Lesson Plan 1 ... mat 156... Schneider


  1. simple arithmetic
    1. evalf
    2. Expressions,Common Symbols
    3. Help
    4. Tasks--> browse gives names of tutors to help you
    5. Tasks--> tutors are tools to help you step through numbers of computations might have in calculus
  2. Defining Functions
    1. simple rules
    2. piecewise functions
    3. implicit functions-- solve
    4. more later
  3. Arithmetic Combinations to get new functions
  4. Compositions
  5. Differentiation
    1. differentiations of common functions, combinations, chain rule
    2. note if just define f:= g(f(x) or sum get the abstract rule
    3. What does differentiation mean???????
  6. Anti-differentiation
      1. same problems as in 6
      2. What does anti-differentiation mean????
  7. Graph of a function
    1. plot(g(x),x=-2..2);
    2. Given a graph you get a function
  8. Functions of two variables
  9. Plot of a function of two variables
    1. plot3d

Homework--Thur  Dont do red problems as didnt cover material yet

  1. calculate pi to 30 decimals
    1. look up evalf in online Help
  2. give an example to show that composition is not in general commutative
    1. a specific example to show g(f(x)) not in general equal to f(g(x)). You should specify particular functions for f and g
    2. Can you give two different functions f and g where g(f(x)) =f(g(x))
  3. differentiate cos(2*x^2+3*x+6) using maple -- check it by hand
  4. differentiate (x^2)^cos(x) using maple. How would you do this by hand? Hint: there is a ln involved
  5. Using maple and by hand antidifferentiate
    1.  cos(x^2)*x
    2. exp(x^3)*x^2 (exp(a) means e raised to a power .. e^a)
    3. (x^3)/(x^4)
  6. plot the following functions from 0 to 1 and then 0 to 10. Explain what you see.
    1. e^x
    2. x^6
  7. look up the plot function in help and plot the above two functions on the same graph
  8. plot the normal function exp(-x^2/2)/(2*pi)^.5 with appropriate limits of the coordinates to see its shape.(pi is the special number3.14159...)