## Lectures

Monday and Wednesday 6:25PM-7:40PM MM 205.Thursdays 6:25PM-7:40PM MM 203

## Literature

*Essential Calculus.*James Stewart.

## Course Contents

Transcendental functions, methods of integration, L'Hospital's Rule and improper integrals, infinite series, polar coordinates, and an introduction to differential equations.Chapters 5,6,8 and part of chapters 7 and 9 from Stewart's book.

## Examination and Grading

### Tests (50%)

There will be 3 tests. These will be given on Thursdays and will be announced at least one week in advance. The test with lower score will be dropped and the other two remaining will be worth 50% towards the final grade. There will be no make-up tests.### Final (30%)

There will be a comprehensive final to be worth 30%.### Homework and Quizzes (20%)

There will be homework to be handed in every week. The homework will be assigned and completed in WebAssign (http://www.webassign.net/) . The homework posted during each week will be due the Friday of the following week. An accesscode for WebAssign is bundled with the new textbook purchased through the UM Bookstore. To get enrolled in the course in WebAssign you should use the class key:**miami 9163 0470**

There may also be some additional homework problems without any due date but that you should complete in order to train the concepts given in class. Some of these problems could appear in the quizzes, tests and the final. These problems will be assigned after some of the classes and also posted in the web page of the course.

There will be (unannounced) quizzes on some Wednesdays.

Homework and quizzes are equally weighted for the remaining 20% of the grade.

### Grading Scale

Percentage | Grade |
---|---|

>=90% | A |

>=80% | B |

>=70% | C |

>=60% | D |

<60% | F |

## Syllabus

This is an approximate schedule of the course containing the syllabus:Date | Topic |
---|---|

Wed 1/18 | Introduction. 5.1 Inverse Functions |

Thu 1/19 | 5.2 The Natural Logarithmic Function |

Mon 1/23 | 5.3 The Natural Exponential Function |

Wed 1/25 | 5.4 General Logarithmic and Exponential Functions |

Thu 1/26 | 5.5 Exponential Growth and Decay |

Mon 1/30 | 5.6 Inverse Trigonometric Functions |

Wed 2/1 | 5.7 Hyperbolic Functions |

Thu 2/2 | 5.8 Indeterminate Forms and l'Hospital's Rule |

Mon 2/6 | 5.8 Indeterminate Forms and l'Hospital's Rule |

Wed 2/8 | 6.1 Integration by Parts |

Thu 2/9 | 6.2 Trigonometric Integrals and Substitutions |

Mon 2/13 | 6.2 Trigonometric Integrals and Substitutions |

Wed 2/15 | Review for Test1 |

Thu 2/16 | Test 1 |

Mon 2/20 | 6.3 Partial Fractions |

Wed 2/22 | 6.3 Partial Fractions |

Thu 2/23 | 6.5 Approximate Integration |

Mon 2/27 | 6.6 Improper Integrals |

Wed 2/29 | 7.4 Arc Length |

Thu 3/1 | 7.4 Arc Length |

Mon 3/5 | 7.6 Differential Equations |

Wed 3/7 | 8.1 Sequences |

Thu 3/8 | 8.2 Series |

Mon 3/19 | 8.3 The Integral and Comparison Tests |

Wed 3/21 | Review for Test 2 |

Thu 3/22 | Test 2 |

Mon 3/26 | 8.4 Other Convergence Tests |

Wed 3/28 | 8.5 Power Series |

Thu 3/29 | 8.6 Representing Functions as Power Series |

Mon 4/2 | 8.7 Taylor and Maclaurin Series |

Wed 4/4 | 8.7 Taylor and Maclaurin Series |

Thu 4/5 | 8.8 Applications of Taylor Polynomials |

Mon 4/9 | 9.1 Parametric Curves |

Wed 4/11 | 9.2 Calculus with Parametric Curves |

Thu 4/12 | 9.3 Polar Coordinates |

Mon 4/16 | 9.4 Areas and Lengths in Polar Coordinates |

Wed 4/18 | Review for Test 3 |

Thu 4/19 | Test 3 |

Mon 4/23 | 9.4 Areas and Lengths in Polar Coordinates |

Wed 4/25 | 9.5 Conic Sections in Polar Coordinates |

Thu 4/26 | Review for the Final |