Introduction
•To this point MATLAB has been used to answer questions with a numeric value▫Variables are assigned specific values▫Answers are numbers
•MATLAB can also solve for symbolic answers▫Example: Solve a*x + b = 0 for x
Answer: x = -b/a•Exact answers can be given instead of
numerically rounded results
Warm-Up Problem
Simplify this expression:
Symbolic Math
•The symbolic math toolbox can be used to solve many types of problems:▫Simplifying complicated expressions▫Solving algebraic equations symbolically▫Factoring polynomials▫Differentiation▫Integration▫Plotting
•We will take a look at simplifying, solving, and factoring equations today.
Simplifying• Lets go back to the warm-up problem:
• Enter this into MATLAB: syms x
s = (x^2*(x-6)+4*(3*x-2))((x+2)^2-8*x)
• Notice the result is not indented in the command window
• Let’s simplify this expression:
simplify(s)
•To generate this answer, MATLAB tries a bunch of different methods and returns the one with the fewest characters – not necessarily the prettiest one to look at
Collect, Expand, Factor• These 3 operations are all performed by simplify• Collect(): Collects like terms of the symbolic
variable (like x, x2, etc.)• Expand(): Uses polynomial multiplication and trig
identities to expand expressions• Factor(): Takes a polynomial and determines the
factors (opposite of expand)• Examples:
▫Try collecting terms in the warm-up problem▫Expand sin(x-y)▫Factor the result of the collect command in the first
example
Solve• The solve() command can solve a system of
equations▫ If the # of equations is equal to the # of variables,
then numerical answers are returned▫ If the # of equations is less than the # of variables,
then a symbolic solution is returned, in terms of the symbolic variables
Example:syms x y t
S = 10*x+12*y+16*t;
[xt yt] = solve(S, ‘5*x-y=13*t’)
Could gaussian elimination be used to solve this system?
Concept Questions
•If you have 3 unknowns and 2 equations, how many solutions are there?
•Are you guaranteed solutions?
Group Problem
•Two ellipses in the x-y plane have the following equations:
Determine the coordinates of the points where the ellipses intersect.
Plot the ellipses, and the intersection points
For Next Time
•Homework Due