Sixth form pure mathematics. Volume 1 / C. Plumpton and W.A. Tomkys.
Sixth Form Pure Mathematics, Volume 1, Second Edition, is the first of a series of volumes on Pure Mathematics and Theoretical Mechanics for Sixth Form students whose aim is entrance into British and Commonwealth Universities or Technical Colleges. A knowledge of Pure Mathematics up to G.C.E. O-leve...
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Full Text (via ScienceDirect) |
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| Main Authors: | , |
| Format: | eBook |
| Language: | English |
| Published: |
Oxford ; New York :
Pergamon Press,
[1968]
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| Edition: | Second edition. |
| Subjects: |
Table of Contents:
- Front Cover; Sixth Form Pure Mathematics; Copyright Page; Table of Contents; PREFACE TO THE SECOND EDITION; CHAPTER 1. INTRODUCTION TO THE CALCULUS; 1.1. Coordinates and loci; 1.2. The idea of a limit; 1.3. The gradient of a curve; 1.4. Differentiation; 1.5. Tangents and normals; 1.6. Rates of change; 1.7. Differentiation of a function of a function; 1.8. Maxima and minima; 1.9. Second derivative; 1.10. Parameters; CHAPTER 2. METHODS OF COORDINATE GEOMETRY; 2.1. The straight line; 2.2. The division of a line; 2.3. The equation of a circle; 2.4. The intersection of lines and circles.
- 2.5. The parabola x = at2, y = 2at> a> 02.6. The rectangular hyperbola x = ct, y = c/t, c> 0; 2.7. The semi-cubical parabola x = at2, y = at3, a> 0; CHAPTER 3. METHODS OF THE CALCULUS; 3.1. Integration as the reverse of differentiation; 3.2. The constant of integration; 3.3. The area under a curve. Definite integrals; 3.4. Volumes of revolution; 3.5. Differentiation of products and quotients; 3.6. Tangents to conic sections; CHAPTER 4. THE CIRCULAR FUNCTIONS; 4.1. Definition of an angle; 4.2. The circular functions; 4.3. General solutions of trigonometric equations.
- 4.4. Circular functions of 30°, 60°, 45°4.5. Relations between the circular functions; 4.6. Circular measure; 4.7. Vectors; 4.8. The addition theorems; 4.9. Double and half angles; 4.10. The addition of sine waves; 4.11. The sum-product transformations; CHAPTER 5. THE CIRCULAR FUNCTIONS IN CALCULUS AND COORDINATE GEOMETRY; 5.1. The derivatives of sin x and cos x; 5.2. Integral forms; 5.3. Differentiation and integration of other circular functions; 5.4. Small increments; 5.5. The angle between two straight lines; 5.6. The sign of Ax+ By + C.
- 7.4. The orthocentre and the altitudes7.5. The centroid and the medians; CHAPTER 8. FINITE SERIES; 8.1. Definition and notation; 8.2. Arithmetical progressions; 8.3. Geometrical progressions; 8.4. Permutations and combinations; 8.5. Mathematical induction; 8.6. The binomial theorem; 8.7. Some other finite series; 8.8. The method of differences; 8.9. Finite power series; CHAPTER 9. INFINITE SERIES. MACLAURIN'S EXPANSION. THE BINOMIAL, EXPONENTIAL AND LOGARITHM FUNCTIONS; 9.1. Successive approximations; 9.2. Maclaurin's expansion; 9.3. The binomial series; 9.4. The exponential function.
- 5.7. The perpendicular form of the equation of a straight line5.8. Tangents to circles; 5.9. The ellipse x = a cos θ, y = b sin θ; CHAPTER 6. THE QUADRATIC FUNCTION AND THE QUADRATIC EQUATION; 6.1. The quadratic function ax2+bx+c; 6.2. The function; 6.3. The quadratic equation ax2+bx+c = 0; 6.4. Some applications to coordinate geometry; 6.5. The cubic function f(x) = ax3+bx2+cx+d; 6.6. Co-normal points; 6.7. The hyperbola; CHAPTER 7. NUMERICAL TRIGONOMETRY; 7.1. The solution of triangles; 7.2. Trigonometry in three dimensions; 7.3. The in-centre and e-centres of a triangle.