Teaching Responsibility
LJMU Schools involved in Delivery:
Computer Science and Mathematics
Learning Methods
Lecture
Practical
Module Offerings
5105MATHS-JAN-CTY
Aims
To build on differential equation theory that was introduced in Mathematical Methods (4101MATHS) and provide a comprehensive coverage of initial value problems in one independent variable and an introduction to boundary value problems.
To introduce students to systems of ordinary differential equations (ODEs) and determine how to solve linear autonomous systems of ODEs.
To introduce the concepts of asymptotic theory as a tool for analytically approximating the solution of differential equations.
Learning Outcomes
1.
Apply appropriate theorems to determine the existence and uniqueness of solutions of first and second order ODEs
2.
Analyse the salient properties of both first and second order ODEs and select appropriate methods to solve them
3.
Construct asymptotic series to approximate the solution of ODEs and evaluate their accuracy
4.
Solve a range of differential equations that model real phenomena and interpret solutions in a real-world context
Module Content
Outline Syllabus:1) First order ODEs
• Separation of variables and integrating factor method to solve initial value problems (IVPs)
• Existence and uniqueness of both linear and non-linear IVPs
2) Second order ODEs
• Existence and uniqueness of solutions of linear ODEs
• Solution of homogeneous ODEs – constant coefficients, Euler equations and series solutions
• Solution of inhomogeneous ODEs – method of undetermined coefficients, variation of parameters
3) Systems of ODEs
• Solution of simple systems, including autonomous systems of ODEs
4) Asymptotic Expansions
• Approximating the roots of equations
• Applications to the solution of differential equations
5) Boundary Value Problems
• Introduction and solution of simple examples
Module Overview:
This module will build on differential equation theory that was introduced in Mathematical Methods. You will be introduced to systems of ordinary differential equations (ODEs) and determine how to solve linear autonomous systems of ODEs and to introduce the concepts of asymptotic theory as a tool for analytically approximating the solution of differential equations.
This module will build on differential equation theory that was introduced in Mathematical Methods. You will be introduced to systems of ordinary differential equations (ODEs) and determine how to solve linear autonomous systems of ODEs and to introduce the concepts of asymptotic theory as a tool for analytically approximating the solution of differential equations.
Additional Information:This module is designed to give students experience and confidence in solving differential equations that depend on only one variable. The theory covered in this module will complement material delivered at level 6.