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
- 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
- Numerical Methods
- Root finding
- Bisection method
- Newton’s method
- Polynomial interpolation
- Difference table
- Newton’s forward difference
- Newton’s backward difference
Textbooks
- Stewart, J. (2003). Calculus. International Student Edition (5th ed.). Brooks/Cole.
- Burden, R. & Faires J. D. (2003). Numerical Methods, (3rd ed.). Pacific Grove.