Calculus Conundrum

4. final result after solving a differential equation using the initial condition
6. process of differentiating when two functions are being multiplied
8. type of series that can be thought of as a polynomial with infinite terms
9. coordinate system centered at the pole with units (r, theta)
12. the instantaneous rate of change at a point on a function
14. a graphical representation of a differential equation with slope lines at each coordinate point
15. distance along a curve of a function
20. an equation that defines the relationship between a function and its derivatives
24. the process of finding the derivative of a function
25. a test to prove convergence or divergence of a series by computing the limit as n approaches infinity of the absolute value of [ a(n+1) / a(n) ]
27. type of problem where all variables are dependent on time
28. inverse derivative, its derivative is equal to the original function

1. the numerical tool for approximating values for solutions of ordinary differential equations with a given initial solution
2. numerical value with both magnitude and direction
3. process of differentiating when one function is inside another
5. error calculation method that uses the next term of a Taylor polynomial
7. method of simplifying a limit by differentiating the numerator and denominator of the limit
10. the value f(x) gets closer to as x approaches a certain value
11. the branch of mathematics that deals with the finding and properties of derivatives and integrals of functions by methods originally based on the summation of infinitesimal differences
13. the rate of change of position of a particle
16. a quantity that is limitless or impossible to calculate
17. term applied to a Taylor series that is centered at x=0
18. set of equations that include more than one independent variable (usually x and t)
19. differentiation technique that allows you to find the derivative of y with respect to x
21. process of differentiating when a function is being divided by another
22. the direction at which a function opens, the second derivative
23. the most common method of evaluating and integral with a complex integrand
26. a straight line that intersects a function exactly one time