my worksheet about maple

1. MA4510 – Problem Solving and computational Mathematics
Maple Worksheet 2:
In this session we will explore basic Maple commands and will practice some of
the important Maple Algebra commands and how to plot a function in a Maple
worksheet.
Remember: you should complete these exercises, and ask questions if not sure.
Command What it does
simplify(expression) Simplify algebraic expressions.
expand(expression) Multiples and expands algebraic expressions.
factor(expression) Factor polynomials of one or more variables or
terms.
solve(equation)
solve(equation, variable)
Solve equations, displays exact solutions.
Solve an equation for an unknown.
fsolve(expression) Solves equations, displays numerical solutions.
Task 1: Simplify the following expressions
i)
!
!!
!
!
ii) 𝑥 + 1/𝑥 – 𝑥𝑦
iii) 2(𝑥 + 𝑥𝑦 − 𝑥!
)
Task 2: Expand the following expression
i) (x-1)(x3 + 5x – x2)
ii) (2x + 3)50
Task 3:Factor the polynomial x3 –x2 +2
Task 4: Solve the following equations:
i) x3 + x + 1 = 3x2
ii) cos(x) = x
iii) ln(x2 – 1) = a solve for x
iv) ln(x2 – 1) = 1
Note: A variation of the solve command is fsolve that can be used to solve an
equation numerically. fsolve, like solve, finds solutions to algebraic equation, but
it uses numerical methods instead of formula manipulation. While solve might
use the analytical method to solve an equation or a system, fsolve might apply a
technique that produces a series of values that converge to the true solution.

2. Task 5: 2D plots:
The command that graphs functions in Maple is the plot command. The plot
command has the structure plot(expression or function, variable =range),
where range gives the interval on the variable-axis. For example let’s plot
𝑓 𝑥 = 𝑥!
− 4𝑥 + 3
Plot the following functions, attach label to the axes and give title to the graph:
i) 𝑓(𝑥) = 𝑠𝑖𝑛(𝑥!
) for −𝜋 ≤ 𝑥 ≤ 𝜋
ii) 𝑓(𝑥) = 𝑒!!
𝑠𝑖𝑛𝑥 for −𝜋 ≤ 𝑥 ≤ 𝜋
Task 6: Multiple 2D plots
To display the graphs of several functions or expressions on the same plot, use a
set of expressions for the first argument. For example;
Plot the following functions on the same graph for x values −𝜋 ≤ 𝑥 ≤ 𝜋,
𝑦! = 2𝑠𝑖𝑛𝑥
𝑦! = 1 + sin (2𝑥)
𝑦! =
𝑠𝑖𝑛𝑥
𝑥
Adjust the plots so that: y1 is red and dashed, y2 is blue and solid, y3 is green and
dotted and add a legend.