about

Multivariable Calculus extends differential and integral calculus concepts to functions in two or more variables. The topics include vectors, dot products, cross products, equations of lines and planes, surfaces, vector-valued functions, derivatives and integrals of vector-valued functions, space curves, partial and directional derivatives, extrema, double and triple integrals, etc. The curriculum may include concepts such as vector fields, line integrals, applications from the natural sciences or content from abstract mathematics topics.

notes / updates


October 15, 2024 | Problem 57, Section 11.5 with SageMath
    
      # Section 11.4 | Problem 57

t = var('t')
P = sphere((0,2,1), 0.2, color='red')
Q = sphere((0,1,2), 0.2, color='purple')
line1 = parametric_plot3d((2*t,1-t,2+t),(t,-3,3))

v = vector([2,-1,1])
u = vector([0,1,-1])
proj = ((u.dot_product(v))/(norm(v)*norm(v)))*v
norml = u - proj
line2 = parametric_plot3d((0 +norml[0]*t,2+norml[1]*t,1+norml[2]*t),(t,-3,3))
P + Q + line1 + line2
    
  

September 25, 2024 | Some code for SageMath and Geogebra
  
  # SageMath start
  # To declare Point objects
  A=(1,2,3)
  B=(1,-2,5)
  C=(3,1,5)

  # To draw a vector as a geometric shape
  arrow(A,B)
  # To draw more than 1 vector (triangle rule)
  arrow(A,B) + arrow(B,C) + arrow (A,C)

  # To form a vector from points
  AB = vector(B[0]-A[0], B[1]-A[1], B[2]-A[2])
  BC = vector(C[0]-B[0], C[1]-B[1], C[2]-B[2])

# To print the vector:
 AB 
 print("BC: ", BC)

 # To plot vectors
 plot(AC, start=A) + plot(AB, start=A) + plot(BC, start=B)

 # To check if two vectors are equal
  
 AB == BC
   
  # SageMath end

   # Geogebra start (save the document if you want to keep your work)
   #declare Point objects
   A=Point({1,1,1})
   B=Point({-1,2,3})
   C=Point({2,2,-1})

   # form vectors from points
   AB = Vector(A,B)
   BC = Vector(B,C)

   # Geogebra end