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Sixth Form Pure Mathematics
Volume 2
- 1st Edition - January 1, 1963
- Authors: C. Plumpton, W. A. Tomkys
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 4 0 8 8 - 9
Sixth Form Pure Mathematics, Volume 2, provides an introduction to inverse trigonometric functions, hyperbolic and inverse hyperbolic functions, and a range of mathematical methods… Read more
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Request a sales quoteSixth Form Pure Mathematics, Volume 2, provides an introduction to inverse trigonometric functions, hyperbolic and inverse hyperbolic functions, and a range of mathematical methods including the use of determinants, the manipulation of inequalities, the solution of easy differential equations, and the use of approximate numerical methods. Complex numbers are defined and the various ways of representing and manipulating them are considered. Polar coordinates, curvature, an elementary study of lengths of curves and areas of surfaces of revolution, a more mature discussion of two-dimensional coordinate geometry than was possible in Volume 1, and an elementary introduction to the methods of three dimensional coordinate geometry comprise the geometrical content of the book. Throughout, the authors have tried to preserve the concentric style which they used in Volume 1 and the many worked examples and exercises in each chapter are designed or chosen to provide a continuous reminder of the work of the preceding chapters. Except for Pure Geometry, the two volumes cover almost all of the syllabuses for Advanced Pure Mathematics of the nine Examining Boards. This book provides an adequate course for mathematical pupils at Grammar Schools and a useful introductory course for Science and Engineering students in their first year at University or Technical College or engaged in private study.
Chapter XI Linear Equations and Determinants
The Solution of Linear Simultaneous Equations in Two Unknowns
Second Order Determinants
Rules of Manipulation for Second Order Determinants
Third Order Determinants
Factorization of Determinants
Geometrical Interpretation.
The Equation of a Straight Line through Two Given Points
The Equation of a Tangent to the Curve
The Equation of a Line-Pair
The Equation of a Circle through Three Given Points
The Area of a Triangle
The Solution of Simultaneous Equations
Summary
The Product of Two Determinants
The Derivative of a Determinant
Chapter XII Inverse Circular Functions, Hyperbolic Functions and Inverse Hyperbolic Functions
Inverse Circular Functions.
The Derivatives of the Inverse Circular Functions
Standard Integrals
The Hyperbolic Functions
Inverse Hyperbolic Functions
Derivatives of the Inverse Hyperbolic Functions
Logarithmic Forms of the Inverse Hyperbolic Functions
Methods of Integration
The Integrals
Summary of Standard Integrals and Methods of Integration So Far Considered
Chapter XIII Definite Integrals. Further Applications of Integration
Properties of Definite Integrals
Infinite Integrals
Reduction Formula
Approximate Numerical Integration
Mean Values and Root Mean Square
Center of Mass
The Theorem of Pappus concerning Volumes
Moments of Inertia
Chapter XIV Some Properties of Curves
Points of Inflexion
The Length of a Curve
The Cycloid
Areas of Surfaces of Revolution
The Theorem of Pappus concerning Surfaces of Revolution
Curvature
Newton's Formula for Radius of Curvature at the Origin
Chapter XV Polar Coordinates
Definitions
Loci in Polar Coordinates
Curve Sketching in Polar Coordinates
The Lengths of Chords of Polar Curves Which are Drawn through The Pole
Transformations from Polar to Cartesian Equations and the Reverse Process
Areas in Polar Coordinates
The Length of an Arc in Polar Coordinates
Volumes of Revolution and Areas of Surfaces of Revolution in Polar Coordinates
The Angle between the Tangent and the Radius Vector
The Tangential Polar Equation—Curvature
Chapter XVI Complex Numbers
The Number System
Definition of Complex Number
The Cube Roots of Unity
Conjugate Pairs of Complex Roots
The Geometry of Complex Numbers
The Polar Coordinate Form of a Complex Number- Modulus and Argument
Products and Quotients
De Moivre's Theorem
The Exponential Form of a Complex Number
Exponential Values of Sine and Cosine
Chapter XVII Differential Equations
Formation of Differential Equations
The Solution of a Differential Equation
First Order Differential Equations with Variables Separable
Homogeneous Equations
The Law of Natural Growth
Linear Equations of the First Order
Bernoulli's Equation
Equations of Higher Orders
Linear Equations of the Second Order with Constant Coefficients
The Complementary Function. The Particular Integral
Chapter XVIII Approximate Numerical Solution of Equations
Graphical Methods
The Number of Real Roots of An Equation
The Approximate Value of a Small Root of a Polynomial Equation
Newton's Method for Obtaining a Closer Approximation to a Real Root of An Equation
Chapter XIX Inequalities
Rules of Manipulation
Fundamental Inequalities
The Calculus Applied to Inequalities
Chapter XX Coordinate Geometry
The Straight Line
Lone Pairs
The Circle
The Radical Axis
Coaxal Circles
Conic Sections
Note on the General Equation of the Second Degree
The Chord of Contact of Tangents Drawn from an External Point to a Conic-Pole and Polar
The Equation of a Pair of Tangents Drawn from an External Point to a Conic
Conjugate Diameters
The Polar Equation of a Conic
Chapter XXI Coordinate Geometry of Three Dimensions
The Coordinate System
The Distance between Two Points
The Coordinates of a Point Which Divides the Line Joining Two Given Points in a Given Ratio
The Equation of a Plane
The Equations of a Line—Direction Cosines
The Angle between Two Directions
The Intersection of Three Planes
Answers to Exercises
Index
- No. of pages: 416
- Language: English
- Edition: 1
- Published: January 1, 1963
- Imprint: Pergamon
- eBook ISBN: 9781483140889
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