# ALG Math Solver – iOS app

## Introduction

The app is intended for students and engineers and anyone who uses mathematical calculations in their studies or work.

The application contains more than 100 calculators for solving various problems in linear algebra, matrix calculations, analytical geometry, elementary geometry, systems of linear equations, quadratic equations and much more. Each calculator contains a small theory on a specific task.
The program, using the necessary formulas, will perform step-by-step calculations and display a detailed solution.
This app also includes a random number generator to quickly create sample expressions with random numbers.

## Matrix operations, Determinants

The following are some of the matrix operations:

• Matrix subtraction
• Matrix multiplication
• Matrix multiplication by scalar
• Matrix transpose
• Matrix square
• Determinant: Sarrus method
• Determinant: Laplace method
• Invertible matrix

## Vector Calculus

The following are some of the vector calculus operations:

• Vector Length
• Vector coordinates by two points
• Vectors subtraction
• Scalar and vector multiplication
• Scalar product of vectors
• Cross product of vectors
• Mixed triple product
• Angle between two vectors
• Projection of a vector onto another vector
• Direction cosines
• Collinear vectors
• Orthogonal vectors
• Coplanar vectors
• Area of triangle formed by vectors
• Area of a parallelogram formed by vectors
• Volume of pyramid formed by vectors
• Volume of a parallelepiped formed by vectors

## Analytic geometry, 2D

The following are some of the analytic geometry on plane operations:

• General equation of a straight line
• Slope equation of a straight line
• Line equation in segments
• Polar parameters of the line
• Relationship between line and point
• Distance between two points
• Dividing a segment in half
• Dividing a segment in a given ratio
• Triangle area
• Condition under which three points lie on the same line
• Condition of parallel lines
• Two lines are perpendicular
• Angle between two lines
• Bunch of lines
• Relationship between a line and a pair of points
• Point to line distance

## Analytic geometry, 3D

The following are some of the analytic geometry on space operations:

• Equation of a plane
• Condition for parallel planes
• Condition for perpendicular planes
• Angle between two planes
• Segments on axes
• Equation of a plane in segments
• Relationship between a plane and a pair of points
• Point to plane distance
• Polar parameters of the plane
• Normal Equation of a Plane
• Reducing the plane equation to normal form
• Equations of a line in space
• Canonical equation of a straight line
• Parametric equations of a straight line
• Direction vectors
• Angles between line and coordinate axes
• Angle between two lines
• Angle between line and plane
• Condition of parallel line and plane
• Condition of perpendicularity of a line and a plane

## Elementary Geometry, plane

The following are some of the plane elementary geometry operations:

• Triangle area
• Median of triangle
• Triangle height
• Pythagorean theorem
• Radius of a circle circumscribing a triangle
• Radius of a circle inscribed in a triangle
• Area of a parallelogram
• Area of a rectangle
• Square area
• Trapezoid area
• Rhombus area
• Circle area
• Sector area
• Length of the arc of a circle

## Elementary Geometry, space

The following are some of the space elementary geometry operations:

• Parallelepiped volume
• Cuboid volume
• Cube volume
• Pyramid lateral surface area
• Pyramid total surface area
• Pyramid volume
• Truncated pyramid lateral surface area
• Truncated pyramid total surface area
• Truncated pyramid volume
• Cylinder lateral surface area
• Cylinder total area
• Cylinder volume
• Cone lateral surface area
• Cone total surface area
• Cone volume
• Sphere surface area
• Sphere volume

## System of linear equations

The following are some of the system of linear equations:

• Substitution method
• Cramer’s method
• Invertible matrix method

## Algebra

The following are some of the elementary algebra operations:

• Arithmetic progression, sum of the first n members
• Arithmetic progression, finding n-th term
• Geometric progression, sum
• Geometric progression, finding n-th term
• Greatest Common Divisor
• Least Common Multiple

The application is being actively developed and supplemented with new calculators. Keep for updates!