Essential Specialist Mathematics with CD-Rom

by Michael Evans , Josian Astruc , Neil Cracknell , Peter Jones , Sue Avery

• ISBN13: 9780521664509
• ISBN10: 0521664500
• Edition: 2nd
• Format: Multimedia
• Copyright: 1999-09-23
• Publisher: Cambridge University Press

Summary

The original text has been completely rewritten for the 2000 Mathematics Study Design and has taken in the many suggestions and requests provided by teachers. Essential Specialist Mathematics provides a single unified course of study which addresses all the key knowledge and skills outcomes. It includes new graphics calculator questions, exercises and theory and includes revision chapters for efficient examination preparation. Included are analysis exercises, multiple choice questions and applications. Current technology is addressed with applications to theory and exercises, and there are answers to all questions. The CD includes navigation by chapter and chapter section as well as the Cambridge Specialist Mathematics Tutor CD-ROM which is a self-help bank of multiple choice questions to consolidated knowledge.

Table of Contents

Introduction

1. A toolbox, 1.1. Circular functions, 1.2. Solving right-angled triangles, 1.3. The sine and cosine rules, 1.4. Geometry prerequisites, 1.5. Sequences and series, 1.6. Circles, 1.7. Ellipses and hyperbolae

2. Vectors, 2.1. Introduction to vectors, 2.2. Resolution of a vector into rectangular components, 2.3. Scalar (or dot) product of vectors, 2.4. Vector resolutes, 2.5. Vector proofs

3. Circular functions, 3.1. The tangent function, 3.2. The reciprocal circular functions, 3.3. Compound and double angle formulae, 3.4. Inverses of circular functions, 3.5. Solution of equations

4. Complex numbers, 4.1. The set of complex numbers, C, 4.2. The complex conjugate and division, 4.3. The modulus-argument form of a complex number, 4.4. Basic operations on complex numbers in the modulus-argument form, 4.5. Factorisation of polynomials in C, 4.6. Solution of polynomial equations, 4.7. Using De Moivre's theorem to solve equations in the form zn=a where a = C, 4.8. Relations and regions of the complex plane

5. Revision of chapters 2-4, 5.1. Summary of chapters 2-4, 5.2. Short answer questions, 5.3. Multiple choice questions, 5.4. Analysis questions

6. Differentiation and rational functions, 6.1. A review, 6.2. Derivatives of x=f(y), 6.3. Derivatives of inverse circular functions, 6.4. Second derivatives, 6.5. Related rates, 6.6. Graphs of some rational functions, 6.7. A summary of differentiation, 6.8. Implicit differentiation

7. Antidifferentiation, 7.1. Antidifferentiation, 7.2. Antiderivatives involving inverse circular functions, 7.3. Integration by substitution, 7.4. Definite integrals by substitution, 7.5. Use of trigonometric identities for integration, 7.6. Partial fractions, 7.7. Further techniques and miscellaneous exercises

8. Applications of integration, 8.1. Areas of regions, 8.2. Area of a region between two curves, 8.3. Integration using a graphics calculator, 8.4. Volumes of solids of revolution, 8.5. Numerical methods of integration

9. Differential equations, 9.1. An introduction to differential equations, 9.2. Solution of differential equations of the form dy/dx=f(x) and d2y/dx2=f(x), 9.3. The solution of differential equations of the form dy/dx=f(y), 9.4. Application of differential equations, 9.5. Differential equations with related rates, 9.6. A numerical solution to a differential equation

10. Kinematics, 10.1. Position velocity and acceleration, 10.2. Constant acceleration, 10.3. Velocity time graphs, 10.4. Differential equations of the form v=f(x) and a=f(v), 10.5. Other expressions for acceleration

11. Revision of chapters 6-10, 11.1. Summary of chapters 6-10, 11.2. Short answer questions, 11.3. Multiple choice questions, 11.4. Analysis questions

12. Vector functions, 12.1. Vector equations, 12.2. Position vectors as a function of time, 12.3. Vector calculus, 12.4. Velocity and acceleration for motion along a curve, 12.5. Distance travelled by a particle along a curve

13. Dynamics, 13.1. Force, 13.2. Newton's laws of motion, 13.3. Resolution of forces and inclined planes, 13.4. Connected particles, 13.5. Variable forces, 13.6. Equilibrium, 13.7. Friction and equilibrium, 13.8. Vector functions

14. Revision of chapters 12-13, 14.1. Summary of chapters 12-13, 14.2. Short answer questions, 14.3. Multiple choice questions, 14.4. Analysis questions

Graphics calculator appendix 1

Answers.