Calculus Resources

5. Built-in Programs and Functions

5.1 ( expr, var [, order ] )

Returns derivative of expr with respect to var. Derivative is of order order. If order is negative integer then result is an anti-derivative. expr can be a list or a matrix.

5.2 nDeriv( expr, var [, h ] )

Returns numerical derivative of expr with respect to var as an expression. If h is included it is used as the step value. Default step is .001

5.3 ( expr, var [, lower ] [, upper ] )

Returns the integral of expr with respect to var from lower to upper. lower is added as a constant of integration if upper is omitted.

5.4 nInt( expr, var, lower, upper )

Returns the numerical integral of expr with respect to var from lower to upper.

5.5 limit( expr, var, point [, direction ] )

Returns the limit of expr as var approaches point from direction direction. If direction is a positive number limit is from right, if negative limit is from left.

5.6

deSolve( ODE, indVar, depVar)

Returns the explicit or implicit general solution with arbitrary constants @n of a First or Second order Ordinary Differential Equation, ODE.

deSolve( ODE and IC1 [ and IC2 ], indVar, depVar)

Returns a particular solution that satisfies a First (or Second) order Ordinary Differential Equation, ODE and initial condition(s) IC1 ( and IC2 )

5.7 arcLen( expr, var, start, end )

Returns the arc length of expr from start to end with respect to variable var.

6. TI Basic Programs

6.1 iDiff( eqn, y, x, n )

Returns n th derivative of y with respect to x

6.2 impdiff( eqn, {varlist}, var )

Returns implicit derivative of eqn in variables {varlist} with respect to var.

6.3

SlvD( eqn, t, y )

SlvD( {eqn, t0, y(t0), y'(t0), ...}, t, y )

A fantastic differential equation solving program by Lars Fredericksen. The latest version may be obtained here under the name Diff Eq 2.05. t represents the dependent variable and y represents the independent variable.

6.4 SimultD( [eqn1; eqn2; ...], [y1(t), y1(0), y1'(0), ...; y2(t), y2(0), y2'(0), ...; ...] )

Solves systems of differential equations. By Lars Fredericksen. The latest version may be obtained here under the name Diff Eq 2.05.

6.5 RK5( {y1', y2',...}, {y1(k), y2(k),...}, k, s, n )  - by Scott Campbell

Uses Butcher's fifth order Runge - Kutta algorithm to obtain a numerical solution to a system of first order differential equations. Begins iteration at value k for the dependent variable and makes n steps with stepsize s. See further documentation in .zip file.

6.6 Simpsum( a, b, n )  - by Ray Kremer

Returns approximate area under the curve y1(x) entered in the equation editor. Uses n steps from limits a to b. Must reside in same directory with midsum and trapsum. (included in .zip)

6.7 curv( f(x), x )

Returns a function that can be evaluated to give the curvature of f(x) for any value of x in the domain of f(x).

6.8 cntrCurv( f(x), x )

Returns a function that can be evaluated to give the center of curvature in rectangular coordinates of the function f(x) for any value of x in the domain of f(x).

6.9 oscCir( f(x), x, t )

Returns a list of parametric equations in parameter t that describe the osculating circle of the function f(x) (in rectangular coordinates) for any value of x in the domain of f(x). Requires that curv( ) and cntrCurv( ) be in the same folder to work.

6.10 tanLn( f(x), x, pt )

Returns the equation in rectangular coordinates of the tangent line to the graph of f(x) at the point x = pt.

6.11 prpdc( f(x), x, pt )

Returns the equation in rectangular coordinates of the perpendicular line to the graph of f(x) at the point x = pt.

6.12 Wronskia( )

Returns the Wronskian and the fundamental set of a set of up to seven functions.

7. Demos

7.1 Newtdemo( )

Shows a Newton iteration of the root of

7.2 LeftBox( eqn, a, b, n )  - by S. L. Hollis (modified)

Finds the approximate area under eqn using the left point. Uses n steps from limits a to b. Number of partitions doubles each time [ENTER] is pressed. The program must be stopped by pressing the ON key. eqn may refer to y1(x). Some window dimensions must be adjusted seperately.

Leftsum( a, b, n )  - by Ray Kremer

Returns approximate area under the curve y1(x) entered in the equation editor using the left point. Uses n steps from limits a to b. Will give the same result as LeftBox for the same number of subdivisions but without a graphical presentation.

7.3 RightBox( eqn, a, b, n )  - by S. L. Hollis (modified)

Finds the approximate area under eqn using the right point. Uses n steps from limits a to b. Number of partitions doubles each time [ENTER] is pressed. The program must be stopped by pressing the ON key. eqn may refer to y1(x). Some window dimensions must be adjusted seperately.

Rightsum( a, b, n )  - by Ray Kremer

Returns approximate area under the curve y1(x) entered in the equation editor using the right point. Uses n steps from limits a to b. Will give the same result as RightBox for the same number of subdivisions but without a graphical presentation.

7.4 MidBox( eqn, a, b, n )  - by S. L. Hollis (modified)

Midpoint Rule. Finds the approximate area under eqn using the midpoint rule. Uses n steps from limits a to b. Number of partitions doubles each time [ENTER] is pressed. The program must be stopped by pressing the ON key. eqn may refer to y1(x). Some window dimensions must be adjusted seperately.

Midsum( a, b, n )  - by Ray Kremer

Returns approximate area under the curve y1(x) entered in the equation editor using the midpoint rule. Uses n steps from limits a to b. Will give the same result as MidBox for the same number of subdivisions but without a graphical presentation.

7.5 Trapez( eqn, a, b, n )  - by S. L. Hollis (modified)

Trapezoidal Rule. Finds the approximate area under eqn using the trapezoidal rule. Uses n steps from limits a to b. Number of partitions doubles each time [ENTER] is pressed. The program must be stopped by pressing the ON key. eqn may refer to y1(x). Some window dimensions must be adjusted seperately.

Trapsum( a, b, n )  - by Ray Kremer

Returns approximate area under the curve y1(x) entered in the equation editor using the trapezoidal rule. Uses n steps from limits a to b. Must reside in same directory with leftsum and rightsum. (included in .zip). Will give the same result as Trapez for the same number of subdivisions but without a graphical presentation.