ODE-Project Review for students

Appendix A Review for students

Here is a list of topics from algebra and calculus that you should make sure you’re familiar with before studying differential equations. To review these topics, click on the links below.

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Completing the square of a quadratic function (i.e., converting an expression of the form $a x^{2} + b x + c$ into one of the form $a (x - h)^{2} + k$ ).
Solve quadratic equations when factoring does not work (e.g., solve $x^{2} - 4 x + 15 = 0$ ).
Solving $2 \times 2$ systems of linear equations (e.g., solve $2 x + y = 1, x - 3 y = 2$ ).
Basic derivatives (power rule, product, chain, and quotient rules, trigonometric functions, exponential and logarithmic functions). Also know basic partial derivatives.
Basic integration (integrals of power functions, including integral of $\frac{1}{x},$ integrals of trigonometric and exponential functions)
Integration by u-substitution.
Integration by parts.
Integration by partial fractions.

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