MAT295: March 2012 – July 2012

Partial Derivatives & Approximation Methods

Class Schedule

APB3Al

  • Tuesday – 1000-1150 – F020
  • Wednesday – 1200-1250 –F020

APB3Bl

  • Monday – 1200-1250 – A001
  • Friday – 1000-1150 –A001

Contents

  1. Functions of Several Variables
    • Introduction to functions of several variables
      • Definitions, notations
      • Graph of functions of two variables
      • Domain and range
      • Limits and continuity
    • Partial Derivatives
      • Definitions (using limits)
      • Interpretations (in three dimensions, derivatives as slope/ rate of change)
      • Finding and evaluating partial derivatives using rules
    • Higher Order Derivatives
      • Notations
      • Higher order derivatives
    • Chain Rule
    • Implicit Differentiation
    • Total Differentials
    • Equation of Tangent Plane
    • Linear Approximations
    • Directional Derivatives
      • Gradient
      • Finding and evaluating directional derivatives
    • Extremum of functions of two variables
      • Second Derivative Test
    • Lagrange Multiplier
  2. Numerical Methods
    • Root finding
      • Bisection method
      • Newton’s method
    • Polynomial interpolation
      • Difference table
      • Newton’s forward difference
      • Newton’s backward difference

Textbooks

  1. Stewart, J. (2003). Calculus. International Student Edition (5th ed.). Brooks/Cole.
  2. Burden, R. & Faires J. D. (2003). Numerical Methods, (3rd ed.). Pacific Grove.
Back to Top