## Partial Derivatives & Approximation Methods

## Class Schedule

#### APB3Al

- Monday – 1430-1620 – A108
- Wednesday – 1200-1250 – F230

## Contents

Week | Date | Topic | ||
---|---|---|---|---|

1 | 9 Sept - 13 Sept 2013 | 1 | FUNCTIONS OF SEVERAL VARIABLES | |

1.1 | Introduction to Functions of Several Variables | |||

ο | Definitions, notations | |||

ο | Graph of functions of two variables | |||

ο | Domain and range | |||

ο | Limits and continuity | |||

2 | 16 Sept - 20 Sept 2013 | 1.2 | Partial Derivatives | |

16 Sept (Malaysia Day) | ο | Definitions (using limits) | ||

ο | Interpretations (in 3 dimensions, derivatives as slope/rate of change | |||

ο | Finding and evaluating partial derivatives using rules | |||

3 | 23 Sept - 27 Sept 2013 | 1.3 | Higher Order Derivatives | |

ο | Notations | |||

ο | Higher order derivatives | |||

Quiz 1 | ||||

4 | 30 Sept - 4 Oct 2013 | 1.4 | Chain Rule | |

1.5 | Implicit Differentiation | |||

5 | 7 Oct - 11 Oct 2013 | 1.6 | Total Diferentials | |

Test 1 | ||||

14 Oct - 20 Oct 2013 | Semester Break | |||

15 & 16 Oct 2013 | Raya Qurban | |||

6 | 21 Oct - 25 Oct 2013 | 1.7 | Equation of Tangent Plane | |

1.8 | Linear Approximations | |||

7 | 28 Oct - 1 Nov 2013 | 1.9 | Directional Derivatives | |

ο | Gradient | |||

ο | Finding and evaluating directional derivatives | |||

8 | 4 Nov - 8 Nov 2013 | 1.10 | Extremum of Functions of Two Variables | |

5 Nov Awal Muharram | ο | Second Derivative Test | ||

Quiz 2 | ||||

9 | 11 Nov - 15 Nov 2013 | 1.11 | Lagrange Multiplier | |

10 | 18 Nov - 22 Nov 2013 | 2 | NUMERICAL METHODS | |

2.1 | Root-Finding Problems | |||

ο | Bisection method | |||

11 | 25 Nov - 29 Nov 2013 | ο | Newton's method | |

Test 2 | ||||

12 | 2 Dec - 6 Dec 2013 | 2.2 | Polynomial Interpolation | |

ο | Difference table | |||

13 | 9 Dec - 13 Dec 2013 | ο | Newton's forward difference | |

Quiz 3 | ||||

14 | 16 Dec - 20 Dec 2013 | ο | Newton's backward difference | |

Test 3 |

## Assessment

Final examination – One 2-hour paper : 60%Continuous assessment : 40%

- Test 1 : 10%
- Test 2 : 10%
- Test 3 : 10%
- Quizzes/Assignments (3) : 10%

## Textbook

- Stewart, J. (2012).
*Calculus (7th Edition)*. Brooks/Cole, Cengage Learning. - Burden, R. & Faires J. D. (2003). Numerical Methods, (3rd ed.). Pacific Grove.