BSc Computer Science and Mathematics

Year of entry: 2022

Course unit details:Calculus and Applications B

Unit code MATH10232 15 Level 1 Semester 2 Department of Mathematics No

Overview

The unit will cover first and second order ordinary differential equations including classification and standard solution methods. Applications will be drawn from the field of classical mechanics, but no prior experience in mechanics is expected or required. Matlab will be used to illustrate some of the ideas and methods.

Pre/co-requisites

Unit title Unit code Requirement type Description
Linear Algebra B MATH10212 Co-Requisite Compulsory

Aims

This course unit aims to introduce students to ordinary differential equations, primarily covering methods of solution and applications to physical situations.

Learning outcomes

On completion of this unit successful students will be able to solve first order and second order linear problems and first order separable equations analytically. Use substitution methods and power series methods to find solutions. Be able to investigate solutions using direction fields and Euler's method. Have used Matlab as a mathematical tool and used differential equations to solve problems in mechanics and other applications.

Syllabus

1.Introduction: concept of mathematical modeling; definition and classification of ordinary differential equations; order; linear and autonomous equations.

2.First-order ordinary differential equations: separable, graphical and numerical solutions; initial conditions; direction fields; Euler's method; use of Matlab; existence and uniqueness of solutions; integrating-factor methods; power series; substitution methods for nonlinear equations; phase plane and stability; population modelling.

3.Higher-order ordinary differential equations: general solution of linear, second-order equations; initial and boundary conditions; homogeneous equations; particular integrals; method of undetermined coefficients; harmonic oscillators; resonance; coupled systems; phase portraits; substitution methods for nonlinear equations; plane autonomous systems; predator-prey systems.

4.Mechanics: particle kinematics in Cartesian and polar coordinates; Newton's laws; forces; Newton's law of gravitation; work and energy; motion along a line (potential wells); equilibrium and stability; simple systems of particles; simple pendulum; compound pendulum; double pendulum.

Assessment methods

Method Weight
Other 25%
Written exam 75%

Coursework; Weighting within unit 15%

Supervision; Weighting within unit 10%

Examination; Weighting within unit 75%

Feedback methods

Feedback supervision will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

Recommended reading

James Stewart, Calculus, Early Transcendentals, Thomson, 5th Edition, International Student Edition, 2003.

C. H Edwards, Elementary differential equations with boundary value problems, Pearson Prentice Hall, 2004.

Study hours

Scheduled activity hours
Lectures 36
Tutorials 12
Independent study hours
Independent study 102

Teaching staff

Staff member Role
Joel Daou Unit coordinator

Additional notes

This course unit detail provides the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.

Please see Blackboard / course unit related emails for any further updates

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