1300 math formulas

Contents

1 NUMBER SETS
1.1 Set Identities 1
1.2 Sets of Numbers 5
1.3 Basic Identities 7
1.4 Complex Numbers 8

2 ALGEBRA
2.1 Factoring Fommlas 12
2.2 Product Formulas 13
2.3 Powers 14
2.4 Roots 15
2.5 Logarithms 16
2.6 Equations 18
2.7 Inequalities 19
2.8 Compound Interest Formulas 22

3 GEOMETRY
3.1 Right Triangle 24
3.2 Isosceles Triangle 27
3.3 Equilateral Triangle 28
3.4 Scalene Triangle 29
3.5 Square 33
3.6 Rectangle 34
3.7 Parallelogram 35
3.8 Rhombus 36
3.9 Trapezoid 37
3.11 Isosceles Trapezoid with Inscribed Circle 40
3.12 Trapezoid with Inscribed Circle 41
3.13 Kite 42
3.14 Cyclic Quadrilateral 43
3.15 Tangential Quadrilateral 45
3.16 General Quadrilateral 46
3.17 Regular Hexagon 47
3.18 Regular Polygon 48
3.19 Circle 50
3.20 Sector of a Circle 53
3.21 Segment of a Circle 54
3.22 Cube 55
3.23 Rectangular Parallelepiped 56
3.24 Prism 57
3.25 Regular Tetrahedron 58
3.26 Regular Pyramid 59
3.27 Frustum of a Regular Pyramid 61
3.28 Rectangular Right Wedge 62
3.29 Platonic Solids 63
3.30 Right Circular Cylinder 66
3.31 Right Circular Cylinder with an Oblique Plane Face 68
3.32 Right Circular Cone 69
3.33 Frustum of a Right Circular Cone 70
3.34 Sphere 72
3.35 Spherical Cap 72
3.36 Spherical Sector 73
3.37 Spherical Segment 74
3.38 Spherical Wedge 75
3.39 Ellipsoid 76
3.40 Circular Torus 78

4 TRIGONOMETRY
4.1 Radian and Degree Measures of Angles 80
4.2 Definitions and Graphs of Trigonometric Functions 81
4.3 Signs of Trigonometric Functions 86
4.4 Trigonometric Functions of Common Angles 87
4.5 Most Important Formulas 88
4.6 Reduction Formulas 89
4.7 Periodicity of Trigonometric Functions 90
4.8 Relations between Trigonometric Functions 90
4.9 Addition and Subtraction Formulas 91
4.10 Double Angle Formulas 92
4.1 1 Multiple Angle Formulas 93
4.12 Half Angle Formulas 94
4.13 Half Angle Tangent Identities 94
4.14 Transforming of Trigonometric Expressions to Product 95
4.15 Transforming of Trigonometric Expressions to Sum 97
4.16 Powers of Trigonometric Functions 98
4.17 Graphs of Inverse Trigonometric thctions 99
4.18 Principal Values of Inverse Trigonometric Functions 102
4.19 Relations between Inverse Trigonometric Functions 103
4.20 Trigonometric Equations 106
4.21 Relations to Hyperbolic thctions 106

5 MATRICES AND DETERMINANTS
5.1 Determinants 107
5.2 Properties of Determinants 109
5.3 Matrices 1 10
5.4 Operations with Matrices 1 1 1
5.5 Systems of Linear Equations 114

6 VECTORS
6.1 Vector Coordinates 118
6.2 Vector Addition 120
6.3 Vector Subtraction 122
6.4 Scaling Vectors 122
6.5 Scalar Product 123
6.6 Vector Product 125
6.7 Triple Product 127

7 ANALYTIC GEOMETRY
7.1 One -Dimensional Coordinate System 130
7.2 Two -Dimensional Coordinate System 131
7.3 Straight Line in Plane 139
7.4 Circle 149
7.5 Ellipse 152
7.6 Hyperbola 154
7.7 Parabola 158
7.8 Three -Dimensional Coordinate System 161
7.9 Plane 165
7.10 Straight Line in Space 175
7.1 1 Quadric Surfaces 180
7.12 Sphere 189

8 DIFFERENTIAL CALCULUS
8.1 Functions and Their Graphs 191
8.2 Limits of Functions 208
8.3 Definition and Properties of the Derivative 209
8.4 Table of Derivatives 211
8.5 Higher Order Derivatives 215
8.6 Applications of Derivative 217
8.7 Differential 221
8.8 Multivariable thctions 222
8.9 Differential Operators 225

9 INTEGRAL CALCULUS
9.1 Indefinite Integral 227
9.2 Integrals of Rational Flmctions 228
9.3 Integrals of Irrational Functions 231
9.4 Integrals of Trigonometric thctions 237
9.5 Integrals of Hyperbolic Flmctions 241
9.6 Integrals of Exponential and Logarithmic Flmctions 242
9.7 Reduction Formulas 243
9.8 Definite Integral 247
9.9 Improper Integral 253
9.10 Double Integral 257
9.1 1 Triple Integral 269
9.12 Line Integral 275
9.13 Surface Integral 285

10 DIFFERENTIAL EQUATIONS
10.1 First Order Ordinary Differential Equations 295
10.2 Second Order Ordinary Differential Equations 298
10.3 Some Partial Differential Equations 302

11 SERIES
11.1 Arithmetic Series 304
11.2 Geometric Series 305
11.3 Some Finite Series 305
11.4 Infinite Series 307
1 1.5 Properties of Convergent Series 307
11.6 Convergence Tests 308
11.7 Alternating Series 310
1 1.8 Power Series 311
11.9 Differentiation and Integration of Power Series 312
11.10 Taylor and Maclaurin Series 313
11.11 Power Series Expansions for Some Flmctions 314
11.12 Binomial Series 316
11.13 Fourier Series 316

12 PROBABILITY
12.1 Permutations and Combinations 318
12.2 Probability Formulas 319