### Applied Mathematics Course Description

#### Level III – Semester I

**AMT311β: Numerical Analysis (30 lecture hrs + 15 tutorial hrs); ( Credit Value 2.5) Op. for students following Applied Mathematics, and not allowed with AMT312β**

Solving Linear Systems: Matrix Notation, Direct Methods Gauss, Jordan, Aitken Method, etc. Iterative Methods Jacobi, Gauss – seidel, S. O. R Method, etc. Numerical solution of Ordinary differential equations: Euler and Modified Euler methods, Runge – Kutta method, Convergence criteria, Errors and error propagation. Numerical solution of partial differential equations: Parabolic type, Elliptic type, Hyperbolic type.

**Method of assessment: end of semester examination**

AMT312β: Mathematical Modelling III (30 lecture hrs + 15 tutorial hrs); ( Credit Value 2.5) Op.for students following Applied Mathematics, and not allowed with AMT311β

Solution of Linear Differential Equations by Laplace Transforms, Mathematical Modelling through Graphs, Mathematical Modelling Through Calculus of Variations and Dynamic Programming or Special Topics and/or Project,Stochastic Modelling, A survey on Ancient Sri Lankan Science and Technological Methods, Topics in Mathematical Modelling of Life-Environmental relationships.

*Method of assessment: end of semester examination*

**AMT313β: Mathematical Methods in Physics and Engineering (30 lecture hrs + 15 tutorial hrs);( Credit Value 2.5) Op. for students following Applied Mathematics, Prerequisite IMT222β or IMT223β**

Laplace transformations, Inverse Laplace Transformations, Gamma, Beta and Bessel functions, Applications in Solving the wave equation and the heat equation, Fourier series.

*Method of assessment: end of semester examination*

**AMT314β: Applied Statistics II (30 lecture hrs + 15 tutorial hrs);following Applied Mathematics, Prerequisite IMT224β**

Testing hypotheses about many population means: Introduction to analysis of variance, Linear model for analysis of variance, variability as sum of squares, Test statistics and rejection rules. The population regression: Formulating hypotheses about regression, Analysis of Variance for regression Nonparametric tests: Chi-square test,Contingency tables (test for independence), Kolmogorov-Smirnov test,The sign test, The Rank test (Mann-Whitney U-test), Runs test (one sample runs test, two sample runs test), Kruskal- Walis, H-test

*Method of assessment: end of semester examination
*

**Level III – Semester II
Refer the Optional course units offered by the Department of Mathematics for Level III- Semester II, for details.**