particles: velocity, acceleration, angular velocity. Part 2 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 in Parts 1 & 2 may include: Kepler's laws of planetary motion;� projectiles in nonresisting and resisting media; pendulums; chaotic double pendulum; spacecraft and celestial dynamics. 
Programme availability: NB. Postgraduate programme information will be added when the postgraduate catalogues are published in August 2021 
MA10236 is Compulsory on the following programmes:Department of Mathematical Sciences

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