What you should know before taking Math 285 (Differential Equations)

In order to take Math 285 you should first be familiar with the following concepts covered in the first three semesters of college calculus:

* Differentiation and partial differentiation of functions (especially trigonometric and exponential functions), chain rule, product rule.
* Partial derivatives

Examples:   
Calculate the derivatives of the following functions     
    a) f(x)=^(-3x)  
    b)  f(x)=^x^2
    c) f(x)=2x ^x^2
    d) f(x)=Sin(3x)
    e) f(x)=Cos(5x^2)
    f) f(x, y) = x^2y Cos[3x y^2], find df/dx and df/dy

* Integration of functions (especially trigonometric and exponential functions), substitution method.

Examples:
Calculate the following integrals
    a) ∫_0^( t)Cos(3x)dx
    b) ∫_0^( t)^(5x)dx
    c) ∫_0^( t)x ^x^2dx

* Solving basic systems of equations, quadratic formula.

Examples:
1) Solve the following system of linear equations:
2x + y + z = 5
x - y = 1
x + z = 2
2) Solve the following system of equations:
x^2+y=0,y-2x=0.
3) Solve the equation x^2+2x - 3 = 0 by factoring the polynomial.     
4) Solve the equation 2x^2-3x-4=0 by using the quadratic formula.


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