**Mathematics I**

Week | Topic | File |

1 | Numbers, Cartesian coordinate system, lines, circles, parabolas, ellipses and hyperbolas | View |

1 | Functions | View |

2 | Trigonometric functions, inverse functions, exponential and logarithmic functions | View |

2 | Inverse trigonometric functions and hyperbolic functions | View |

3 | The concept of limit | View |

3 | Limits involving infinity, Continuity, The Max-Min Theorem, The Intermediate Value Theorem | View |

4 | Formal definition of limit, derivatives | View |

4 | Derivative as a function, one-sided derivatives, Differentiation rules, The chain rule | View |

5 | Derivatives of trigonometric functions, using differentials | View |

5 | The Mean Value Theorem, Rolle's Theorem, Implicit Differentiation | View |

6 | Derivatives of inverse functions, Logarithmic Differentiation, Related Rates Problems | View |

6 | Finding Roots of Equations: Newton's Method, Indeterminate Forms in Limits - l'Hospital's Rule | View |

6 | Critical points, Finding absolute extreme values, Concavity | View |

7 | Sketching the graph of a function, extreme value problems | View |

7 | The area problem | View |

8 | Definite integral | View |

8 | The Fundamental Theorem of Calculus, The substitution method, trigonometric integrals | View |

9 | Areas of plane regions, integration by parts | View |

10 | Integrals of rational functions, Inverse substitution method | View |

10 | Improper Integrals, volumes | View |

11 | Arc length, surface area, infinite sequences | View |

11 | Sequences, Infinite series | View |

12 | Convergence tests | View |

12 | Power series | View |

13 | Taylor and Maclaurin series | View |