MAT495: Sept 2013 – Jan 2014

Partial Derivatives & Approximation Methods

Class Schedule

APB3Al

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

Contents

WeekDate

Topic
19 Sept - 13 Sept 20131
FUNCTIONS OF SEVERAL VARIABLES


1.1
Introduction to Functions of Several Variables



οDefinitions, notations



οGraph of functions of two variables



οDomain and range



οLimits and continuity





216 Sept - 20 Sept 20131.2
Partial Derivatives

16 Sept (Malaysia Day)
οDefinitions (using limits)



οInterpretations (in 3 dimensions, derivatives as slope/rate of change



οFinding and evaluating partial derivatives using rules





323 Sept - 27 Sept 20131.3
Higher Order Derivatives



οNotations



οHigher order derivatives




Quiz 1





430 Sept - 4 Oct 20131.4
Chain Rule


1.5
Implicit Differentiation





57 Oct - 11 Oct 20131.6
Total Diferentials




Test 1






14 Oct - 20 Oct 2013

Semester Break

15 & 16 Oct 2013

Raya Qurban





621 Oct - 25 Oct 20131.7
Equation of Tangent Plane


1.8
Linear Approximations





728 Oct - 1 Nov 20131.9
Directional Derivatives



οGradient



οFinding and evaluating directional derivatives





84 Nov - 8 Nov 20131.10
Extremum of Functions of Two Variables

5 Nov Awal Muharram
οSecond Derivative Test




Quiz 2





911 Nov - 15 Nov 20131.11
Lagrange Multiplier





1018 Nov - 22 Nov 20132
NUMERICAL METHODS


2.1
Root-Finding Problems



οBisection method





1125 Nov - 29 Nov 2013
οNewton's method




Test 2





122 Dec - 6 Dec 20132.2
Polynomial Interpolation



οDifference table





139 Dec - 13 Dec 2013
οNewton's forward difference




Quiz 3





1416 Dec - 20 Dec 2013
οNewton's backward difference




Test 3

Assessment

Final examination – One 2-hour paper : 60%

Continuous assessment : 40%
  1. Test 1 : 10%
  2. Test 2 : 10%
  3. Test 3 : 10%
  4. Quizzes/Assignments (3) : 10%

Textbook

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