Week 1 |

Parametric Equations & Polar Coordinates: Parametric equations, polar coordinate system. Relationship between Cartesian and polar coordinates. |

Week 2 |

Graphs of polar equation and intersections point in polar coordinates. |

Week 3 |

Review: Graphs of trigonometric functions, exponential, trigonometric identities, and graphs of f and f ^{–1 }in general. Transcendental Functions: Hyperbolic functions, Inverse trigonometric functions, and inverse hyperbolic functions. |

Week 4 |

Graphs of hyperbolic, hyperbolic inverses and trigonometric inverses. Identities of hyperbolic and trigonometric inverses, and solving related equations |

Week 5 |

Differentiation (including implicit relation) of functions and relations involving hyperbolic and inverses. |

Week 6 |

Integration of functions involving hyperbolic and inverses using definition, identities and integration by parts. |

Week 7 |

Integration using substitution method, partial fraction, trigonometric and hyperbolic substitutions. |

Week 8 |

Further Applications of Integration: Arc length, area of surface of revolution in Cartesian form. |

Week 9 |

Arc length, area of surface of revolution in polar and parametric form. |

Week 10 |

Improper Integrals. L’Hopital’s Rule, Integral of first kind |

Week 11 |

Integral of second kind |

Week 12 |

Multivariable Functions: Terminology and notation, domain and range of two and three variables functions. Graphs of two variable functions: Surfaces and level curves. |

Week 13 |

Graphs of three variable functions: Level surfaces. |

Week 14 |

Limits and continuity: Notions of limits and continuity for functions of two variables including non-existence of limits (two paths rule). |