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EULA
by Graham Shaw, Brian R. Martin
Mathematics for Physicists
Editors' preface to the Manchester Physics Series
Authors' preface
Notes and website information
‘Starred’ material
Website
Examples, problems and solutions
1 Real numbers, variables and functions
1.1 Real numbers
1.2 Real variables
1.3 Functions, graphs and co-ordinates
Problems 1
Notes
2 Some basic functions and equations
2.1 Algebraic functions
2.2 Trigonometric functions
2.3 Logarithms and exponentials
2.4 Conic sections
Problems 2
Notes
3 Differential calculus
3.1 Limits and continuity
3.2 Differentiation
3.3 General methods
3.4 Higher derivatives and stationary points
3.5 Curve sketching
Problems 3
Notes
4 Integral calculus
4.1 Indefinite integrals
4.2 Definite integrals
4.3 Change of variables and substitutions
4.4 Integration by parts
4.5 Numerical integration
4.6 Improper integrals
4.7 Applications of integration
Problems 4
Notes
5 Series and expansions
5.1 Series
5.2 Convergence of infinite series
5.3 Taylor's theorem and its applications
5.4 Series expansions
*5.5 Proof of d'Alembert's ratio test
*5.6 Alternating and other series
Problems 5
Notes
6 Complex numbers and variables
6.1 Complex numbers
6.2 Complex plane: Argand diagrams
6.3 Complex variables and series
6.4 Euler's formula
Problems 6
Notes
7 Partial differentiation
7.1 Partial derivatives
7.2 Differentials
7.3 Change of variables
7.4 Taylor series
7.5 Stationary points
*7.6 Lagrange multipliers
*7.7 Differentiation of integrals
Problems 7
Notes
8 Vectors
8.1 Scalars and vectors
8.2 Products of vectors
8.3 Applications to geometry
8.4 Differentiation and integration
Problems 8
Notes
9 Determinants, Vectors and Matrices
9.1 Determinants
9.2 Vectors in n Dimensions
9.3 Matrices and linear transformations
9.4 Square Matrices
Problems 9
Notes
10 Eigenvalues and eigenvectors
10.1 The eigenvalue equation
*10.2 Diagonalisation of matrices
Problems 10
Notes
11 Line and multiple integrals
11.1 Line integrals
11.2 Double integrals
11.3 Curvilinear co-ordinates in three dimensions
11.4 Triple or volume integrals
Problems 11
12 Vector calculus
12.1 Scalar and vector fields
12.2 Line, surface, and volume integrals
12.3 The divergence theorem
12.4 Stokes' theorem
Problems 12
Notes
13 Fourier analysis
13.1 Fourier series
13.2 Complex Fourier series
13.3 Fourier transforms
Problems 13
Notes
14 Ordinary differential equations
14.1 First-order equations
14.2 Linear ODEs with constant coefficients
*14.3 Euler's equation
Problems 14
Notes
15 Series solutions of ordinary differential equations
15.1 Series solutions
15.2 Eigenvalue equations
15.3 Legendre's equation
15.4 Bessel's equation
Problems 15
Notes
16 Partial differential equations
16.1 Some important PDEs in physics
16.2 Separation of variables: Cartesian co-ordinates
16.3 Separation of variables: polar co-ordinates
*16.4 The wave equation: d'Alembert's solution
*16.5 Euler Equations
*16.6 Boundary conditions and uniqueness
Problems 16
Notes
Answers to selected problems
Problems 1
Problems 2
Problems 3
Problems 4
Problems 5
Problems 6
Problems 7
Problems 8
Problems 9
Problems 10
Problems 11
Problems 12
Problems 13
Problems 14
Problems 15
Problems 16
Index
EULA
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