what are the practical application of differential and integral calculus?
929142
In electronics, which is my specialty, determining the dynamic response of a circuit (with respect to time or with respect to frequency) often requires the use of differential and integral calculus.  In structural engineering, designing buildings or bridges to make them strong and earthquake resistant also requires calculus.  Certainly physics and mechanics rely heavily upon calculus.  I'm not sure about chemistry or biology.
809456
The practical applications of math are endless. The basic math like algebra and geometry is vital knowledge for being able to solve everyday problems. The higher math is very useful in professions. If you're any kind of scientist, you'll need to know everything up until at least differential equations, and definitely further for chemistry and physics. Statistics is a real, very common application of mathematics that shows up everywhere- being able to take a set of real data that probably isn't perfect and still managing to analyze it to find patterns. Calculus also shows up frequently in businesses when they are attempting to optimize conditions in order to maximize profit or decrease cost.\n\nAside from applications, math fosters more analytical, rational thinking. This is why Plato taught geometry and arithmetic to his students before subjecting them to philosophy: so that he could develop their critical thinking skills. Just being able to solve complex problems is a wonderful skill that can be developed through mathematics. The mathematical study of logic is also quite practical.\n\nAnd surely you don't think that all of the world's technology just popped out of the air without somebody doing a lot of math along the way?
460400
You would need to know how to integrate (that is, find anti-derivatives). The proceedure forthis type of problem can usually be understood after first semester calculus. The specific integrations may need some second semester calculus.
125046
I have a bit of calc links from when I took the AP exams.\nhttp://www.jimmyr.com/education.php\n\nunder the section calculus. those sites were really useful.
147855
Try http://integrals.wolfram.com/
354018
I am also preparing for the AP Calculus Exam in 2006 and I can tell you that the points that I saw emphasized most in taking practice former AP tests were solids of rotation (disc, washer, and shell), the fundamental thereom of Calculus (what integral means), U-substitution, derivative rules, Riemann sums, speed, linearization (finding the slope of the tangent line),  volume of known cross sections, concavity and inflection points, the area between two curves, differentiability and continuity, local and global extrema (critical points and end points), implicit differentiation equations, trignometric derivatives, the rule of exponential growth (like volume increasing at a rate proportional to the radius), average value of a function, optimization, and related rates.  I know that is a lot but I have taken 5 complete practice AP tests (former tests) in class since February and all of these concepts were reccuring.
1139073
Differential Equations
1186465
The calculus of variations is essential or useful in a wide range of fields including mathematics (eigenvalue problems, PDE's), optics (Fermat's principle), mechanics (Hamiltonian), engineering (optimization of surfaces and paths, control theory), economics (optimization and control), biology (population dynamics), ...\n\nThe calculus of variations has its roots in optimizing geometric figures to some criterion.  The first problems in the calculus of variations were the tautochrone and brachistochrone problems, which are respectively the problems of finding a curve down which a ball will roll in the same time no matter where it is released and a curve down which a ball will roll between two points in the shortest possible time.\n\nThe double bubble conjecture (proved in 2000) is to do with the configuration of surfaces enclosing two volumes that minimizes surface area.  This obviously involves finding optimized geometric figures and is therefore an ideal problem for the calculus of variations.
183373
Try the inside cover of your Calculus book - it usually summarizes the rules for derivatives and some key integrals.
815232
Calculus is a central branch of mathematics. The word stems from the nascent development of mathematics: the early Greeks used pebbles arranged in patterns to learn arithmetic and geometry, and the Latin word for "pebble" is "calculus."\n\nCalculus is built on two major complementary ideas, both of which rely critically on the concept of limits. The first is differential calculus, which is concerned with the instantaneous rate of change of quantities with respect to other quantities, or more precisely, the local behavior of functions. This can be illustrated by the slope of a function's graph. The second is integral calculus, which studies the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced. These two processes act inversely to each other, as shown by the fundamental theorem of calculus.\n\nExamples of typical differential calculus problems include:\n\nfinding the acceleration and velocity of a free-falling body at a particular moment. \nfinding the optimal number of units a company should produce to maximize its profit. \nExamples of integral calculus problems include:\n\nfinding areas and volumes \nfinding the amount of a liquid pumped by a pump with a set power input but varying conditions of pumping losses and pressure \nfinding the amount of parking lot plowed by a snowplow of given power with varying rates of snowfall.
763507
Calculus is a pure mathematical theory. It has 2 main applications 1 to enable calculation of the gradiant of a curve at any point on the curve, this gives you rate of change of x with respect to y. e.g. if y axis was metres and x axis was seconds this would give you the rate of change of distance with respect to time in m/s i.e. speed.\n\nIf you want to understand differentiation, I suggest you google differentiton from first principles.\n\nThis is one of the physical applications of differentiation.\n\nThe other application is to take a curve and calculate the area underneath it between two points on the curve. Say you have a curve where the y axis is speed in m/s and the x axis is time in seconds. Then the area under the curve would give you the distance travelled between points x=m and x=n. So if you integrate a velocity vs time formula you get distance travelled. This is an application of integration. To understand integration google "simpsons rule".\n\nThere are many more applications of this in physics relating to rate of change & intergration \n\ne.g Electical current is the rate of change of voltage with respect to resistance. dv/dr\n\ne.g. Power in an electical circuit is the integral of current (I) w.r.t to resistance dr
969006
I've done a good bit with linear transforms in general (LaPlace,Fourier, Z), so hopefully I can help you. The most important thing for your class is to know whether or not they will allow the use of tables or not. Even the simplest function will usually require integration by parts to compute a transform directly. Usually I use tables of transforms coupled with properties of transforms (like the differentiation property, which lets you use algebra instead of calculus to solve an ordinary linear DE). I really can't go into any depth without pencil and paper. Check out the link below (it contains an example of using LaPlace transforms to solve a linear ordinary DE).
57176
http://www.calculus.org/
612079
Partial differential equation can be solved by two methods one is by Calculus type and other is by Numerical Methods.\n\nOne of the conventional way of programming the partial functions is used by the numerical methods the the equation is simpled to simple algebric equations and this equation is consider as the base for developing program. IN programming using looping, conditions assigning etc., the algrebic equation is more easier way.
892428
To provide a simple answer that does not involve a lot of mathematics, differential equations are used in almost every scientific field to provide a mathematical description of a process.  They are useful because most processes can be described in terms of changes that result from small differences in elements of the process.  When these small changes are represented in mathematical form the result is a differential equation.  Because the changes are small, it is possible to make assumptions that simplify the expression of the process.\n\nFor example, consider the discharge of a capacitor into a resistor.  We know that the charge stored in the capacitor is Q = V*C, where V=voltage on the capacitor, and C is the capacitance.  A small change in charge, dQ will cause a small change in voltage, dV.  The voltage across the resitor will be V, and the current in the resitor V/R.  The current is the amount of charge divided by the time, or change in current is change in charge divided by change in time, or dI = dQ/dt.  (Note: here is the simplifying assumption:) For very small changes in Q, we can assume that the voltage does not change, so that the current is constant in that interval.  Therefore dV=(1/C)dQ = idt = (V/C*R)dt; rewriting this as a differential equation gives\n\ndV/dt = V/(C*R),\n\nwhich describes the discharge of a capacitor into a resistor.  This is a particularly simple example, and differential equations of more complex processes can get very messy, and many cannot be solved explicitly.
766099
Get a book from your library on applied math.\n\nInternate must be full of such applictions.
1172462
Infinite series provide an excellent way to estimate the solution of a differential equation, which applies to anything from automotive suspension systems to predicting market behavior.