Mathematics for physicists - Instructors' manual (solution to even numbered problems)

EvenNumberedSolutions
	EvenNumberedSolutionsContents
	EvenNumberedSolutions
		Even-numbered solutions
		Problems: Linear Algebra
			Mathematics before numbers
				Sets and Maps
				Groups
				Fields
			Vector spaces
				Vector spaces: examples
				Basis and dimension
			Euclidean geometry
				Normalization and orthogonality
				Inner product spaces
			Vector product
				Algebraic formulation
				Further properties of the vector product
			Linear Maps
				Linear maps
				Matrix multiplication
				The inverse of a matrix
				General linear maps and matrices
				Matrices describing coordinate changes
			Determinants
				Computing determinants
			Matrix diagonalization
				Matrix diagonalization
				Functions of matrices
			Unitarity and Hermiticity
				Unitarity and orthogonality
				Hermiticity and symmetry
				Relation between Hermitian and unitary matrices
			Multilinear algebra
				Direct sum and direct product of vector spaces
				Dual space
				Tensors
				Alternating forms
				Wedge product
				Inner derivative
				Pullback
				Metric structures
		Solutions: Calculus
			Differentiation of one-dimensional functions
				Definition of differentiability
				Differentiation rules
				Derivatives of selected functions
			Integration of one-dimensional functions
				One-dimensional integration
				Integration rules
				Practical remarks on one-dimensional integration
			Partial differentiation
				Partial derivative
				Multiple partial derivatives
				Chain rule for functions of several variables
			Multi-dimensional integration
				Cartesian area and volume integrals
				Curvilinear area integrals
				Curvilinear volume integrals
				Curvilinear integration in arbitrary dimensions
				Changes of variables in higher-dimensional integration
			Taylor series
				Complex Taylor series
				Finite-order expansion
				Solving equations by Taylor expansion
				Higher-dimensional Taylor series
			Fourier calculus
				The -Function
				Fourier series
				Fourier transform
				Case study: Frequency comb for high-precision measurements
			Differential equations
				Separable differential equations
				Linear first-order differential equations
				Systems of linear first-order differential equations
				Linear higher-order differential equations
				General higher-order differential equations
				Linearizing differential equations
			Functional calculus
				Euler-Lagrange equations
			Calculus of complex functions
				Holomorphic functions
				Complex integration
				Singularities
				Residue theorem
		Solutions: Vector Calculus
			Curves
				Curve velocity
				Curve length
				Line integral
			Curvilinear Coordinates
				Cylindrical and spherical coordinates
				Local coordinate bases and linear algebra
			Fields
				Definition of fields
				Scalar fields
				Extrema of functions with constraints
				Gradient fields
				Sources of vector fields
				Circulation of vector fields
				Practical aspects of three-dimensional vector calculus
			Introductory concepts of differential geometry
				Differentiable manifolds
				Tangent space
			Alternating differential forms
				Cotangent space and differential one-forms
				Pushforward and Pullback
				Forms of higher degree
				Integration of forms
			Riemannian differential geometry
				Definition of the metric on a manifold
				Volume form and Hodge star
			Differential forms and electrodynamics
				Laws of electrodynamics II: Maxwell equations
				Invariant formulation
0687bE_s