Sixth Form Pure Mathematics Volume 1

• Main Authors: Plumpton, C, Tomkys, W. A
• Format: eBook
• Language: English
• Published: Chantilly Elsevier Science & Technology 1968
• Edition: 2
• Subjects: Mathematics
• ISBN: 9780080093741; 0080093744

Table of Contents:

• 5.7. The perpendicular form of the equation of a straight line -- 5.8. 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 -- 7.4. The orthocentre and the altitudes -- 7.5. 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 -- 9.5. The expansion of ex -- 9.6. Logarithms to any base -- 9.7. Natural logarithms -- 9.8. Logarithmic differentiation -- 9.9. The logarithm series -- CHAPTER 10. PARTIAL FRACTIONS AND THEIR APPLICATIONS SOME FURTHER METHODS OF INTEGRATION -- 10.1. Partial fractions -- 10.2. Application of partial fractions to series expansions -- 10.3. Application of partial fractions to the summation of series -- 10.4. Application of partial fractions to integration -- 10.5. Integration by substitution -- 10.6. Integration by parts -- ANSWERS TO THE EXERCISES -- INDEX
• 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&gt -- a &gt -- 0 -- 2.6. The rectangular hyperbola x = ct, y = c/t, c &gt -- 0 -- 2.7. The semi-cubical parabola x = at2, y = at3, a &gt -- 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