Maplets for Calculus: Contents

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Pre-Calculus	Basic 7 Functions View the graphs of 7 basic functions. Shifting Functions Learn to shift the graph of a function left or right and up or down. Reflecting Functions Understand the reflection of a function through the x-axis, the y-axis and the origin. Solving Absolute Value Linear Equations Practice solving equations involving the absolute value of a linear function. Factor a Quadratic Practice factoring quadratic functions. The Shape of a Quadratic Function with a Completed Square Determine how the shape of the graph of a quadratic function depends on the parameters when the square has been completed. The Shape of a Quadratic, Dependence on Coefficients Determine how the shape of the graph of a quadratic function depends on its coefficients (without completing the square). Maximum or Minimum of a Quadratic Find the maximum or minimum of a quadratic function by completing the square. Finding Vertical Asymptotes (beta version) Find the vertical asymptotes of a rational function. Domain and Range Finder Identify the domain and range of a function. Shifting Transcendental Functions Learn the graphs of exponential, logarithmic and trigonometric functions by shifting them left or right and up or down. Radioactive Decay Calculate the exponential decay of a radioactive element. Bacteria Growth Calculate the exponential growth of a bacteria culture. Solving Logarithmic Equations Practice solving logarithmic equations and checking for extraneous roots. Pythagorean Theorem Practice computing the third side of a right triangle using the Pythagorean Theorem. Triangle Definition of Trig Functions Practice the definitions of sin, cos, tan, cot, sec. and csc using a triangle. Circle Definition of Trig Functions (beta version) Practice the definitions of sin, cos, tan, cot, sec. and csc using a circle. Shifting Trigonometric Functions Practice identifying the graphs of shifted trigonometric functions. Properties of Sine and Cosine Curves Identify the mean value, amplitude, period and phase shift of the graph of a sine or cosine curve. Solving ASA Triangles using Trig Laws Practice finding the sides and angles of a triangle using the Law of Sines for Angle-Side-Angle triangles. Solving SAS Triangles using Trig Laws Practice finding the sides and angles of a triangle using the Laws of Sines and Cosines for Side-Angle-Side triangles. 2D Vector Algebra Practice the algebra of 2 dimensional vectors.

Limits	Left and Right Limits and Continuity, using a Graph Learn to identify left and right limits, continuity from the left and right and their relation to 2-sided limits and continuity from the graph of the function. Left and Right Limits and Continuity, using Numeric Data Learn to identify left and right limits, continuity from the left and right and their relation to 2-sided limits and continuity from the numerical values of the function. Left and Right Limits and Continuity, using a Formula Learn to identify left and right limits, continuity from the left and right and their relation to 2-sided limits and continuity from the formula for the function. The Epsilon-Delta Definition of Continuity Visualize the precise definition of continuity by finding the delta for a given epsilon. Precise Definition of Limits, Linear Proofs Practice proving the limit of a linear function exists by using the precise definition of a limit. Continuity of Piecewise Defined Functions (beta version) Find the constant which makes a piecewise defined function continuous. Intermediate Value Theorem (beta version) Use the Intermediate Value Theorem to find an interval on which a continuous function has a prescribed value. Bisection Method of Solving Continuous Equations (beta version) Use the bisection method to solve a continuous equation.

Derivatives	From Secant Slopes to Tangent Slope, using a Graph and Numeric Data Calculate the slopes of secant lines and use them to find the slope of the tangent line. From Secant Slopes to Tangent Slope, using a Formula Use the slopes of secant lines to find the slope of the tangent line, algebraically. Try some numeric points and then some symbolic points. Computing Tangent Lines Find the equation of the line tangent to the graph of a function. Try some numeric points and then some symbolic points. Chain Rule Practice computing derivatives with the chain rule. Derivative Drill Practice computing derivatives. Implicit Differentiation Find the derivative of an implicitly defined function. Logarithmic Differentiation Practice computing derivatives using logarithmic differentiation. Derivatives of Inverse Functions Learn how the graph of an inverse function is related to the graph of the function. Compute the derivative of the inverse function at a specific point and then view the respective tangent lines. Linear Approximation Practice finding the linear approximation to a function and using it to estimate the value of the function at a nearby point. Related Rates When two variables are related by an equation their derivatives are also related. Related Rates: The Ladder (beta version) Solve a related rates problem involving a ladder sliding down a wall. From Position to Velocity and Acceleration Given the position of an object, find its velocity and acceleration. L'Hospital's Rule Practice using l'Hospital's rule for computing limits. Parametric Tangent Lines Find the parametric line tangent to a parametric curve. Properties of the Graph of a Function - Terminology Learn the terminology to describe the properties of the graph of a function. Properties of the Graph of a Function Learn to identify the properties of a function, its derivative and its second derivative from the graph of the function. Properties of the Graph of the First Derivative Learn to identify the properties of a function, its derivative and its second derivative from the graph of the first derivative. Properties of the Graph of the Second Derivative Learn to identify the properties of a function, its derivative and its second derivative from the graph of the second derivative. Max/Min: The Tin Can (beta version) Minimize the surface area of a tin can with fixed volume. Linear & Quadratic Approximation Practice finding the linear and quadratic approximations to a function and using them to estimate the value of the function at a nearby point. Anti-Derivative Drill Practice finding anti-derivatives of simple functions. From Acceleration to Velocity and Position Given the acceleration of an object with initial conditions, find its velocity and position. Area as an Antiderivative: Derive the Fundamental Theorem of Calculus Derive the Fundamental Theorem of Calculus by computing the derivative of the area under the graph of a function. Area as an Antiderivative: Compute the Area Using the fact that the area under the graph of a function is an antiderivative of the function, set up a initial value problem for the area under a curve and solve it.

Integrals	Integration by Substitution Practice computing integrals by the method of substitution. Integration by Parts Practice computing integrals by integration by parts. Integration by Parts using Tabular Integration (beta version) Practice integration by parts using tabular integration. Trig Integrals Practice computing integrals of products of powers of trig functions. Trig Substitutions Practice computing integrals by making trig substitutions. Partial Fractions: General Decomposition Practice finding general partial fraction decompositions. Partial Fractions: Finding Coefficients Practice finding the coefficients in a partial fraction decomposition. Partial Fractions: Evaluating the Integral Practice evaluating the integrals that arise from a partial fraction decomposition. Indefinite Integral Drill Practice computing indefinite integrals. Definite Integral Drill Practice computing definite integrals. Left Riemann Sums Practice approximating definite integrals using left Riemann sums. Right Riemann Sums Practice approximating definite integrals using right Riemann sums. Trapezoid Rule Practice approximating definite integrals using the trapezoid rule. Simpson's Rule Practice approximating definite integrals using Simpson's rule. Simpson's Rule Error Formula (beta version) Find a bound on the error when approximating a definite integral using Simpson's rule. Area of a Region Visualize the slicing of a region and compute its area. Average Value of a Function Find the average value of a function approximately and exactly. Volume by Slicing Visualize the slicing of a solid and compute its volume. Volume of Revolution Visualize a solid of revolution and compute its volume using disks, washers or cylinders. Arc Length Visualize and compute the arc length of a curve. Surface Area Visualize and compute the surface area of a surface. Center of Mass of a Bar (beta version) Compute the center of mass of a bar with non-uniform density. Center of Mass of a Uniform Plate (beta version) Compute the center of mass of a plate with uniform density. Work: Spring Compute the force and work requigreen to stretch a spring. Work: Gravity Compute the force and work due to gravity. Work: Lifting with a Rope Compute the work needed to lift a weight using a massive rope. Work: Pumping a Liquid (beta version) Compute the work needed to pump water out of a tank. Fluid Force Compute the fluid force on a plate submerged in a bucket of water.

Differential Equations	Separable Differential Equations Practice solving separable differential equations. Linear Differential Equations Practice solving linear differential equations. Direction Fields (beta version) Identify the direction field of a differential equations. Mixing Problems (beta version) Set up and solve mixing problems using differential equations and initial conditions.

Sequences and Series	Sequence Drill Determining the convergence and limit of a sequence of numbers. Geometric Series Practice computing geometric series. Telescoping Series Practice computing telescoping series with one or two term telescoping. Series Convergence Test Drill Identify and apply convergence and divergence tests for series.

Curvilinear Coordinates	Basic 14 Polar Curves View the graphs of 14 basic polar curves. Polar Curve Identification Identify the graphs of polar curves.

Games	Cryptogram Puzzle (beta version) Solve a cryptogram. By replacing each letter of the alphabet by another letter you can find the hidden quotation. The Plotting Game (beta version) Guess points in the plane until you find the hidden zero. Once you discover the rule you should be able to find the zero with only 4 guesses.

Philip B. Yasskin Department of Mathematics Texas A&M University yasskin@math.tamu.edu (979) 845-3734	Maplesoft, a division of Waterloo Maple, Inc. (800) 267-6583	Douglas B. Meade Department of Mathematics University of South Carolina meade@math.sc.edu (803) 777-6183

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