Lesson Plan 1 ... mat 156... Schneider
- simple arithmetic
- evalf
- Expressions,Common Symbols
- Help
- Tasks--> browse gives names of tutors to help you
- Tasks--> tutors are tools to help you step through
numbers of computations might have in calculus
- Defining Functions
- simple rules
- piecewise functions
- implicit functions-- solve
- more later
- Arithmetic Combinations to get new functions
- Compositions
- Differentiation
- differentiations of common functions, combinations, chain
rule
- note if just define f:= g(f(x) or sum get the abstract rule
- What does differentiation mean???????
- Anti-differentiation
- same problems as in 6
- What does anti-differentiation mean????
- Graph of a function
- plot(g(x),x=-2..2);
- Given a graph you get a function
- Functions of two variables
- Plot of a function of two variables
- plot3d
Homework--Thur Dont do red problems as didnt cover
material yet
- calculate pi to 30 decimals
- look up evalf in online Help
- give an example to show that composition is not in general
commutative
- 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
- Can you give two different functions f and g where g(f(x))
=f(g(x))
- differentiate cos(2*x^2+3*x+6) using maple -- check it by hand
- differentiate (x^2)^cos(x) using maple. How would you do this
by hand? Hint: there is a ln involved
- Using maple and by hand antidifferentiate
- cos(x^2)*x
- exp(x^3)*x^2 (exp(a) means e raised to a power .. e^a)
- (x^3)/(x^4)
- plot the following functions from 0 to 1 and then 0 to 10.
Explain what you see.
- e^x
- x^6
- look up the plot function in help and plot the above two
functions on the same graph
- 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...)