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Sub Topics of the book; A Course of Pure Mathematics
- Rational numbers
- Irrational numbers
- Real numbers
- Relations of magnitude between real numbers
- Algebraical operations with real numbers
- The number √2
- Quadratic surds
- The continuum
- The continuous real variable
- Sections of the real numbers. Dedekind’s Theorem
- Points of condensation
- Weierstrass’s Theorem
- The idea of a function
- The graphical representation of functions. Coordinates
- Polar coordinates
- Polynomials
- Rational functions
- Algebraical functions
- Transcendental functions
- Graphical solution of equations
- Functions of two variables and their graphical representation
- Curves in a plane
- Loci in space
- Displacements
- Complex numbers
- The quadratic equation with real coefficients
- Argand’s diagram
- De Moivre’s Theorem
- Rational functions of a complex variable
- Roots of complex numbers
- Functions of a positive integral variable
- Interpolation
- Finite and infinite classes
- Properties possessed by a function of n for large values of n
- Definition of a limit and other definitions
- Oscillating functions
- General theorems concerning limits
- Steadily increasing or decreasing functions
- Infinite series
- The bounds of a bounded function
- Limits as x → a
- Continuous functions of a real variable
- Derivatives
- General rules for differentiation
- Derivatives of complex functions
- Differentiation of polynomials
- Repeated differentiation
- Maxima and minima
- Areas of plane curves
- Power series
Chapters of “A Course of Pure Mathematics” G. H. (Godfrey Harold) Hardy
- REAL VARIABLES
- FUNCTIONS OF REAL VARIABLES
- COMPLEX NUMBERS
- LIMITS OF FUNCTIONS OF A POSITIVE INTEGRAL VARIABLE
- LIMITS OF FUNCTIONS OF A CONTINUOUS VARIABLE. CONTINUOUS AND DISCONTINUOUS FUNCTIONS
- DERIVATIVES AND INTEGRALS
- ADDITIONAL THEOREMS IN THE DIFFERENTIAL AND INTEGRAL CALCULUS
- THE CONVERGENCE OF INFINITE SERIES AND INFINITE INTEGRALS
- THE LOGARITHMIC AND EXPONENTIAL FUNCTIONS OF A REAL VARIABLE
- THE GENERAL THEORY OF THE LOGARITHMIC, EXPONENTIAL, AND CIRCULAR FUNCTIONS
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