William Lee

• Theoretical Mechanics
• Engineering Mathematics
• Scientific Computation

• Sinking bubbles
• Bubble nucleation

MS4414 MS6021

Timetable: Weeks 1-13.

Module description suggests 7 hours of private study per week for this course.
My office hours for this course are ??. A2016a.

Exams

• 20% Midterm exam.
• 80% End of term exam.

Both exams are open book, i.e. textbooks and notes are allowed.

Midterm Topics

The midterm will focus on all of partial differentiation (calculating derivatives, errors and rates of change), and integration of elementary functions and integration using substitution.

Syllabus

Partial differentiation. Integration. Ordinary differential equations. Laplace Transforms. Fourier Series. Matrices and vectors

Details: Functions of several variables and partial differentiation. The indefinite integral. Integration techniques: of standard functions, by substitution, by parts and using partial fractions. The definite integral. Finding areas, lengths, surface areas, volumes, and moments of inertial. Numerical integration: trapezoidal rule, Simpson's rule. Ordinary differential equations. First order including linear and separable. Linear second order equations with constant coefficients. Numerical solution by Runge-Kutta. The Laplace transform: tables and theorems and solution of linear ODEs. Fourier series: functions of arbitary period, even and odd functions, half-range expansions. Application of Fourier series to solving ODEs. Matrix representation of and solution of systems of linear equations. Matrix algebra: invertibility, determinants. Vector spaces: linear independence, spanning, bases, row and column spaces, rank. Inner products: norms, orthogonanality. Eigenvalues and eignenvectors. Numerical solution of systems of linear equations. Gauss elimination, LU decomposition, Cholesky decomposition, iterative methods. Extension to non-linear systems using Newton's method.

Textbooks

• K. Stroud. Engineering Mathematics.
• H. Anton. Elementary Linear Algebra.
• E. Kreyszig. Advanced Engineering Mathematics.

• K. Atkinson. Elementary Numerical Analysis
• H. Anton and C. Rorres. Elementary Linear Algebra with Applications.
• W. H. Press et al. Numerical Recipes.

Lectures

Lecture 1. Lecture 2. Lecture 3. Lecture 3a: Partial Fractions. Lecture 4. Lecture 5, (table of Laplace transforms).

Worksheets

Worksheet 1, answers. Worksheet 2, answers. Worksheet 3. Worksheet 4. Fourier Series Worksheet.

Videos

Worksheet 1 (partial).

RC circuit inhomogeneous differential equations by lucky guess and variation of constant methods.

Second order differential equations with constant coefficients homogeneous1 homogeneous2 homogeneous3 inhomogeneous1 inhomogeneous2 inhomogeneous3.

Past Exam Papers

2003. 2004. 2005. 2006. 2007. 2008. 2009. 2010. 2011. 2012. 2013.

Example Midterm Exam

Midterm 2009. Midterm 2010

Links

Khan Academy.
5 minute screencasts on mathematics. Also on YouTube.

Wolfram Mathworld.
Encyclopaedic website on mathematics.

Wolfram Alpha.
Use to check your solutions.

Maths Learning Centre.
Free support for students of courses with a mathematics component.