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Timetable: Weeks 1-13.
Module description suggests 7 hours of private study per week for
this course. Exams
Both exams are open book, i.e. textbooks and notes are allowed. Midterm TopicsThe midterm will focus on all of partial differentiation (calculating derivatives, errors and rates of change), and integration of elementary functions and integration using substitution. SyllabusPartial 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
LecturesLecture 1. Lecture 2. Lecture 3. Lecture 3a: Partial Fractions. Lecture 4. Lecture 5, (table of Laplace transforms). WorksheetsWorksheet 1, answers. Worksheet 2, answers. Worksheet 3. Worksheet 4. Fourier Series Worksheet. VideosWorksheet 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 Papers2003. 2004. 2005. 2006. 2007. 2008. 2009. 2010. 2011. 2012. 2013. Example Midterm Exam |
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Links
Khan Academy.
Wolfram Mathworld.
Wolfram Alpha.
Maths Learning Centre. |