**Week** |
**Topics** |
**Study Materials** |

1 |
Limits of functions, Limits at infinity and infinite limits |
(From textbook) 1.2,1.3 |

2 |
Continuity, The formal definition of limit, Tangent lines and their slopes, |
1.4,1.5,2.1 |

3 |
The derivative , Differentiation rules, The chain rule, |
2.2,2.3,2.4 |

4 |
Derivatives of trigonometric functions, Higher order derivatives, The Mean-Value Theorem, |
2.5,2.6,2.8 |

5 |
Implicit differentiation, Antiderivatives and Initial-Value Problems, Inverse functions, Exponential and logarithmic functions, |
2.9,2.10,3.1,3.2 |

6 |
The natural logarithm and exponential, The inverse trigonometric functions, |
3.3,3.5 |

7 |
Related rates , Indeterminate forms, |
4.1,4.3 |

8 |
Extreme values, Concavity and inflections |
4.4,4.5 |

9 |
Sketching the graph of a function, Extreme-value problems, |
4.6,4.8 |

10 |
Linear approximations , Sums and sigma notation, Areas as limits of sums, The definite integral, |
4.9,5.1,5.2,5.3 |

11 |
Properties of the definite integral, The Fundamental Theorem of Calculus |
5.4,5.5 |

12 |
The method of substitution, Areas of plane regions |
5.6,5.7 |

13 |
Integration by parts, Integrals of rational functions |
6.1,6.2 |

14 |
Inverse substitutions, Improper integrals |
6.3,6.5 |