**Advanced Engineering Mathematics**

This is a level 3 course aimed at students pursuing a degree in Engineering disciplines such as electrical, civil, or mechanical engineering. Teaching in this course will always be supported by practice problems and computer simulations. It covers the following topics.

The Laplace Transform
Solutions of initial value problems using the Laplace Transform |

Shifting Theorem
Vector Functions of one Variable |

The Gradient Field
Divergence and Curl |

Line Integrals
Green’s Theorem |

Independence of Path and Potential Theory
Surface Integrals |

Divergence Theorem of Gauss
The integral theorem of stokes. |

Why Fourier Series?
The Fourier Series of a function |

Convergence of Fourier Series
The Fourier integral |

Fourier Cosine and Sine Integrals
The Complex Fourier integral and the Fourier Transform |

The Wave Equation and Initial and boundary conditions |

Fourier Series Solution of the wave equation |

The Heat Equation and Initial and boundary conditions |

Fourier Series Solution of the heat equation |