Differentiation | Mathematics Centre

Functions of two variables and their derivatives

• Functions of several variables (Centrum Matematyki PG)
• Partial derivatives - examples (Centrum Matematyki PG)
• 3D function plotting (Centrum Matematyki PG)
• Various surfaces (Centrum Matematyki PG)
• How to show that a limit does not exist (Centrum Matematyki PG)
• How to calculate limits (Centrum Matematyki PG)
• Limits and polar coordinates (Centrum Matematyki PG)
• Exercises I - graphs and limits (Centrum Matematyki PG)
• Exercises II - partial derivatives (Centrum Matematyki PG)

Optimization, i.e. finding maximum and minimum

• Minima, maxima and saddle points
  (Centrum Matematyki PG)
• Exercises
  (Centrum Matematyki PG)
• Example: f(x,y)=x³+3xy²-51x-24y - Karolina K. (II year EMP)
  (Centrum Matematyki PG)
• Example: f(x,y)=xy²(12-x-y) - Kamila Stankiewicz (II year EMP)
  (Centrum Matematyki PG)
• Example: f(x,y)=x³+8y³-6xy+2 - Alicja Szpejnowska (II year EMP)
  (Centrum Matematyki PG)
• Example: f(x,y)=4xy-x⁴-y⁴ - Kamila Zawadzka (II year EMP) 
  (Centrum Matematyki PG)
• Example: f(x,y)=2x²+y²+3xy-2x-y+1 - Marek Kowalczuk (II year EMP)
  (Centrum Matematyki PG)
• Example: f(x,y)=x³+y³-9xy+27 - Kamila Szczepańska (II year EMP)
  (Centrum Matematyki PG)
• Example: f(x,y)=48xy-32x³-24y - Milena Lipowska (II year EMP)
  (Centrum Matematyki PG)
• Example: f(x,y)=1/(5x)+5/y-xy - Dominik Bożyk (II year EMP)
  (Centrum Matematyki PG)
• Example: f(x,y)=2xy+1/x+2/y - Marta Niedźwiecka (II year EMP) 
  (Centrum Matematyki PG)
• Example: f(x,y)=xy(x+y-6) - Martyna Tokarska (II year EMP)
  (Centrum Matematyki PG)
• Example: f(x,y)=xy(x+y-6) - Paula Makuch (II year EMP)
  (Centrum Matematyki PG)
• Example: f(x,y)=x²-2xy+2y²-2y - A.Z. (II year EMP)
  (Centrum Matematyki PG)
• Example: f(x,y)=x²+y² - Magdalena Roczkowska (II year EMP)
  (Centrum Matematyki PG)
• Example: f(x,y)=1-Sqrt(x²-y²) - Wojciech Twarużek (II year EMP)
  (Centrum Matematyki PG)
• Example: f(x,y)=4x²y - x³y-x²y² - Aleksandra Lis (II year EMP)
  (Centrum Matematyki PG)