Essential Mathematical Methods 3 and 4 with CD-Rom

Introduction; 1. Functions, 1.1. Introduction, 1.2. Set notation, 1.3. Sets of numbers, 1.4. Relations, 1.5. Functions, 1.6. Sums and products of functions, 1.7. Composite functions, 1.8. Inverse functions, 1.9. Inverse relations, 1.10. Applications; 2. Revising linear functions, 2.1. Revision of linear equations, 2.2. Linear functions, 2.3. 'Fitting' data; 3. Graphing with transformations, 3.1. Introduction, 3.2. The functions with rules f(x)=xn, where n=-1, -2, 1/2, 3.3. Composition of transformations, 3.4. Quadratic functions, 3.5. Determining the rule for a function of a graph, 3.6. Possible models for data, 3.7. Addition of ordinates, 3.8. Graphing inverse functions; 4. Polynomial functions, 4.1. Summation notation, 4.2. The Binomial Theorem, 4.3. Cubic functions of the form f: R > R, f(x)=a(x+h)3 + k, 4.4. The general cubic function, 4.5. Cubic equations, 4.6. Determining rules for graphs of cubic functions, 4.7. Quartic functions, 4.8. Graphics calculator exercise; 5. Exponential and logarithmic functions, 5.1. Exponential functions, 5.2. Exponential models, 5.3. The exponential function f(x)=ex, 5.4. Exponential equations, 5.5. Logarithmic functions, 5.6. Inverses, 5.7. Determining rules for graphs of exponential and logarithmic functions, 5.8. Solution of exponential equations and inequations with logarithms, 5.9. Graphics calculator exercise, 5.10. Applications; 6. Trigonometric functions, 6.1. Review of trigonometric functions, 6.2. Graphs of sine and cosine, 6.3. Transformations applied to graphs of y = sin x and y = cos x, 6.4. Addition of ordinates, 6.5. Determining the rule for graphs of trigonometric functions, 6.6. The function tan, 6.7. Graphics calculator exercise, 6.8. Identities, 6.9. Applications; 7. Revision of chapters 1-6, 7.1. Summary of chapters 1-6, 7.2. Short answer questions, 7.3. Multiple choice questions, 7.4. Analysis questions; 8. Differentiation of polynomials and rational functions, 8.1. The gradient of a curve at a point, 8.2. The derived function, 8.3. Differentiating xn where n is negative integer, 8.4. The Chain Rule, 8.5. Differentiating rational powers (x p/q), 8.6. Product Rule and Quotient Rule, 8.7. The graph of the gradient function, 8.8. Graphics calculator exercise, 8.9. Miscellaneous exercise; 9. Applications of differentiation, 9.1. Tangents and normals, 9.2. Angles between curves, 9.3. Linear approximation, 9.4. Stationary points, 9.5. Types of stationary points, 9.6. Maxima and minima problems, 9.7. Rates of change, 9.8. Graphics calculator exercise; 10. Differentiation of transcendental functions, 10.1. Differentiation of ex, 10.2. Differentiation of the natural logarithm function, 10.3. Derivatives of trigonometric functions, 10.4. Graphics calculator exercise, 10.5. Applications; 11. Integration, 11.1. Approximations leading to integrals, 11.2. Antidifferentiation, 11.3. Area - the definite integral, 11.4. Integration of trigonometric functions, 11.5. Integration of functions of the form f(x) = 1/ax+b, 11.6. Miscellaneous exercise, 11.7. Area of a region between two curves, 11.8. The fundamental theorem of calculus revisited, 11.9. Graphics calculator exercise, 11.10. Applications; 12. Revision of chapters 8-11, 12.1. Summary of chapters 8-11, 12.2. Short answer questions, 12.3. Multiple choice questions, 12.4. Analysis questions; 13. Discrete random variables and their probability distributions, 13.1. Review of probability, 13.2. Discrete random variables, 13.3. Discrete probability distributions, 13.4. Expectation and variance; 14. The binomial distribution, 14.1. The binomial probability distribution, 14.2. The graph of the binomial probability distribution, 14.3. Expectation and variance, 14.4. Using the graphics calculator; 15. The hypergeometric distribution, 15.1. The hypergeometric probability distribution, 15.2. Mean and variance, 15.3. The binomial and hy