![]() Modeling with & Solving Differential Equations (2): Jennifer Wexler, AP Calculus Instructor, New Trier High School, Winnetka, IL. ![]() ![]() Modeling with & Solving Differential Equations (1): Jennifer Wexler, AP Calculus Instructor, New Trier High School, Winnetka, IL.Functions Defined by Definite Integrals: Scott Pass, AP Calculus Instructor, McCallum High School, Austin, TX.Riemann Sums : Peter Atlas, AP Calculus Instructor, Concord Carlisle Regional High School, Concord, MA.L’Hospital’s Rule : Mark Howell, AP Calculus Instructor, Gonzaga High School, Washington, DC.Parametric Equations : Vicki Carter, AP Calculus Instructor, West Florence High School, Florence, SC.Rectilinear Motion, Vicki Carter, AP Calculus Instructor, West Florence High School, Florence, SC.Implicit Differentiation : Monique Morton, Mathematics Director, AdvanceKentucky, Lexington, KY.Chain Rule : Monique Morton, Mathematics Director, AdvanceKentucky, Lexington, KY.Limits : Pario-Lee Law, AP Calculus Instructor, D'Evelyn Junior/Senior High School, Littleton, CO.Practice for your exam with graded exam-style questions (with explanations).Build graphical intuition through interactive graphing.Build confidence in the material as you learn concepts from experienced AP® Calculus teachers.Mastery of challenging concepts from the AP® Calculus AB & BC curricula.*Advanced Placement® and AP® are trademarks registered and/or owned by the College Board, which was not involved in the production of, and does not endorse, these offerings. This course is specifically designed for blended learning in AP classrooms, but can also be used by AP students independently as supplementary help and exam review. AB/BC: Modeling & Solving Differential Equations (2).AB/BC: Modeling & Solving Differential Equations (1).AB/BC: Functions Defined by Definite Integrals.These tricky topics are broken up into bite-sized pieces-with short instructional videos, interactive graphs, and practice problems written by many of the same people who write and grade your AP® Calculus exams. What's also certain is that the race car changed its position over time, which means that its Position is a function of time: $x(t)$Īnd this is the somewhat "indirect" way that $v$ changes with respect to $t$, because $x$ does.Well-respected AP instructors from around the United States will lead you through video instruction, exam-style questions and interactive activities to help you master the most challenging concepts in the AP® Calculus AB & Calculus BC curriculum.Įach module will cover one of the most demanding concepts in this AP® Calculus AB & Calculus BC (based on College Board data from 2011–2013 Advanced Placement® exams). The race car did have a different speed at different times. Is $v$ a constant value in respect to $t$? Certainly not. What is the derivative of $v$ with respect to $t$? $v$ does not depend on $t$. Remember the goal: the acceleration $a$ of the car is what you want to know. You now have a function of the speed $v$ with respect to $x$, like so: $v(x)$. (for example by fitting a curve to the data points). Let's say you somehow create a function out of those discrete values. The result of your measurements would be discrete values for $v$ depending at the positions $x$ that you measured it at. Say you can measure the speed $v$ of the car at known positions $x$ on the track. Say for example you want to measure the acceleration $a$ of a race car on a race track. It is sometimes easier to find functions with respect to something that is not what you use to derivate. You will find some nice examples here, too: Will the pressure build up in the cylinder? Temperature rises at the rate of 2 degrees per minute. Oxygen gas has been carelessly placed near a radiator, so that its Suppose that a 1 litre size gas cylinder containing 100 moles of The properties of gases have been studied for centuries, and it hasīeen found that many gases satisfy an approximate relationship called I searched for "chain rule application problems" and found a few sites that might help you.Įxample 2: Chemistry and The Ideal Gas Law The answer lies in the applications of calculus, both in the word problems you find in textbooks and in physics and other disciplines that use calculus. ![]() The other answers focus on what the chain rule is and on how mathematicians view it.
0 Comments
Leave a Reply. |