Edexcel A Level Further Mathematics Year 2
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Description
Contents
Reviews
Language
English
ISBN
9781471851803
Cover
Title Page
Copyright
Contents
Getting the most from this book
Prior knowledge
1 Series and induction
1.1 Review: Sequences and series
1.2 The method of differences
1.3 Summing series using partial fractions
1.4 Review: Proof by induction
2 Further calculus
2.1 Improper integrals
2.2 Calculus with inverse trigonometric functions
2.3 Partial fractions
2.4 Further integration
3 Maclaurin series
3.1 Polynomial approximations and Maclaurin series
3.2 Using Maclaurin series for standard functions
Review: Matrices and transformations
R.1 Matrices
R.2 Using matrices to represent transformations
R.3 Invariance
R.4 The inverse of a 2 × 2 matrix
R.5 The inverse of a 3 × 3 matrix
R.6 Intersection of three planes
Practice questions Further Mathematics 1
Review: Complex numbers
R.1 Working with complex numbers
R.2 Representing complex numbers geometrically
R.3 The modulus and argument of a complex number
R.4 Multiplying and dividing complex numbers in modulus-argument form
R.5 Loci in the Argand diagram
4 Polar coordinates
4.1 Polar coordinates
4.2 Sketching curves with polar equations
4.3 Finding the area enclosed by a polar curve
5 Hyperbolic functions
5.1 Hyperbolic functions
5.2 Inverse hyperbolic functions
5.3 Integration using inverse hyperbolic functions
6 Applications of integration
6.1 Volumes of revolution
6.2 The mean value of a function
6.3 General integration
Practice questions Further Mathematics 2
Review: Roots of polynomials
R.1 Roots and coefficients
R.2 Complex roots of polynomial equations
7 First order differential equations
7.1 Modelling rates of change
7.2 Separation of variables
7.3 Integrating factors
8 De Moivre’s theorem
8.1 De Moivre’s theorem
8.2 The nth roots of a complex number
8.3 Finding multiple angle identities by using de Moivre’s theorem
8.4 The form z = re iθ
8.5 Summing series using de Moivre’s theorem
9 Second order differential equations
9.1 Higher order differential equations
9.2 Auxiliary equations with complex roots
9.3 Non-homogeneous differential equations
9.4 Systems of differential equations
Review: Vectors
R.1 Lines and planes
R.2 Intersections, angles and distances
Practice questions Further Mathematics 3
Appendix: The vector product
Answers
Index
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