A Little Calculus vs Matrix Solver Step by Step

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.

“Matrix Solver Step by Step” Linear Algebra learning tool and a Matrix Calculator: * Performs most commonly used matrix calculations and decompositions (see list below). * Demonstrates and explains algorithm steps for almost all the functions. * Draws interactive geometric references when appropriate. * Provides tutorials (explanations and proofs) for most Linear Algebra concepts. The tutorial topics have links to all other relevant topics, making them understandable for users with minimal prior knowledge of Linear Algebra. Every effort is being made to ensure user friendly interface and factual accuracy. The app is, so far, free of charge and free of ads. It is being continuously updated with new functions, graphs, and proofs. Suggestions and corrections are welcome! Write to us at graphmath@aol.com. List of functions (matrix size up to 8x8): 1. Solution for linear systems, real and complex. 2. Geometric solutions for 3 equation linear systems. 3. Matrix multiplication. 4. Matrix inverse, real and complex. 5. Determinant (row reduction, recursive and permutations methods). 6. Eigenvectors and eigenvalues, both real and complex. 7. Diagonalization. 8. Rotation-scaling similarity transformation. 9. Block-diagonalization transformation. 10. PLU factorization for square matrices. 11. LD(L transposed) factorization for symmetric matrices. 12. Column-Row factorization. 13. QR factorization by 3 existing methods: Gram-Schmidt, Givens rotations and Householder reflections. 14. Singular Value Decomposition (SVD), including using of SVD for Image compression. 15. Polar factorization. 16. Interactive graphs for transformation by 2x2 and 3x3 matrices, with derivation of specific matrix types, such as rotation or reflection. 17. Raising a Matrix to power n, where n is any integer between -10 and 10. 18. Matrix exponentials, x = exp(A*t) * x0. 19. Markov chain calculator. 20. Calculation of Correlation matrices and Principal Component Analysis (PCA). UI features: Most recent matrix entry for particular operation and size is saved between program runs. Input or output matrices can be saved to clipboard and pasted into other input screens in the app, text files and spreadsheets. Matrix and Linear Equations entries can be saved into table and are available after application is closed and re opened. Matrix entries can be filled with random numbers, different options for range are provided. Solutions as fractions are available for many functions. Eigenvalues and eigenvectors are shown as fractions and radicals for 2x2 matrices. Tutorial items can be saved into "My Tutorial Chapters" list. Comments can be added to most tutorial chapters and saved into "My Comments" list.