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ALL IN ONE
MATHEMATICS CHEAT SHEET
V2.10
eiπ + 1 = 0
CONTAINING FORMULAE FOR ELEMENTARY, HIGH SCHOOL
AND UNIVERSITY MATHEMATICS
COMPILED FROM MANY SOURCES BY ALEX SPARTALIS
2009-2013
4/9/2013 9:44:00 PM
Euler’s Identity:
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ALL IN ONE
MATHEMATICS CHEAT SHEET
V2.
e
i π
CONTAINING FORMULAE FOR ELEMENTARY, HIGH SCHOOL
AND UNIVERSITY MATHEMATICS
COMPILED FROM MANY SOURCES BY ALEX SPARTALIS 2009- 4/9/2013 9:44:00 PM
Euler’s Identity:
REVISION HISTORY 2.1. 08/06/ UPDATED: Format NEW: Multivariable Calculus UPDATED: Convergence tests UPDATED: Composite Functions 2.2. 10/07/ NEW: Three Phase – Delta & Y NEW: Electrical Power 2.3. 14/08/ NEW: Factorial NEW: Electromagnetics NEW: Linear Algebra NEW: Mathematical Symbols NEW: Algebraic Identities NEW: Graph Theory UPDATED: Linear Algebra UPDATED: Linear Transformations 2.4. 31/08/ NEW: Graphical Functions NEW: Prime numbers NEW: Power Series Expansion NEW: Inner Products UPDATED: Pi Formulas UPDATED: General Trigonometric Functions Expansion UPDATED: Linear Algebra UPDATED: Matrix Inverse 2.5. 10/09/ NEW: Machin-Like Formulae NEW: Infinite Summations To Pi NEW: Classical Mechanics NEW: Relativistic Formulae NEW: Statistical Distributions NEW: Logarithm Power Series NEW: Spherical Triangle Identities NEW: Bernoulli Expansion UPDATED: Pi Formulas UPDATED: Logarithm Identities UPDATED: Riemann Zeta Function UPDATED: Eigenvalues and Eigenvectors 2.6. 3/10/ NEW: QR Factorisation NEW: Jordan Forms NEW: Macroeconomics NEW: Golden Ratio & Fibonacci Sequence NEW: Complex Vectors and Matrices NEW: Numerical Computations for Matrices UPDATED: Prime Numbers UPDATED: Errors within Matrix Formula 2.7. 25/10/ NEW: USV Decomposition NEW: Ordinary Differential Equations Using Matrices NEW: Exponential Identities UPDATED: Matrix Inverse CORRECTION: Left and Right Matrix Inverse 2.8. 31/12/ NEW: Applications of Functions NEW: Higher Order Integration NEW: Root Expansions
CONTENTS
- REVISION HISTORY
- CONTENTS
- PART 1: PHYSICAL CONSTANTS
- 1.1 SI PREFIXES:
- 1.2 SI BASE UNITS:
- 1.3 SI DERIVED UNITS:
- 1.4 UNIVERSAL CONSTANTS:
- 1.5 ELECTROMAGNETIC CONSTANTS:
- 1.6 ATOMIC AND NUCLEAR CONSTANTS:
- 1.7 PHYSICO-CHEMICAL CONSTANTS:
- 1.8 ADOPTED VALUES:
- 1.9 NATURAL UNITS:
- 1.10 MATHEMATICAL CONSTANTS:
- PART 2: MATHEMTAICAL SYMBOLS
- 2.1 BASIC MATH SYMBOLS
- 2.2 GEOMETRY SYMBOLS
- 2.3 ALGEBRA SYMBOLS
- 2.4 LINEAR ALGEBRA SYMBOLS
- 2.5 PROBABILITY AND STATISTICS SYMBOLS
- 2.6 COMBINATORICS SYMBOLS
- 2.7 SET THEORY SYMBOLS
- 2.8 LOGIC SYMBOLS
- 2.9 CALCULUS & ANALYSIS SYMBOLS
- PART 3: AREA, VOLUME AND SURFACE AREA
- 3.1 AREA:
- TRIANGLE:
- RECTANGLE:
- SQUARE:
- PARALLELOGRAM:
- RHOMBUS:
- TRAPEZIUM:
- QUADRILATERAL:
- RECTANGLE WITH ROUNDED CORNERS:
- REGULAR HEXAGON:
- REGULAR OCTAGON:
- REGULAR POLYGON:
- 3.2 VOLUME:
- CUBE:
- CUBOID:
- PRISIM:
- PYRAMID:
- TETRAHEDRON:
- OCTAHEDRON:
- DODECAHEDRON:
- ICOSAHEDRON:
- 3.3 SURFACE AREA:
- CUBE:
- CUBOIDS:
- TETRAHEDRON:
- OCTAHEDRON:
- DODECAHEDRON:
- ICOSAHEDRON:
- CYLINDER:
- 3.4 MISCELLANEOUS:
- DIAGONAL OF A RECTANGLE
- DIAGONAL OF A CUBOID
- LONGEST DIAGONAL (EVEN SIDES)
- LONGEST DIAGONAL (ODD SIDES)
- TOTAL LENGTH OF EDGES (CUBE):
- TOTAL LENGTH OF EDGES (CUBOID):
- CIRCUMFERENCE
- PERIMETER OF RECTANGLE
- SEMI PERIMETER
- EULER’S FORMULA
- 3.5 ABBREVIATIONS (3.1, 3.2, 3.3, 3.4)
- PART 4: ALGEBRA & ARITHMETIC
- 4.1 POLYNOMIAL FORMULA:
- QUDARATIC:
- CUBIC:
- 4.2 FUNDAMENTALS OF ARITHMETIC:
- RATIONAL NUMBERS:
- IRRATIONAL NUMBERS:
- 4.3 ALGEBRAIC EXPANSION:
- BABYLONIAN IDENTITY:
- COMMON PRODUCTS AND FACTORS:
- BINOMIAL THEOREM:
- BINOMIAL EXPANSION:
- DIFFERENCE OF TWO SQUARES:
- BRAHMAGUPTA–FIBONACCI IDENTITY:
- DEGEN'S EIGHT-SQUARE IDENTITY:
- 4.4 ROOT EXPANSIONS:
- 4.5 LIMIT MANIPULATIONS:
- L’HOPITAL’S RULE:
- 4.6 SUMMATION MANIPULATIONS:
- 4.7 COMMON FUNCTIONS:
- CONSTANT FUNCTION:
- LINE/LINEAR FUNCTION:
- PARABOLA/QUADRATIC FUNCTION:
- CIRCLE:
- ELLIPSE:
- HYPERBOLA:
- 4.8 LINEAR ALGEBRA:
- VECTOR SPACE AXIOMS:
- SUBSPACE:
- COMMON SPACES:
- ROWSPACE OF A SPANNING SET IN RN
- COLUMNSPACE OF A SPANNING SET IN RN
- NULLSPACE:
- NULLITY:
- LINEAR DEPENDENCE:
- BASIS:
- STANDARD BASIS:
- ORTHOGONAL COMPLEMENT:
- ORTHONORMAL BASIS:
- GRAM-SCHMIDT PROCESS:
- COORDINATE VECTOR:
- DIMENSION:
- 4.9 COMPLEX VECTOR SPACES:
- FORM:
- DOT PRODUCT:
- INNER PRODUCT:
- 4.10 LINEAR TRANSITIONS & TRANSFORMATIONS:
- TRANSITION MATRIX:
- CHANGE OF BASIS TRANSITION MATRIX:
- TRANSFORMATION MATRIX:
- 4.11 INNER PRODUCTS:
- DEFINITION:
- AXIOMS:
- UNIT VECTOR:
- CAVCHY-SCHUARZ INEQUALITY:
- INNER PRODUCT SPACE:
- ANGLE BETWEEN TWO VECTORS:
- DISTANCE BETWEEN TWO VECTORS:
- GENERALISED PYTHAGORAS FOR ORTHOGONAL VECTORS:
- 4.12 PRIME NUMBERS:
- DETERMINATE:
- LIST OF PRIME NUMBERS:
- FUNDAMENTAL THEORY OF ARITHMETIC:
- LAPRANGE’S THEOREM:
- ADDITIVE PRIMES:
- ANNIHILATING PRIMES:
- BELL NUMBER PRIMES:
- CAROL PRIMES:
- CENTERED DECAGONAL PRIMES:
- CENTERED HEPTAGONAL PRIMES:
- CENTERED SQUARE PRIMES:
- CENTERED TRIANGULAR PRIMES:
- CHEN PRIMES:
- CIRCULAR PRIMES:
- COUSIN PRIMES:
- CUBAN PRIMES:
- CULLEN PRIMES:
- DIHEDRAL PRIMES:
- DOUBLE FACTORIAL PRIMES:
- DOUBLE MERSENNE PRIMES:
- EISENSTEIN PRIMES WITHOUT IMAGINARY PART:
- EMIRPS:
- EUCLID PRIMES:
- EVEN PRIME:
- FACTORIAL PRIMES:
- FERMAT PRIMES:
- FIBONACCI PRIMES:
- FORTUNATE PRIMES:
- GAUSSIAN PRIMES:
- GENERALIZED FERMAT PRIMES BASE 10:
- GENOCCHI NUMBER PRIMES:
- GILDA'S PRIMES:
- GOOD PRIMES:
- HAPPY PRIMES:
- HARMONIC PRIMES:
- HIGGS PRIMES FOR SQUARES:
- HIGHLY COTOTIENT NUMBER PRIMES:
- IRREGULAR PRIMES:
- (P, P−5) IRREGULAR PRIMES:
- (P, P−9) IRREGULAR PRIMES:
- ISOLATED PRIMES:
- KYNEA PRIMES:
- LEFT-TRUNCATABLE PRIMES:
- LEYLAND PRIMES:
- LONG PRIMES:
- LUCAS PRIMES:
- LUCKY PRIMES:
- MARKOV PRIMES:
- MERSENNE PRIMES:
- MERSENNE PRIME EXPONENTS:
- MILLS PRIMES:
- MINIMAL PRIMES:
- MOTZKIN PRIMES:
- NEWMAN–SHANKS–WILLIAMS PRIMES:
- NON-GENEROUS PRIMES:
- ODD PRIMES:
- PADOVAN PRIMES:
- PALINDROMIC PRIMES:
- PALINDROMIC WING PRIMES:
- PARTITION PRIMES:
- PELL PRIMES:
- PERMUTABLE PRIMES:
- PERRIN PRIMES:
- PIERPONT PRIMES:
- PILLAI PRIMES:
- PRIMEVAL PRIMES:
- PRIMORIAL PRIMES:
- PROTH PRIMES:
- PYTHAGOREAN PRIMES:
- PRIME QUADRUPLETS:
- PRIMES OF BINARY QUADRATIC FORM:
- QUARTAN PRIMES:
- RAMANUJAN PRIMES:
- REGULAR PRIMES:
- REPUNIT PRIMES:
- PRIMES IN RESIDUE CLASSES:
- RIGHT-TRUNCATABLE PRIMES:
- SAFE PRIMES:
- SELF PRIMES IN BASE 10:
- SEXY PRIMES:
- SMARANDACHE–WELLIN PRIMES:
- SOLINAS PRIMES:
- SOPHIE GERMAIN PRIMES:
- STAR PRIMES:
- STERN PRIMES:
- SUPER-PRIMES:
- SUPERSINGULAR PRIMES:
- SWINGING PRIMES:
- THABIT NUMBER PRIMES:
- PRIME TRIPLETS:
- TWIN PRIMES:
- TWO-SIDED PRIMES:
- ULAM NUMBER PRIMES:
- UNIQUE PRIMES:
- WAGSTAFF PRIMES:
- WALL-SUN-SUN PRIMES:
- WEAKLY PRIME NUMBERS
- WIEFERICH PRIMES:
- WIEFERICH PRIMES: BASE 3 (MIRIMANOFF PRIMES:)
- WIEFERICH PRIMES: BASE
- WIEFERICH PRIMES: BASE
- WIEFERICH PRIMES: BASE
- WIEFERICH PRIMES: BASE
- WIEFERICH PRIMES: BASE
- WIEFERICH PRIMES: BASE
- WIEFERICH PRIMES: BASE
- WIEFERICH PRIMES: BASE
- WIEFERICH PRIMES: BASE
- WILSON PRIMES:
- WOLSTENHOLME PRIMES:
- WOODALL PRIMES:
- 4.13 GENERALISATIONS FROM PRIME NUMBERS:
- PERFECT NUMBERS:
- LIST OF PERFECT NUMBERS:
- AMICABLE NUMBERS:
- LIST OF AMICABLE NUMBERS:
- SOCIABLE NUMBERS:
- LIST OF SOCIABLE NUMBERS:
- 4.14 GOLDEN RATIO & FIBONACCI SEQUENCE:
- RELATIONSHIP:
- INFINITE SERIES:
- CONTINUED FRACTIONS:
- TRIGONOMETRIC EXPRESSIONS:
- FIBONACCI SEQUENCE:
- 4.15 FERMAT’S LAST THEOREM:
- 4.16 BOOLEAN ALGEBRA:
- AXIOMS:
- THEOREMS OF ONE VARIABLE:
- THEOREMS OF SEVERAL VARIABLES:
- PART 5: COUNTING TECHNIQUES & PROBABILITY
- 5.1 2D
- TRIANGLE NUMBER
- SQUARE NUMBER
- PENTAGONAL NUMBER
- 5.2 3D
- TETRAHEDRAL NUMBER
- SQUARE PYRAMID NUMBER
- 5.3 PERMUTATIONS
- PERMUTATIONS:
- PERMUTATIONS (WITH REPEATS):
- 5.4 COMBINATIONS
- ORDERED COMBINATIONS:
- UNORDERED COMBINATIONS:
- ORDERED REPEATED COMBINATIONS:
- UNORDERED REPEATED COMBINATIONS:
- GROUPING:
- 5.5 MISCELLANEOUS:
- TOTAL NUMBER OF RECTANGLES AND SQUARES FROM A A X B RECTANGLE:
- NUMBER OF INTERPRETERS:
- MAX NUMBER OF PIZZA PIECES:
- MAX PIECES OF A CRESCENT:
- MAX PIECES OF CHEESE:
- CARDS IN A CARD HOUSE:
- DIFFERENT ARRANGEMENT OF DOMINOS:
- UNIT FRACTIONS:
- ANGLE BETWEEN TWO HANDS OF A CLOCK:
- WINNING LINES IN NOUGHTS AND CROSSES:
- BAD RESTAURANT SPREAD:
- FIBONACCI SEQUENCE:
- ABBREVIATIONS (5.1, 5.2, 5.3, 5.4, 5.5)
- 5.6 FACTORIAL:
- DEFINITION:
- TABLE OF FACTORIALS:
- APPROXIMATION:
- 5.7 THE DAY OF THE WEEK:
- 5.8 BASIC PROBABILITY:
- AXIOM’S OF PROBABILITY:
- COMMUTATIVE LAWS:
- ASSOCIATIVE LAWS:
- DISTRIBUTIVE LAWS:
- INDICATOR FUNCTION:
- 5.9 VENN DIAGRAMS:
- COMPLEMENTARY EVENTS:
- NULL SET:
- TOTALITY:
- CONDITIONAL PROBABILITY:
- UNION:
- INDEPENDENT EVENTS:
- MUTUALLY EXCLUSIVE:
- SUBSETS:
- BAYE’S THEOREM:
- 5.11 BASIC STATISTICAL OPERATIONS:
- VARIANCE:
- ARITHMETIC MEAN:
- GEOMETRIC MEAN:
- HARMONIC MEAN:
- STANDARDIZED SCORE:
- QUANTILE:
- 5.12 DISCRETE RANDOM VARIABLES:
- STANDARD DEVIATION:
- EXPECTED VALUE:
- VARIANCE:
- PROBABILITY MASS FUNCTION:
- CUMULATIVE DISTRIBUTION FUNCTION:
- 5.13 COMMON DRVS:
- BERNOULLI TRIAL:
- BINOMIAL TRIAL:
- POISSON DISTRIBUTION:
- GEOMETRIC BINOMIAL TRIAL:
- NEGATIVE BINOMIAL TRIAL:
- HYPERGEOMETRIC TRIAL:
- 5.14 CONTINUOUS RANDOM VARIABLES:
- PROBABILITY DENSITY FUNCTION:
- CUMULATIVE DISTRIBUTION FUNCTION:
- INTERVAL PROBABILITY:
- EXPECTED VALUE:
- VARIANCE:
- 5.15 COMMON CRVS:
- UNIFORM DISTRIBUTION:
- EXPONENTIAL DISTRIBUTION:
- NORMAL DISTRIBUTION:
- 5.16 BIVARIABLE DISCRETE:
- PROBABILITY:
- MARGINAL DISTRIBUTION:
- EXPECTED VALUE:
- INDEPENDENCE:
- COVARIANCE:
- 5.17 BIVARIABLE CONTINUOUS:
- CONDITIONS:
- PROBABILITY:
- MARGINAL DISTRIBUTION:
- MEASURE:
- EXPECTED VALUE:
- INDEPENDENCE:
- CONDITIONAL:
- COVARIANCE:
- CORRELATION COEFFICIENT:
- BIVARIATE UNIFROM DISTRIBUTION:
- MULTIVARIATE UNIFORM DISTRIBUTION:
- BIVARIATE NORMAL DISTRIBUTION:
- 5.18 FUNCTIONS OF RANDOM VARIABLES:
- SUMS (DISCRETE):
- SUMS (CONTINUOUS):
- QUOTIENTS (DISCRETE):
- QUOTIENTS (CONTINUOUS):
- MAXIMUM:
- MINIMUM:
- ORDER STATISTICS:
- 5.19 TRANSFORMATION OF THE JOINT DENSITY:
- BIVARIATE FUNCTIONS:
- MULTIVARIATE FUNCTIONS:
- JACOBIAN:
- JOINT DENSITY:
- ABBREVIATIONS
- PART 6: STATISTICAL ANALYSIS
- 6.1 GENERAL PRINCIPLES:
- MEAN SQUARE VALUE OF X:
- F-STATISTIC OF X:
- F-STATISTIC OF THE NULL HYPOTHESIS:
- P-VALUE:
- RELATIVE EFFICIENCY:
- 6.2 CONTINUOUS REPLICATE DESIGN (CRD):
- TREATMENTS:
- FACTORS:
- REPLICATIONS PER TREATMENT:
- TOTAL TREATMENTS:
- MATHEMATICAL MODEL:
- TEST FOR TREATMENT EFFECT:
- ANOVA:
- 6.3 RANDOMISED BLOCK DESIGN (RBD):
- TREATMENTS:
- FACTORS:
- REPLICATIONS PER TREATMENT:
- TOTAL TREATMENTS:
- MATHEMATICAL MODEL:
- TEST FOR TREATMENT EFFECT:
- TEST FOR BLOCK EFFECT:
- RELATIVE EFFICIENCY:
- ANOVA:
- 6.4 LATIN SQUARE DESIGN (LSD):
- TREATMENTS:
- FACTORS:
- REPLICATIONS PER TREATMENT:
- TOTAL TREATMENTS:
- MATHEMATICAL MODEL:
- TEST FOR TREATMENT EFFECT:
- RELATIVE EFFICIENCY:
- ANOVA:
- 6.5 ANALYSIS OF COVARIANCE:
- MATHEMATICAL MODEL:
- ASSUMPTIONS:
- 6.6 RESPONSE SURFACE METHODOLOGY:
- DEFINITION:
- 1 ST ORDER:
- 2 ND ORDER:
- COMMON DESIGNS
- CRITERION FOR DETERMINING THE OPTIMATILITY OF A DESIGN:
- 6.7 FACTORIAL OF THE FORM 2 N:
- GENERAL DEFINITION:
- CONTRASTS FOR A 22 DESIGN:
- SUM OF SQUARES FOR A 22 DESIGN:
- HYPOTHESIS FOR A CRD 22 DESIGN:
- HYPOTHESIS FOR A RBD 22 DESIGN:
- 6.8 GENERAL FACTORIAL:
- GENERAL DEFINITION:
- ORDER:
- DEGREES OF FREEDOM FOR MAIN EFFECTS:
- DEGREES OF FREEDOM FOR HIGHER ORDER EFFECTS:
- 6.9 ANOVA ASSUMPTIONS:
- ASSUMPTIONS:
- LEVENE’S TEST:
- 6.10 CONTRASTS:
- LINEAR CONTRAST:
- ESTIMATED MEAN OF CONTRAST:
- ESTIMATED VARIANCE OF CONTRAST:
- F OF CONTRAST:
- ORTHOGONAL CONTRASTS:
- 6.11 POST ANOVA MULTIPLE COMPARISONS:
- BONDERRONI METHOD:
- FISHER’S LEAST SIGNIFICANT DIFFERENCE:
- TUKEY’S W PROCEDURE:
- SCHEFFE’S METHOD:
- PART 7: PI
- 7.1 AREA:
- CIRCLE:
- CYCLIC QUADRILATERAL:
- AREA OF A SECTOR (DEGREES)
- AREA OF A SECTOR (RADIANS)
- AREA OF A SEGMENT (DEGREES)
- AREA OF AN ANNULUS:
- ELLIPSE:
- 7.2 VOLUME:
- SPHERE:
- CAP OF A SPHERE:
- CONE:
- ICE-CREAM & CONE:
- DOUGHNUT:
- SAUSAGE:
- ELLIPSOID:
- 7.3 SURFACE AREA:
- SPHERE:
- HEMISPHERE:
- DOUGHNUT:
- SAUSAGE:
- CONE:
- 7.4 MISELANIOUS:
- LENGTH OF ARC (DEGREES)
- LENGTH OF CHORD (DEGREES)
- PERIMETER OF AN ELLIPSE
- 7.6 PI:
- ARCHIMEDES’ BOUNDS:
- JOHN WALLIS:
- ISAAC NEWTON:
- JAMES GREGORY:
- SCHULZ VON STRASSNITZKY:
- JOHN MACHIN:
- LEONARD EULER:
- JOZEF HOENE-WRONSKI:
- FRANCISCUS VIETA:
- INTEGRALS:
- INFINITE SERIES:
- CONTINUED FRACTIONS:
- 7.7 CIRCLE GEOMETRY:
- RADIUS OF CIRCUMSCRIBED CIRCLE FOR RECTANGLES:
- RADIUS OF CIRCUMSCRIBED CIRCLE FOR SQUARES:
- RADIUS OF CIRCUMSCRIBED CIRCLE FOR TRIANGLES:
- RADIUS OF CIRCUMSCRIBED CIRCLE FOR QUADRILATERALS:
- RADIUS OF INSCRIBED CIRCLE FOR SQUARES:
- RADIUS OF INSCRIBED CIRCLE FOR TRIANGLES:
- RADIUS OF CIRCUMSCRIBED CIRCLE:
- RADIUS OF INSCRIBED CIRCLE:
- 7.8 ABBREVIATIONS (7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7):
- 7.9 CRESCENT GEOMETRY:
- AREA OF A LUNAR CRESCENT:
- AREA OF AN ECLIPSE CRESCENT:
- 7.10 ABBREVIATIONS (7.9):
- PART 8: APPLIED FIELDS:
- 8.1 MOVEMENT:
- STOPPING DISTANCE:
- CENTRIPETAL ACCELERATION:
- CENTRIPETAL FORCE:
- DROPPING TIME :
- FORCE:
- KINETIC ENERGY:
- MAXIMUM HEIGHT OF A CANNON:
- PENDULUM SWING TIME:
- POTENTIAL ENERGY:
- RANGE OF A CANNON:
- TIME IN FLIGHT OF A CANNON:
- UNIVERSAL GRAVITATION:
- ABBREVIATIONS (8.1):
- 8.2 CLASSICAL MECHANICS:
- NEWTON’S LAWS:
- INERTIA:
- MOMENTS OF INERTIA:
- VELOCITY AND SPEED:
- ACCELERATION:
- TRAJECTORY (DISPLACEMENT):
- KINETIC ENERGY:
- CENTRIPETAL FORCE:
- CIRCULAR MOTION:
- ANGULAR MOMENTUM:
- TORQUE:
- WORK:
- LAWS OF CONSERVATION:
- ABBREVIATIONS (8.2)
- 8.3 RELATIVISTIC EQUATIONS:
- KINETIC ENERGY:
- MOMENTUM:
- TIME DILATION:
- LENGTH CONTRACTION:
- RELATIVISTIC MASS:
- 8.4 ACCOUNTING:
- PROFIT:
- PROFIT MARGIN:
- SIMPLE INTEREST:
- COMPOUND INTEREST:
- CONTINUOUS INTEREST:
- ABBREVIATIONS (8.4):
- 8.5 MACROECONOMICS:
- GDP:
- RGDP:
- NGDP:
- GROWTH:
- NET EXPORTS:
- WORKING AGE POPULATION:
- LABOR FORCE:
- UNEMPLOYMENT:
- NATURAL UNEMPLOYMENT:
- UNEMPLOYMENT RATE:
- EMPLOYMENT RATE:
- PARTICIPATION RATE:
- CPI:
- INFLATION RATE:
- ABBREVIATIONS (8.5)
- PART 9: TRIGONOMETRY
- 9.1 CONVERSIONS:
- 9.2 BASIC RULES:
- SIN RULE:
- COS RULE:
- TAN RULE:
- AUXILIARY ANGLE:
- PYTHAGORAS THEOREM:
- PERIODICY:
- 9.3 RECIPROCAL FUNCTIONS
- 9.4 BASIC IDENTITES:
- 9.5 IDENTITIES BETWEEN RELATIONSHIPS:
- 9.6 ADDITION FORMULAE:
- 9.7 DOUBLE ANGLE FORMULAE:
- 9.8 TRIPLE ANGLE FORMULAE:
- 9.9 HALF ANGLE FORMULAE:
- 9.10 POWER REDUCTION:
- 9.11 PRODUCT TO SUM:
- 9.12 SUM TO PRODUCT:
- 9.13 HYPERBOLIC EXPRESSIONS:
- 9.14 HYPERBOLIC RELATIONS:
- 9.15 MACHIN-LIKE FORMULAE:
- FORM:
- FORMULAE:
- IDENTITIES:
- 9.16 SPHERICAL TRIANGLE IDENTITIES:
- 9.17 ABBREVIATIONS (9.1-9.16)
- PART 10: EXPONENTIALS & LOGARITHIMS
- 10.1 FUNDAMENTAL THEORY:
- 10.2 EXPONENTIAL IDENTITIES:
- 10.3 LOG IDENTITIES:
- 10.4 LAWS FOR LOG TABLES:
- 10.5 COMPLEX NUMBERS:
- 10.6 LIMITS INVOLVING LOGARITHMIC TERMS
- PART 11: COMPLEX NUMBERS
- 11.1 GENERAL:
- FUNDAMENTAL:
- STANDARD FORM:
- POLAR FORM:
- ARGUMENT:
- MODULUS:
- CONJUGATE:
- EXPONENTIAL:
- DE MOIVRE’S FORMULA:
- EULER’S IDENTITY:
- 11.2 OPERATIONS:
- ADDITION:
- SUBTRACTION:
- MULTIPLICATION:
- DIVISION:
- SUM OF SQUARES:
- 11.3 IDENTITIES:
- EXPONENTIAL:
- LOGARITHMIC:
- TRIGONOMETRIC:
- HYPERBOLIC:
- PART 12: DIFFERENTIATION
- 12.1 GENERAL RULES:
- PLUS OR MINUS:
- PRODUCT RULE:
- QUOTIENT RULE:
- POWER RULE:
- CHAIN RULE:
- BLOB RULE:
- BASE A LOG:
- NATURAL LOG:
- EXPONENTIAL (X):
- FIRST PRINCIPLES:
- ANGLE OF INTERSECTION BETWEEN TWO CURVES:
- 12.2 EXPONETIAL FUNCTIONS:
- 12.3 LOGARITHMIC FUNCTIONS:
- 12.4 TRIGONOMETRIC FUNCTIONS:
- 12.5 HYPERBOLIC FUNCTIONS:
- 12.5 PARTIAL DIFFERENTIATION:
- FIRST PRINCIPLES:
- GRADIENT:
- TOTAL DIFFERENTIAL:
- CHAIN RULE:
- IMPLICIT DIFFERENTIATION:
- HIGHER ORDER DERIVATIVES:
- PART 13: INTEGRATION
- 13.1 GENERAL RULES:
- POWER RULE:
- BY PARTS:
- CONSTANTS:
- 13.2 RATIONAL FUNCTIONS:
- 13.3 TRIGONOMETRIC FUNCTIONS (SINE):
- 13.4 TRIGONOMETRIC FUNCTIONS (COSINE):
- 13.5 TRIGONOMETRIC FUNCTIONS (TANGENT):
- 13.6 TRIGONOMETRIC FUNCTIONS (SECANT):
- 13.7 TRIGONOMETRIC FUNCTIONS (COTANGENT):
- 13.8 TRIGONOMETRIC FUNCTIONS (SINE & COSINE):
- 13.9 TRIGONOMETRIC FUNCTIONS (SINE & TANGENT):
- 13.10 TRIGONOMETRIC FUNCTIONS (COSINE & TANGENT):
- 13.11 TRIGONOMETRIC FUNCTIONS (SINE & COTANGENT):
- 13.12 TRIGONOMETRIC FUNCTIONS (COSINE & COTANGENT):
- 13.13 TRIGONOMETRIC FUNCTIONS (ARCSINE):
- 13.14 TRIGONOMETRIC FUNCTIONS (ARCCOSINE):
- 13.15 TRIGONOMETRIC FUNCTIONS (ARCTANGENT):
- 13.16 TRIGONOMETRIC FUNCTIONS (ARCCOSECANT):
- 13.17 TRIGONOMETRIC FUNCTIONS (ARCSECANT):
- 13.18 TRIGONOMETRIC FUNCTIONS (ARCCOTANGENT):
- 13.19 EXPONETIAL FUNCTIONS
- 13.20 LOGARITHMIC FUNCTIONS
- 13.21 HYPERBOLIC FUNCTIONS
- 13.22 INVERSE HYPERBOLIC FUNCTIONS
- 13.23 ABSOLUTE VALUE FUNCTIONS
- 13.24 SUMMARY TABLE
- 13.25 SQUARE ROOT PROOFS
- 13.26 CARTESIAN APPLICATIONS
- AREA UNDER THE CURVE:
- VOLUME:
- VOLUME ABOUT X AXIS:
- VOLUME ABOUT Y AXIS:
- SURFACE AREA ABOUT X AXIS:
- LENGTH WRT X-ORDINATES:
- LENGTH WRT Y-ORDINATES:
- LENGTH PARAMETRICALLY:
- LINE INTEGRAL OF A SCALAR FIELD:
- LINE INTEGRAL OF A VECTOR FIELD:
- AREA OF A SURFACE:
- 13.27 HIGHER ORDER INTEGRATION
- PROPERTIES OF DOUBLE INTEGRALS:
- VOLUME USING DOUBLE INTEGRALS:
- VOLUME USING TRIPLE INTEGRALS:
- CENTRE OF MASS:
- 13.28 WORKING IN DIFFERENT COORDINATE SYSTEMS:
- CARTESIAN:
- POLAR:
- CYLINDRICAL:
- SPHERICAL:
- CARTESIAN TO POLAR:
- POLAR TO CARTESIAN:
- CARTESIAN TO CYLINDRICAL:
- CYLINDRICAL TO CARTESIAN:
- SPHERICAL TO CARTESIAN:
- PART 14: FUNCTIONS
- 14.1 ODD & EVEN FUNCTIONS:
- DEFINITIONS:
- COMPOSITE FUNCTIONS:
- BASIC INTEGRATION:
- 14.2 MULTIVARIABLE FUNCTIONS:
- LIMIT:
- DISCRIMINANT:
- CRITICAL POINTS:
- 14.3 FIRST ORDER, FIRST DEGREE, DIFFERENTIAL EQUATIONS:
- SEPARABLE
- LINEAR
- HOMOGENEOUS
- EXACT
- BERNOULLI FORM:
- 14.4 SECOND ORDE, FIRST DEGREE, DIFFERENTIAL EQUATIONS:
- GREG’S LEMMA:
- HOMOGENEOUS
- UNDETERMINED COEFFICIENTS
- VARIATION OF PARAMETERS
- EULER TYPE
- REDUCTION OF ORDER
- POWER SERIES SOLUTIONS:
- 14.5 ORDINARY DIFFERENTIAL EQUATIONS USING MATRICES:
- DERIVATION OF METHODS:
- FUNDAMENTAL MATRIX:
- HOMOGENEOUS SOLUTION:
- INHOMOGENEOUS SOLUTION:
- NTH ORDER LINEAR, CONSTANT COEFFICIENT ODE:
- 14.6 APPLICATIONS OF FUNCTIONS
- TERMINOLOGY:
- GRADIENT VECTOR OF A SCALAR FIELD:
- DIRECTIONAL DERIVATIVES:
- OPTIMISING THE DIRECTIONAL DERIVATIVE:
- 14.7 ANALYTIC FUNCTIONS
- PART 15: MATRICIES
- 15.1 BASIC PRINICPLES:
- SIZE
- 15.2 BASIC OPERTAIONS:
- ADDITION:
- SUBTRACTION:
- SCALAR MULTIPLE:
- TRANSPOSE:
- SCALAR PRODUCT:
- SYMMETRY:
- CRAMER’S RULE:
- LEAST SQUARES SOLUTION
- 15.3 SQUARE MATRIX:
- DIAGONAL:
- LOWER TRIANGLE MATRIX:
- UPPER TRIANGLE MATRIX:
- 15.4 DETERMINATE:
- 2 X
- 3 X
- NXN
- RULES
- 15.5 INVERSE
- 2 X2:
- 3 X3:
- MINOR:
- COFACTOR:
- ADJOINT METHOD FOR INVERSE:
- LEFT INVERSE:
- RIGHT INVERSE:
- PSEUDO INVERSE:
- 15.6 LINEAR TRANSFORMATION
- AXIOMS FOR A LINEAR TRANSFORMATION:
- TRANSITION MATRIX:
- ZERO TRANSFORMATION:
- IDENTITY TRANSFORMATION:
- 15.7 COMMON TRANSITION MATRICIES
- ROTATION (CLOCKWISE):
- ROTATION (ANTICLOCKWISE):
- SCALING:
- SHEARING (PARALLEL TO X-AXIS):
- SHEARING (PARALLEL TO Y-AXIS):
- 15.8 EIGENVALUES AND EIGENVECTORS
- DEFINITIONS:
- EIGENVALUES:
- EIGENVECTORS:
- CHARACTERISTIC POLYNOMIAL:
- ALGEBRAIC MULTIPLICITY:
- GEOMETRIC MULTIPLICITY:
- TRANSFORMATION:
- LINEARLY INDEPENDENCE:
- DIGITALIZATION:
- CAYLEY-HAMILTON THEOREM:
- ORTHONORMAL SET:
- QR FACTORISATION:
- 15.9 JORDAN FORMS
- GENERALISED DIAGONLISATION:
- JORDAN BLOCK:
- JORDAN FORM:
- ALGEBRAIC MULTIPLICITY:
- GEOMETRIC MULTIPLICITY:
- GENERALISED CHAIN:
- POWERS:
- 15.12 SINGULAR VALUE DECOMPOSITION
- FUNDAMENTALLY:
- SIZE:
- PSEUDO INVERSE:
- PROCEDURE:
- 15.11 COMPLEX MATRICIS:
- CONJUGATE TRANSPOSE:
- HERMITIAN MATRIX:
- SKEW-HERMITIAN:
- UNITARY MATRIX:
- NORMAL MATRIX:
- DIAGONALISATION:
- SPECTRAL THEOREM:
- 15.12 NUMERICAL COMPUTATIONS:
- RAYLEIGH QUOTIENT:
- POWER METHOD:
- 15.13 POWER SERIES:
- PART 16: VECTORS
- 16.1 BASIC OPERATIONS:
- ADDITION:
- SUBTRACTION:
- EQUALITY:
- SCALAR MULTIPLICATION:
- PARALLEL:
- MAGNITUDE:
- UNIT VECTOR:
- ZERO VECTOR:
- DOT PRODUCT:
- ANGLE BETWEEN TWO VECTORS:
- ANGLE OF A VECTOR IN 3D:
- PERPENDICULAR TEST:
- SCALAR PROJECTION:
- VECTOR PROJECTION:
- CROSS PRODUCT:
- 16.2 LINES
- 16.3 PLANES
- GENERALLY:
- TANGENT PLANE:
- NORMAL LINE:
- 16.4 CLOSEST APPROACH
- TWO POINTS:
- POINT AND LINE:
- POINT AND PLANE:
- TWO SKEW LINES:
- 16.5 GEOMETRY
- AREA OF A TRIANGLE:
- AREA OF A PARALLELOGRAM:
- AREA OF A PARALLELEPIPED:
- 16.6 SPACE CURVES
- WHERE:
- VELOCITY:
- ACCELERATION:
- DEFINITION OF “S”:
- UNIT TANGENT:
- CHAIN RULE:
- NORMAL:
- CURVATURE:
- UNIT BINOMIAL:
- TORTION:
- ABBREVIATIONS
- PART 17: SERIES
- 17.1 MISCELLANEOUS
- GENERAL FORM:
- INFINITE FORM:
- PARTIAL SUM OF A SERIES:
- 0.99…=1:
- 17.2 TEST FOR CONVERGENCE AND DIVERGENCE
- TEST FOR CONVERGENCE:
- TEST FOR DIVERGENCE:
- GEOMETRIC SERIES
- P SERIES
- THE SANDWICH THEOREM
- THE INTEGRAL TEST
- THE DIRECT COMPARISON TEST
- THE LIMIT COMPARISON TEST
- D’ALMBERT’S RATIO COMPARISON TEST
- THE NTH ROOT TEST
- ABEL’S TEST:
- NEGATIVE TERMS
- ALTERNATING SERIES TEST
- ALTERNATING SERIES ERROR
- 17.3 ARITHMETIC PROGRESSION:
- DEFINITION:
- NTH TERM:
- SUM OF THE FIRST N TERMS:
- 17.4 GEOMETRIC PROGRESSION:
- DEFINITION:
- NTH TERM:
- SUM OF THE FIRST N TERMS:
- SUM TO INFINITY:
- GEOMETRIC MEAN:
- 17.5 SUMMATION SERIES
- LINEAR:
- QUADRATIC:
- CUBIC:
- 17.6 APPROXIMATION SERIES
- TAYLOR SERIES
- MACLAURUN SERIES
- LINEAR APPROXIMATION:
- QUADRATIC APPROXIMATION:
- CUBIC APPROXIMATION:
- 17.7 MONOTONE SERIES
- STRICTLY INCREASING:
- NON-DECREASING:
- STRICTLY DECREASING:
- NON-INCREASING:
- CONVERGENCE:
- 17.8 RIEMANN ZETA FUNCTION
- FORM:
- EULER’S TABLE:
- ALTERNATING SERIES: