In this class, the students will learn the basic concept and techniques on

differentiation and integration and their basic applications. We start from

to introduce elementary functions such as trigonometric, exponential, logarithmic,

inverse trigonometric and hyperbolic functions and will learn their derivatives

and integration. Limits of functions, the convergence of sequences, Newton’s

method and Taylor expansions, length of curves, area and volume of revolutions

will also be covered.

1. Numbers and Functions, |

2. Trigonometric functions, Inverse trigonometric functions |

3. Exp-Log functions and Hyperbolic functions |

4. Differentiation 1 (Definition, product rule, quotient rule, chain rule) |

5. Differentiation 2 (Derivatives of Inverse function and implicit function) |

6. L’ Hospital’s rule and Graph sketching |

7. Intermediate value theorem, Mean value theorm |

8. Polynomial equation and Newton’s method |

9. Power series, Taylor expansion |

10. Integration 1 (Definition, Fundamental theorem of calculus) |

11. Integration 2 (Change variables, Integration by parts) |

12. Integration 3 (Infinite integral) |

13. Computation of Length, Area and Volume |

14. Fourier expansions |

15. Ordinary differential equations |

16. Final Examination |

This class is half of a joint class, together with “Exercise Session (Mathematics)”. Students must take both classes together.