## Partial Derivatives & Approximation Methods

## Contents

Week | Date | Topic |

1 | 3/3/2014 - 7/3/2014 | 1. FUNCTIONS OF SEVERAL VARIABLES |

1.1. Introduction to functions of several variables | ||

Definitions and notations | ||

Graph of functions of two variables | ||

Domain and range | ||

Limits and continuity | ||

Tutorial | ||

2 | 10/3/2014 - 14/3/2014 | 1.2. Partial Derivatives |

Definitions (using limits) and notations | ||

Interpretations (partial derivative as slopes in three dimensions Cartesian coordinate or as rates of change) | ||

Rules of partial differentiation | ||

Tutorial | ||

3 | 17/3/2014 - 21/3/2014 | 1.3. Higher Order Partial Derivatives |

Notations | ||

Determination and evaluation of higher order partial derivatives | ||

Tutorial | ||

QUIZ 1 | ||

4 | 24/3/2014 - 28/3/2014 | 1.4. Chain Rule |

One independent variable | ||

Two independent variables | ||

1.5. Implicit Differentiation | ||

Tutorial | ||

5 | 31/3/2014 - 4/4/2014 | 1.6. Total Differentials |

TEST 1 | ||

6 | 7/4/2014 - 11/4/2014 | 1.7: Equation of Tangent Plane |

1.8: Linear Approximations (Tangent Plane Approximations) | ||

Tutorial | ||

14/4/2014 - 20/4/2014 | Mid-semester Break | |

7 | 21/4/2014 - 25/4/2014 | 1.9. Directional Derivatives and Gradients |

Gradient Vectors | ||

Determination and evaluation of directional derivatives | ||

Tutorial | ||

8 | 28/4/2014 - 2/5/2014 | 1.10. Extremum of functions of two variables |

Second Partial Derivative Test | ||

Tutorial | ||

QUIZ 2 | ||

1/5/2014 (Thursday) | Labour Day | |

9 | 5/5/2014 - 9/5/2014 | 1.11. Lagrange Multiplier |

Extreme values with one constraint | ||

Tutorial | ||

10 | 12/5/2014 - 16/5/2014 | 2. APPROXIMATION METHODS |

2.1. Solving Non-Linear Equations | ||

Bisection Method: | ||

- Existence of roots (root finding) | ||

- Bisection procedure | ||

Tutorial | ||

13/5/2014 (Tuesday) | Wesak Day | |

17/5/2014 (Saturday) | Hari Keputeraan Tuanku Raja Perlis | |

11 | 19/5/2014 - 23/5/2014 | Newton’s Method: |

- Newton’s formula | ||

- Application of Newton’s method | ||

Tutorial | ||

26/5/2014-1/6/2014 | SPECIAL BREAK | |

27/5/2014 (Tuesday) | Israk dan Mikraj | |

12 | 2/6/2013 - 6/6/2013 | 2.2. Polynomial Interpolation |

Difference table | ||

TEST 2 | ||

7/6/2014 (Saturday) | Keputeraan YDP Agong | |

13 | 9/6/2014 - 13/6/2014 | Newton’s forward difference |

Tutorial | ||

QUIZ 3 | ||

14 | 16/6/2014 - 20/6/2014 | Newton’s backward difference |

TEST 3 | ||

23/6/2014 - 24/6/2014 | Revision Week | |

25/6/2014 - 13/7/2014 | Examination | |

## Assessment

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

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