A Little Calculus vs GraphMath

A LITTLE CALCULUS is a collection of more than 70 interactive topics from a first year calculus course. To be used by both teachers and students, this app is designed to aid in the teaching and learning of calculus and should serve as a nice supplement to any introductory calculus textbook. Can be used to numerically and/or graphically verify computations for a wide variety of problems. Ultimately, the purpose of this app is to interact with and to gain a conceptual understanding of the fundamental topics of calculus. TOPICS: • Graph functions of one variable, as well as parametric and polar curves. • Investigate precalculus topics such as the equation of a line, graphing polynomials, Pythagorean Theorem, trigonometric functions, etc. • Understand the fundamental notion of a limit from a formal or informal point of view. • Study rates of change using the ideas from differential calculus (e.g., secant and tangent lines, derivatives, Mean Value Theorem, Newton's method, etc.) • Calculate the area of a region or surface, length of a curve, and volume of a solid using the techniques of integral calculus. • Interact with parametric and polar curves (e.g., slopes, areas, arc lengths, etc.) • Learn about sequences and series (geometric, harmonic, alternating, etc.) and approximate functions using Taylor polynomials. • Future releases to include more features, topics, and background information on each topic. FEATURES: • Customize each topic by changing any function, variable, and/or interval and by selecting from a variety of options. • Save current settings for each topic under the Options menu for easy retrieval. • Interact with every graph (drag to change the value of a variable or to move/rotate the graph, pinch to zoom, etc.) • Universal App (requires iOS 10 or later running on iPad, iPhone, or iPod Touch.) • Fully functional, built-in calculator. • No internet required, except for initial download and updates. • No in-app purchases or advertising.

This graphing calculator is user friendly and powerful.  It is fully compatible with iOS 14 and 15, and mostly compatible with iOS 13 and Mac OS. Cartesian 3D Z = F (X, Y) functions:  ——————————————————— Graphs can be:  1. Drawn as surface, lines, or dots. 2. Drawn with or without perspective, and with different light and reflection settings. 3. Tilted up or down. 4. Rotated to any position. 5. Drawing is animated by either X, Y, or Z. Table of all points can be sorted by either X or Y. Cylindrical 3D Z = F (Θ, R) functions:  ——————————————————— Graphs can be:  1. Drawn as surface, lines, or dots. 2. Drawn with or without perspective, and with different light and reflection settings. 3. Tilted up or down. 4. Rotated to any position. 5. Drawing is animated by Θ, R, or Z. Table of all points can be sorted by either Θ or R. Spherical 3D R = F (Θ, Φ) functions:  ——————————————————— Graphs can be:  1. Drawn as surface, lines, or dots. 2. Drawn with or without perspective, and with different light and reflection settings. 3. Tilted up or down. 4. Rotated to any position. 5. Drawing is animated by either Θ or Φ. Table of all points can be sorted by Θ, Φ, or R. Cartesian 2D Y = F (X) functions:  ———————————————— Graph displays the following curves: 1. One or two Y = F (X) functions. 2. Derivative of the first function. 3. Integral of the first function as a shade and a curve.  Graph features:  1. Drawing is animated by X. 2. Clicking on the curves shows curve values, and finds closest point in the table. Tables: 1.  All function, integral, and derivative values. 2.  Zero intersections of first function. 3.  Intersections between first and second functions. Polar 2D R = F (Θ) functions: ———————————————  Graph displays the following curves: 1. One or two R = F (Θ) functions. 2. Integral of the first function as a shade and a curve. Graph features:  1. Drawing is animated by Θ.  2. Clicking on the curves shows curve values, and finds closest point in the table. Tables: 1.  Table of all function and integral values  2.  Table of zero intersections of first function. 3.  Table of intersections between first and second functions. Parametric 2D X = F1 (T), Y = F2 (T) functions: —————————————————————————  Graph features:  1. Drawing is animated by T.  2. Clicking on the curves shows T, X, and Y values, and finds them in the table. Table of all points. F (X, Y) = 0  equations: ———————————— Graph displays solutions as points. Clicking on the points shows X, and Y values, and finds them in the table. Table of all points. Common features: —————————— 1. List of previous entries. 2. List of preset entries. 3. Undo and redo buttons for formula entries. 4. Automatic correction of errors in function limits or steps are offered. 5. All function points can be saved to clipboard in a table format. 6. All function points can be displayed on corresponding graphs. 7. Control colors can be changed to black and white. 8. Link to Vectors and Planes 3D Geometry Guide App. 9. Link to Matrix Calculator Step by Step App. Common features of all images:  1. Animation frames can be frozen and moved back or forward. 2. Animation speed can be adjusted. 3. Zoom. 4. Scroll. 5. Save to Clipboard. 6. Save to Photos 7. Color picker. New functions and further UI improvements for our apps are coming! Developers hope to get feedback at graphmath@aol.com.