# MA4J1 Continuum Mechanics

**Lecturer: **Thomas Hudson

**Term(s): **Term 1

**Status for Mathematics students:** List C

**Commitment:** 30 lectures

**Assessment:** 100% 3 hour written examination

**Formal registration prerequisites: **None

**Assumed knowledge: **This module assumes knowledge of various aspects of first and second year core maths material. Modules from other departments may also cover the necessary background. We list where the relevant material can be found for Maths and joint degree students.

- MA106 Linear Algebra: an understanding of vectors and matrices, including the ability to compute eigenvalues and eigenvectors
- MA134 Geometry and Motion or MA259 Multivariable Calculus: knowledge of multivariable calculus, including partial derivatives, divergence, curl and accompanying integral theorems
- MA133 Differential Equations or MA113 Differential Equations A: an ability to compute explicit solutions to simple ODEs
- MA131 Analysis or MA137 Mathematical Analysis or MA259 Multivariable Calculus: an appreciation of continuity and the ability to take limits

**Useful background: **MA3D1 Fluid Dynamics or MA3J4 Mathematical Modelling with PDE will serve as useful background to the modelling aspect of this module. Some background on the theory of ODEs and PDEs would also be useful, as covered in MA254 Theory of ODEs and MA3G1 Theory of PDEs

**Synergies: **The third year modules listed above would go well alongside this module. Fourth year modules which would also synergise well are:

**Leads to:** The following modules have this module listed as **assumed knowledge** or **useful background:**

**Content**: The modelling and simulation of fluids and solids with significant coupling and thermal effects is an important area of study in applied mathematics and engineering. Necessary for such studies is a fundamental understanding of the basic principles of continuum mechanics and thermodynamics. This course, which will closely follow the text "A First Course in Continuum Mechanics'' by Andrew Stuart, is a clear introduction to these principles.

The outline will be as follows: we will begin with a review of tensor algebra and calculus, followed by mass and force concepts, kinematics, and then balance laws. We will then proceed to derive some commonly used models governing isothermal fluids and solids, consisting of systems of partial differential equations (PDEs). If time permits we will also explore the thermal case.

**Book(s)**:

Oscar Gonzalez, Andrew Stuart, *A First Course in Continuum Mechanics*, Cambridge University Press, 2008.