Algebra & Calculus

Some Basic Algebra

Log[E^3]

Log[2, 8]

Factor[x^2 - 4]

Factor[x^2 - 5]

"Factor" factors a polynomial with integer coefficients over the integers only!

Factor[x^2 - 5.]

Factor[x^2 + 4]

Factor[x^2 + 4, GaussianIntegers -> True]

Factor[x^5 + 3  x^3 - 4  x^2 + 8  x - 8]

Solve[x^5 + 3  x^3 - 4  x^2 + 8  x - 8 == 0, x]

Solve[a x^2 + b x + c == 0, x]

Solve[a x^2 + b x  + c  == 0, a]

Solve[{x^2 + y^2 == 1, y == 2  x}, {x, y}]

Solve[Exp[x] == 5  x, x]

NSolve[Exp[x] == 5  x, x]

"FindRoot " uses something like Newton's Method to find ONE root of an equation.

FindRoot[Exp[x] == 5  x, {x, 0, 2}]

Some Basic Calculus

Integrate[x^7 Sin[2  x], x]

Integrate[x^7 Sin[2  x], {x, 0, 5}]

Integrate[x^2 Sin[x + y], x]

Integrate[x^2 Sin[x + y], {x, 0, 3}, {y, 1, x}]

Integrate[Exp[Cos[x^2]], {x, 0, 5}]

NIntegrate[Exp[Cos[x^2]], {x, 0, 5}]

D[x^k, x]

Log'[x]

D[x^k, {x, 2}]

D[x^2  y + y^3, x]

D[D[f[x, y], y], x] == D[D[f[x, y], x], y]

D[Integrate[f[x], x], x]

Integrate[D[f[x], x], x]

DSolve[x''[t] + 4  x[t] == 0, x[t], t]

DSolve[{x''[t] + 4  x[t] == 0, x[0] == 1, x'[0] == 2}, 
      x[t], t]

Etc

\(Needs["Graphics`Master`"]; 
Needs["Calculus`Master`"]; \)

Helmut Knaust, email: helmut@math.utep.edu. Created 2-23-1999.