A2 Pure Mathematics (C3 and C4) (Mei structured math 3rd ed)
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Catherine Berry
Val Hanrahan
Roger Porkess
Peter Secker
pure math
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A2 Pure Mathematics (C3 and C4) (Mei structured math 3rd ed)
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C3: Methods for Advanced Mathematics
Theory
Page 12
Chapter 1: Proof
Theory
Page 13
Proof by Direct Argument
Theory
Page 13
Proof by Exhaustion
Theory
Page 14
Proof by Contradiction
Theory
Page 15
Disproof by the Use of a Counter-example
Theory
Page 17
Chapter 2: Natural Logarithms and Exponentials
Theory
Page 19
A New Function
Theory
Page 20
The Natural Logarithm Function
Theory
Page 22
The Exponential Function
Theory
Page 23
Chapter 3: Functions
Theory
Page 30
The Language of Functions
Theory
Page 30
Using Transformations to Sketch the Curves of Functions
Theory
Page 36
Composite Functions
Theory
Page 47
Inverse Functions
Theory
Page 50
Inverse Trigonometrical Functions
Theory
Page 56
Even, Odd and Periodic Functions
Theory
Page 60
The Modulus Function
Theory
Page 67
Curve Sketching
Theory
Page 71
Chapter 4: Techniques for Differentiation
Theory
Page 74
The Chain Rule
Theory
Page 74
The Product Rule
Theory
Page 79
The Quotient Rule
Theory
Page 82
Differentiating an Inverse Function
Theory
Page 88
Differentiating Natural Logarithms and Exponentials
Theory
Page 93
Differentiating sin x and cos x
Theory
Page 102
Differentiating Functions Defined Implicitly
Theory
Page 107
Chapter 5: Techniques for Integration
Theory
Page 114
Integration by Substitution
Theory
Page 114
Integrals Involving the Exponential Function
Theory
Page 121
Integrals Involving the Natural Logarithm Function
Theory
Page 122
Extending the Domain for Logarithmic Integrals
Theory
Page 124
Integrating sin x and cos x
Theory
Page 134
Integration by Parts
Theory
Page 136
Chapter 6: Numerical Solution of Equations
Theory
Page 146
Interval Estimation – Change of Sign Methods
Theory
Page 147
Fixed Point Iteration
Theory
Page 154
Rearranging the Equation f(x) = 0 into the Form x = g(x)
Theory
Page 154
The Newton–Raphson Method
Theory
Page 161
C4: Applications of Advanced Mathematics
Theory
Page 166
Chapter 7: Algebra
Theory
Page 167
The General Binomial Expansion
Theory
Page 168
Review of Algebraic Fractions
Theory
Page 177
Partial Fractions
Theory
Page 184
Chapter 8: Trigonometry
Theory
Page 194
Reciprocal Trigonometrical Functions
Theory
Page 195
Compound-angle Formulae
Theory
Page 198
Double-angle Formulae
Theory
Page 203
The Factor Formulae
Theory
Page 208
The Forms r cos(θ ± α), r sin(θ ± α)
Theory
Page 212
Small-angle Approximations
Theory
Page 221
The General Solutions of Trigonometrical Equations
Theory
Page 229
Using Trigonometrical Identities in Integration
Theory
Page 231
Chapter 9: Parametric Equations
Theory
Page 235
Graphs from Parametric Equations
Theory
Page 237
Finding the Equation by Eliminating the Parameter
Theory
Page 238
The Parametric Equation of a Circle
Theory
Page 242
The Parametric Equations of Other Standard Curves
Theory
Page 243
Parametric Differentiation
Theory
Page 249
Chapter 10: Further Techniques for Integration
Theory
Page 264
Finding Volumes by Integration
Theory
Page 265
The Use of Partial Fractions in Integration
Theory
Page 272
General Integration
Theory
Page 277
Integrals You Cannot Do
Theory
Page 280
Chapter 11: Vectors
Theory
Page 286
Vectors
Theory
Page 286
Co-ordinate Geometry Using Vectors: Two Dimensions
Theory
Page 300
Co-ordinate Geometry Using Vectors: Three Dimensions
Theory
Page 314
Chapter 12: Differential Equations
Theory
Page 346
Forming Differential Equations from Rates of Change
Theory
Page 347
Solving Differential Equations
Theory
Page 352
Answers
Answer
Page 369
Chapter 1 Answers
Answer
Page 369
Chapter 2 Answers
Answer
Page 369
Chapter 3 Answers
Answer
Page 370
Chapter 4 Answers
Answer
Page 380
Chapter 5 Answers
Answer
Page 387
Chapter 6 Answers
Answer
Page 391
Chapter 7 Answers
Answer
Page 394
Chapter 8 Answers
Answer
Page 397
Chapter 9 Answers
Answer
Page 403
Chapter 10 Answers
Answer
Page 408
Chapter 11 Answers
Answer
Page 414
Chapter 12 Answers
Answer
Page 421
Index
Other
Page 424
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