## MA10236: Vectors, vector calculus and mechanics

[Page last updated: 20 April 2021]

Owning Department/School: Department of Mathematical Sciences
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Certificate (FHEQ level 4)
Period:
Semester 2
Assessment Summary: EX 100%
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
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 vector-based 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 three-dimensions, 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: vector-valued 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 non-resisting and resisting media; pendulums; chaotic double pendulum; spacecraft and celestial dynamics.

Programme availability:

#### MA10236 is Compulsory on the following programmes:

Department of Mathematical Sciences
• USMA-AFB15 : BSc(Hons) Mathematical Sciences (Year 1)
• USMA-AAB16 : BSc(Hons) Mathematical Sciences with Study year abroad (Year 1)
• USMA-AKB16 : BSc(Hons) Mathematical Sciences with Year long work placement (Year 1)
• USMA-AFB13 : BSc(Hons) Mathematics (Year 1)
• USMA-AAB14 : BSc(Hons) Mathematics with Study year abroad (Year 1)
• USMA-AKB14 : BSc(Hons) Mathematics with Year long work placement (Year 1)
• USMA-AFB01 : BSc(Hons) Mathematics and Statistics (Year 1)
• USMA-AAB02 : BSc(Hons) Mathematics and Statistics with Study year abroad (Year 1)
• USMA-AKB02 : BSc(Hons) Mathematics and Statistics with Year long work placement (Year 1)
• USMA-AFB20 : BSc(Hons) Mathematics, Statistics, and Data Science (Year 1)
• USMA-AAB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Study year abroad (Year 1)
• USMA-AKB20 : BSc(Hons) Mathematics, Statistics, and Data Science with Industrial Placement (Year 1)
• USMA-AFM14 : MMath(Hons) Mathematics (Year 1)
• USMA-AAM15 : MMath(Hons) Mathematics with Study year abroad (Year 1)
• USMA-AKM15 : MMath(Hons) Mathematics with Year long work placement (Year 1)
Department of Physics
• USXX-AFB03 : BSc(Hons) Mathematics and Physics (Year 1)
• USXX-AAB04 : BSc(Hons) Mathematics and Physics with Study year abroad (Year 1)
• USXX-AKB04 : BSc(Hons) Mathematics and Physics with Year long work placement (Year 1)
• USXX-AFM01 : MSci(Hons) Mathematics and Physics (Year 1)
• USXX-AAM01 : MSci(Hons) Mathematics and Physics with Study year abroad (Year 1)
• USXX-AKM01 : MSci(Hons) Mathematics and Physics with Year long work placement (Year 1)

 Notes: This unit catalogue is applicable for the 2021/22 academic year only. Students continuing their studies into 2022/23 and beyond should not assume that this unit will be available in future years in the format displayed here for 2021/22. Programmes 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.