appears in the integrand.
| This is the integral version of the chain rule for differentiation. |
| What is substitution? (or u-subtitution?) |
|
This technique is often used when the basic form appears in the integrand.
|
| What is trig substitution? |
| This numerical technique estimates the value of a definite integral by approximating the function with parabolas. |
| What is Simpson's Rule? |
| This is the integral version of the product rule for differentiation. |
| What is integration by parts? |
| This technique can be used to integrate any rational function. |
| What is the method of partial fractions? |
{\bf Definitions and Theorems}
| This is the curve traced out by a fixed point on a rolling circle. |
| What is a cycloid? |
| This theorem states that the slope of the secant line of a differentiable function is actually attained as its derivative somewhere between the two endpoints. |
| What is the Mean Value Theorem? |
| This is the length of the longest section in a partition. |
| What is the mesh of the partition? |
| A function is said to be integrable if the limit of Riemann sums defining the definite integral do not depend on these two things. |
| What are the sequence of partitions taken and the points of evaluation for the function? |
| This theorem states that if c is a zero of a polynomial P, then x-c is a factor of P. |
| What is the Fundamental Theorem of Algebra? |
{\bf Easy Computations}
| This is the maximum value of 4-x2? |
| What is 4? |
| This is the derivative of cos(t)sin(t). |
| What is cos2(t)-sin2(t)? |
(Daily Double) This is the anti-derivative of
 .
|
What is  ?
|
| (Daily Double) This is the rate at which the circumference of a circle is changing if the diameter is changing at a rate of 1 meter per second. |
What is  meters per second?
|
| This is the distance a marble released from rest will fall in 10 seconds. |
| What is 490 meters? |
{\bf Potpourri}
This is the anti-derivative of
 .
|
|
What is a houseboat? (Get it? ...log cabin + sea?) |
| Reaching as much as 60 feet or more in length, this awesome dweller of the seas has spawned fear and tales of terror for centuries. Despite its reputation, it has never been observed alive in its natural habitat. |
| What is Architeuthis, the giant squid? |
| This city in Denmark is the home office of the Lego corporation. |
| What is Legoland? |
| This is the maximum number of bananas you can transport 1000 miles across the desert if you begin with 3000 bananas and a camel which can carry 1000 bananas at a time but eats one banana every mile he walks. |
| What is 533+1/3 bananas? |
| This university is the largest in the United States. |
| What is the University of Texas at Austin? |
{\bf Famous Mathematicians}
| This astronomer paid for the publication of Isaac Newton's Principia. |
| Who was Edmund Halley? |
| In honor of this Irish mathematician, the bold letter H is often used in mathematics to represent the quaternions. |
| Who was Sir William Rowan Hamilton? |
| This Jewish mathematician was the first woman to receive a PhD from Erlangen University. She fled Nazi Germany in the 30's. |
| Who was Emmy Noether? |
| In 1688, when Brook Taylor was three years old and ten years before Colin Maclaurin was born, this English mathematician published Taylor series for functions and also knew the Maclaurin series for tan x, sec x, tan-1x, and sec-1x. |
| Who was James Gregory? |
The curve r= in polar coordinates bears this
mathematician's name.
|
| Who was Archimedes? |
{\bf DOUBLE JEOPARDY} {\bf Sequences and Series}
The p-series 
diverges for these
values of p.
|
What is  ?
|
This is the radius of convergence for the Maclaurin
series for  .
|
What is  ?
|
| The terms in this type of series can be rearranged to converge to any real number. |
| What is a conditionally convergent series? |
| These two tests are the most commonly used when trying to find the interval of convergence of a power series. |
| What are the root test and the ratio test? |
| This is the exact time between 2 and 3 o'clock when the hands on a clock coincide. |
| What is 2+2/11 o'clock? (roughly 10 minutes and 55 seconds past 2 o'clock) |
{\bf Orbital Mechanics}
| This is the point of closest approach of a planet to its sun. |
| What is the perihelion? |
| Objects in an inverse square central force field move in these types of paths. |
| What are conic sections? (What are elliptic, parabolic, and hyperbolic paths?) |
| This type of orbit is used for communications satellites. The roots of its name come from the Greek words for earth, same, and time. |
| What is geosynchronous orbit? |
| These two words meaning “shortest time” and “same time” are often used to describe properties of a cycloid. Specifically, a cycloid is the curve among all smooth curves joining two given points along which a bead subject only to the force of gravity might slide in the shortest time. Also the time required to slide from any point to the lowest point remains the same regardless of the initial position. |
| What are brachistochrone and tautochrone? |
This English word comes from the Greek word
meaning “wanderer.”
|
| What is “planet?” |
{\bf Vectors}
| The dot product may be used to obtain these two pieces of geometric information about vectors. |
| What are lengths and angles? |
| This rule determines the direction in which the cross product of two vectors point. |
| What is the right hand rule? |
| These are the only four division algebras over the real numbers. |
| What are the real numbers, the complex numbers, the quaternions, and the octonians? |
| This is the geometric interpretation of the length of the cross product of two vectors. |
| What is the area of the parallelogram spanned by the two vectors? |
| This algebraic operation on three vectors gives the volume of the parallelepiped spanned by the vectors. |
| What is the scalar triple product? |
{\bf Differential Equations}
| This geometric object is the graph of a solution to the equation x dx + y dy = 0. |
| What is a half circle? |
| This is the solution passing through the origin to the equation y '=yey5sinx. |
| What is y=0? |
| This determinant of a matrix of functions and their derivatives can be used to discern whether the functions are linearly independent (and thus whether they can form a fundamental set of solutions). |
| What is the Wronskian (or Wronskian Determinant)? |
| This theorem implies that the Wronskian of a set of solutions to a homogeneous linear ODE is either identically zero or never zero. |
| What is Abel's Theorem? |
| The continuity of these functions is required in the hypotheses of the existence and uniqueness theorem for a general first order ODE y'=f(x,y). |
| What are f and fy? |
{\bf Famous Mathematicians}
| The foundations of an entire branch of mathematics rest on notes scribbled franticly one night by this French mathematician. He knew he would die the following day, at the age of 21, in a duel defending the honor of a woman. |
| Who was Evariste Galois |
| Though Newton is often credited with formulating Calculus, this German philosopher and mathematician independently made the same discoveries. Our modern notation for derivatives come from his work. |
| Who was Baron Gottfried Wilhelm Leibniz? |
| This Greek mathematician and Philosopher of the fifth century B.C.E. posed four problems that came to be famous paradoxes bearing his name. Some early work on limits was motivated by these unresolved problems. |
| Who was Zeno? |
| This French mathematician of the late 17th century wrote what is considered the first calculus textbook ever written. |
| Who was L'Hôpital? |
| This French mathematician is credited with the idea of realizing the slope of a curve as the limit of slopes of secant lines. |
| Who was Pierre de Fermat? |
\centerline{\bf FINAL JEOPARDY}
| Jody Williams was a co-winner of the Nobel Peace Prize in 1997 for this work which was opposed by the U.S. because of its potential military impact on the Korean Peninsula. |
| What is her work for the banning and clearing of anti-personell mines? |