Essential Specialist Mathematics with CD-ROM

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.