Rizauddin Saian: MAT495: Sept 2013

Partial Derivatives & Approximation Methods

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

Final examination – One 2-hour paper : 60%

Continuous assessment : 40%