Cover
Half-title
Title
Copyright
Contents
Preface
1 Preliminary algebra
Polynomial equations
Trigonometric identities
Coordinate geometry
Partial fractions
Binomial expansion
Proof by induction and contradiction
Necessary and su.cient conditions
2 Preliminary calculus
3 Complex numbers and hyperbolic functions
4 Series and limits
5 Partial differentiation
6 Multiple integrals
7 Vector algebra
8 Matrices and vector spaces
9 Normal modes
10 Vector calculus
11 Line, surface and volume integrals
12 Fourier series
13 Integral transforms
Note
14 First-order ordinary di.erential equations
15 Higher-order ordinary differential equations
16 Series solutions of ordinary differential equations
17 Eigenfunction methods for differential equations
18 Special functions
19 Quantum operators
20 Partial differential equations: general and particular solutions
21 Partial differential equations: separation of variables and other methods
22 Calculus of variations
23 Integral equations
24 Complex variables
25 Applications of complex variables
26 Tensors
27 Numerical methods
28 Group theory
29 Representation theory
30 Probability
31 Statistics