# William Lee

## MA4005. Engineering Maths T1

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### Timetable: Weeks 1-13.

 Lecture Monday 9am P1003 Lecture Tuesday 12noon P1006 Lecture Friday 10am P1003

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

### 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