First Course in the Theory of Equations
Index of terms
Every concept, theorem, method and person the concept graph places in a chapter of this book, with the chapters that teach it and the other books on the shelf that teach it too.
Concepts (80)
- abscissa
Taught in: The Graph of an Equation, Appendix
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Mathematical Recreations and Essays
- absolute value
Taught in: Appendix
Also in: A Course of Pure Mathematics, The First Steps in Algebra
- augmented matrix
Taught in: Determinants; Systems of Linear Equations
- bend point
Taught in: The Graph of an Equation, Isolation of the Real Roots of a Real Equation, Solution of Numerical Equations
- circle
Taught in: Determinants; Systems of Linear Equations, Appendix
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Elementary Illustrations of the Differential and Integral Calculus, Mathematical Recreations and Essays, Plane Geometry, Solid Geometry with Problems and Applications, Spherical Trigonometry, for the Use of Colleges and Schools
- coefficient
Taught in: Isolation of the Real Roots of a Real Equation, Determinants; Systems of Linear Equations, Elimination, Resultants And Discriminants
Also in: A First Book in Algebra, Elementary Illustrations of the Differential and Integral Calculus, The First Steps in Algebra
- common root
Taught in: Elimination, Resultants And Discriminants
- complementary minor
Taught in: Determinants; Systems of Linear Equations
- complex number
Taught in: Elementary Theorems on the Roots of an Equation, Appendix
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Vector Analysis and Quaternions
- conic section
Taught in: Elimination, Resultants And Discriminants
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Mathematical Recreations and Essays
- conjugate complex numbers
Taught in: The Graph of an Equation
Also in: A Course of Pure Mathematics
- continuous function
Taught in: Appendix
Also in: A Course of Pure Mathematics, An Introduction to Mathematics
- cube root of unity
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants, Determinants; Systems of Linear Equations
Also in: A Course of Pure Mathematics
- cubic equation
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants, The Graph of an Equation, Isolation of the Real Roots of a Real Equation, Determinants; Systems of Linear Equations, Elimination, Resultants And Discriminants
Also in: An Introduction to Mathematics, Mathematical Recreations and Essays
- curve
Taught in: Appendix
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Elementary Illustrations of the Differential and Integral Calculus
- degree
Taught in: Isolation of the Real Roots of a Real Equation, Elimination, Resultants And Discriminants, Appendix
Also in: A First Book in Algebra, Elementary Illustrations of the Differential and Integral Calculus, The First Steps in Algebra
- derivative
Taught in: The Graph of an Equation, Isolation of the Real Roots of a Real Equation, Solution of Numerical Equations
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus
- determinant
Taught in: Determinants; Systems of Linear Equations, Elimination, Resultants And Discriminants
Also in: A Course of Pure Mathematics, Vector Analysis and Quaternions
- diagonal term of a determinant
Taught in: Determinants; Systems of Linear Equations
- discriminant
Taught in: Elementary Theorems on the Roots of an Equation, Solution of Cubic and Quartic Equations; Their Discriminants, Isolation of the Real Roots of a Real Equation, Elimination, Resultants And Discriminants
Also in: A Course of Pure Mathematics
- element of a determinant
Taught in: Determinants; Systems of Linear Equations
- elementary symmetric function
Taught in: Symmetric Functions, Elimination, Resultants And Discriminants
- extraneous factor
Taught in: Elimination, Resultants And Discriminants
- factor
Taught in: Determinants; Systems of Linear Equations
Also in: A Course of Pure Mathematics, A First Book in Algebra, Calculus Made Easy, Mathematical Recreations and Essays, The First Steps in Algebra
- factored form
- factorial
Taught in: The Graph of an Equation
Also in: A Course of Pure Mathematics, An Introduction to Mathematics
- function of two variables
Taught in: Appendix
Also in: A Course of Pure Mathematics
- graph of a function
Taught in: The Graph of an Equation, Isolation of the Real Roots of a Real Equation, Appendix
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Elementary Illustrations of the Differential and Integral Calculus
- higher-order derivative
Taught in: The Graph of an Equation, Isolation of the Real Roots of a Real Equation
Also in: A Course of Pure Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus
- highest common factor
Taught in: The Graph of an Equation, Isolation of the Real Roots of a Real Equation
Also in: A Course of Pure Mathematics, A First Book in Algebra, The First Steps in Algebra
- homogeneous linear equations
Taught in: Determinants; Systems of Linear Equations, Elimination, Resultants And Discriminants
- imaginary root
Taught in: The Graph of an Equation, Isolation of the Real Roots of a Real Equation, Solution of Numerical Equations
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Mathematical Recreations and Essays, The First Steps in Algebra
- infinity
Taught in: The Graph of an Equation
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Elementary Illustrations of the Differential and Integral Calculus
- inflection point
Taught in: The Graph of an Equation, Solution of Numerical Equations
- inflection tangent
Taught in: The Graph of an Equation
- interval
Taught in: Isolation of the Real Roots of a Real Equation
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Elementary Illustrations of the Differential and Integral Calculus
- irreducible case
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants
- known term
Taught in: Determinants; Systems of Linear Equations
- linear equation
Taught in: Determinants; Systems of Linear Equations
Also in: A Course of Pure Mathematics, A First Book in Algebra, An Introduction to Mathematics, The First Steps in Algebra
- linear factor
- lower limit to the roots
- matrix
Taught in: Determinants; Systems of Linear Equations
- maximum
Taught in: The Graph of an Equation
Also in: A Course of Pure Mathematics, Calculus Made Easy, Mathematical Recreations and Essays, Plane Geometry, Treatise on Thermodynamics
- minimum
Taught in: The Graph of an Equation, Appendix
Also in: A Course of Pure Mathematics, Calculus Made Easy, Plane Geometry
- minor
Taught in: Determinants; Systems of Linear Equations
- multiple root
Taught in: Elementary Theorems on the Roots of an Equation, The Graph of an Equation, Isolation of the Real Roots of a Real Equation, Elimination, Resultants And Discriminants
Also in: A Course of Pure Mathematics
- ordinary tangent
Taught in: The Graph of an Equation
- ordinate
Taught in: The Graph of an Equation
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus
- origin
Taught in: The Graph of an Equation
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Elementary Illustrations of the Differential and Integral Calculus, Elements of Plane Trigonometry
- permutation
Taught in: Symmetric Functions
Also in: An Introduction to Mathematics, Mathematical Recreations and Essays
- point of tangency
Taught in: The Graph of an Equation
Also in: Calculus Made Easy, Plane Geometry, Treatise on Thermodynamics
- polynomial
Taught in: The Graph of an Equation, Isolation of the Real Roots of a Real Equation, Solution of Numerical Equations, Elimination, Resultants And Discriminants, Appendix
Also in: A Course of Pure Mathematics, A First Book in Algebra, Calculus Made Easy, The First Steps in Algebra
- proof
Taught in: Appendix
Also in: Plane Geometry
- quadratic equation
Taught in: The Graph of an Equation
Also in: A Course of Pure Mathematics, A First Book in Algebra, An Introduction to Mathematics, Calculus Made Easy, Mathematical Recreations and Essays, The First Steps in Algebra
- quartic equation
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants, Isolation of the Real Roots of a Real Equation
- rank of a determinant
Taught in: Determinants; Systems of Linear Equations
- rational function
Taught in: Symmetric Functions
Also in: A Course of Pure Mathematics
- real root
Taught in: The Graph of an Equation, Isolation of the Real Roots of a Real Equation, Solution of Numerical Equations
Also in: A Course of Pure Mathematics, The First Steps in Algebra
- reduced cubic equation
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants, The Graph of an Equation
- reduced quartic equation
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants, Isolation of the Real Roots of a Real Equation
- remainder
Taught in: Solution of Numerical Equations
Also in: A First Book in Algebra, Mathematical Recreations and Essays, The First Steps in Algebra
- resolvent cubic
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants
- resultant
Taught in: Elimination, Resultants And Discriminants
- right circular cylinder
Taught in: Appendix
- root
Taught in: Appendix
Also in: A Course of Pure Mathematics, A First Book in Algebra, An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, The First Steps in Algebra
- root of an equation
Taught in: Elementary Theorems on the Roots of an Equation, The Graph of an Equation, Isolation of the Real Roots of a Real Equation, Solution of Numerical Equations, Symmetric Functions, Elimination, Resultants And Discriminants
Also in: A Course of Pure Mathematics, Elementary Illustrations of the Differential and Integral Calculus
- sigma function
Taught in: Symmetric Functions
- sign
Taught in: Isolation of the Real Roots of a Real Equation
Also in: Elementary Illustrations of the Differential and Integral Calculus, The First Steps in Algebra
- sign of a polynomial at infinity
Taught in: The Graph of an Equation
- simultaneous equations
Taught in: Determinants; Systems of Linear Equations
Also in: A First Book in Algebra, Calculus Made Easy, The First Steps in Algebra
- slope of a curve
Taught in: The Graph of an Equation
Also in: An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus
- Sturm's functions
- subtangent
Taught in: Solution of Numerical Equations
- symmetric function
Taught in: Symmetric Functions
- tangent
Taught in: The Graph of an Equation
Also in: A Course of Pure Mathematics, An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Elements of Plane Trigonometry, Mathematical Recreations and Essays, Plane Geometry, Treatise on Thermodynamics
- transformed equation
Taught in: Solution of Numerical Equations
- trigonometric form of a complex number
Taught in: Appendix
- unknown
Taught in: Determinants; Systems of Linear Equations
Also in: A First Book in Algebra, An Introduction to Mathematics, Calculus Made Easy, The First Steps in Algebra
- upper limit to the roots
- variation of sign
Theorems (24)
- binomial theorem
Taught in: Appendix
Also in: A Course of Pure Mathematics, A First Book in Algebra, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Vector Analysis and Quaternions
- Budan's theorem
- Cardan's formulas
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants
- consistency of a linear system
Taught in: Determinants; Systems of Linear Equations
- Cramer's rule
Taught in: Determinants; Systems of Linear Equations
- Descartes' rule of signs
- discriminant formula for the cubic
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants
- discriminant of a quartic equals that of its resolvent cubic
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants
- equation of degree n has at most n roots
- factor theorem
Taught in: Elementary Theorems on the Roots of an Equation
Also in: A Course of Pure Mathematics
- fundamental theorem of algebra
Taught in: Elementary Theorems on the Roots of an Equation, Appendix
Also in: A Course of Pure Mathematics
- imaginary roots occur in pairs
- intermediate value theorem
Taught in: The Graph of an Equation
Also in: A Course of Pure Mathematics
- number of real roots of a cubic
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants
- power rule for differentiation
Taught in: The Graph of an Equation
Also in: Calculus Made Easy
- product of determinants
Taught in: Determinants; Systems of Linear Equations
- relations between roots and coefficients
Taught in: Elementary Theorems on the Roots of an Equation, Symmetric Functions
Also in: A Course of Pure Mathematics
- remainder theorem
Taught in: Elementary Theorems on the Roots of an Equation
Also in: A Course of Pure Mathematics
- Rolle's theorem
Taught in: The Graph of an Equation, Isolation of the Real Roots of a Real Equation
Also in: A Course of Pure Mathematics
- Sturm's theorem
- sum rule for differentiation
Taught in: The Graph of an Equation
Also in: Calculus Made Easy
- Taylor's theorem
Taught in: The Graph of an Equation, Isolation of the Real Roots of a Real Equation, Solution of Numerical Equations, Appendix
Also in: A Course of Pure Mathematics, Elementary Illustrations of the Differential and Integral Calculus, Treatise on Thermodynamics
- upper limit theorem by coefficient ratios
- upper limit theorem by greatest negative coefficient
Methods (21)
- Bézout's method of elimination
Taught in: Elimination, Resultants And Discriminants
- Descartes' solution of the quartic equation
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants
- differentiation
Taught in: The Graph of an Equation
Also in: A Course of Pure Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Mathematical Recreations and Essays
- elimination
Taught in: Elimination, Resultants And Discriminants
Also in: A First Book in Algebra, The First Steps in Algebra, Treatise on Thermodynamics
- Euler's method of elimination
Taught in: Elimination, Resultants And Discriminants
- Ferrari's solution of the quartic equation
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants
- graphical solution of an equation
Taught in: The Graph of an Equation
Also in: A Course of Pure Mathematics
- Horner's method
Taught in: Solution of Numerical Equations
- interpolating in logarithmic tables
Taught in: Solution of Numerical Equations
Also in: Elements of Plane Trigonometry, Solid Geometry with Problems and Applications
- isolation of a root
Taught in: Isolation of the Real Roots of a Real Equation, Solution of Numerical Equations
- Laplace's development
Taught in: Determinants; Systems of Linear Equations, Elimination, Resultants And Discriminants
- mathematical induction
Taught in: Elementary Theorems on the Roots of an Equation
Also in: A Course of Pure Mathematics
- Newton's method
Taught in: Solution of Numerical Equations
Also in: A Course of Pure Mathematics, Elementary Illustrations of the Differential and Integral Calculus
- plotting a curve
Taught in: The Graph of an Equation
Also in: Calculus Made Easy
- quadratic formula
- regula falsi
Taught in: Solution of Numerical Equations
- solving an equation graphically
Taught in: The Graph of an Equation
Also in: A Course of Pure Mathematics
- solving simultaneous equations by determinants
Taught in: Determinants; Systems of Linear Equations
- Sylvester's dialytic method
Taught in: Elimination, Resultants And Discriminants
- synthetic division
Taught in: Elementary Theorems on the Roots of an Equation, Solution of Numerical Equations
- trigonometric solution of a cubic
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants
Quantities (1)
- modulus of a complex number
Taught in: Appendix
Also in: A Course of Pure Mathematics
Units (1)
People (11)
- Augustin-Louis Cauchy
Taught in: Appendix
Also in: A Course of Pure Mathematics, Mathematical Recreations and Essays, Spherical Trigonometry, for the Use of Colleges and Schools
- Carl Friedrich Gauss
Taught in: Appendix
Also in: A Course of Pure Mathematics, Mathematical Recreations and Essays
- Gabriel Cramer
Taught in: Determinants; Systems of Linear Equations
- Girolamo Cardano
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants
Also in: Mathematical Recreations and Essays
- Isaac Newton
Taught in: Solution of Numerical Equations
Also in: An Introduction to Mathematics, Calculus Made Easy, Elementary Illustrations of the Differential and Integral Calculus, Elements of Plane Trigonometry, Mathematical Recreations and Essays
- James Joseph Sylvester
Taught in: Elimination, Resultants And Discriminants
Also in: Mathematical Recreations and Essays
- Leonhard Euler
Taught in: Elimination, Resultants And Discriminants
Also in: Elementary Illustrations of the Differential and Integral Calculus, Mathematical Recreations and Essays, Spherical Trigonometry, for the Use of Colleges and Schools, Treatise on Thermodynamics
- Lodovico Ferrari
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants
- René Descartes
Taught in: Solution of Cubic and Quartic Equations; Their Discriminants
Also in: An Introduction to Mathematics, Mathematical Recreations and Essays
- William George Horner
Taught in: Solution of Numerical Equations
- Étienne Bézout
Taught in: Elimination, Resultants And Discriminants