A first course in mathematical physics. (2016)

• Record Type: Book
• Further Information: Note: Colm T. Whelan.
• Authors: Whelan, Colm T
• Contents: Preface page ix; ; Part I: Mathematics 1; ; 1 Functions of one variable 2; 1.1 Limits 2; 1.2 Elementary Calculus 6; 1.2.1 Chain Rule 7; 1.2.2 Differentiation products and quotients 8; 1.2.3 Inverse Functions 9; 1.3 Integration 10; 1.4 The Binomial Expansion 13; 1.5 Taylor's series 15; 1.6 Extrema 17; 1.7 Power Series 18; 1.8 Basic Functions 19; 1.8.1 Exponential 19; 1.8.2 Logarithm 23; 1.9 1st order ordinary differential equations 24; 1.10 Trigonometric Functions 26; 1.10.1 L'Hopital's rule 28; 1.11 Problems 30; ; 2 Complex numbers 33; 2.1 Exponential function of a complex variable 34; 2.2 Argrand Diagrams and the Complex Plane 36; 2.3 Hyperbolic functions 38; 2.4 The simple harmonic oscillator 40; 2.4.1 Mechanics in one dimension 42; 2.5 Problems 45; ; 3 Functions of Several Variables 48; 3.1 Partial derivatives 48; 3.1.1 Definition of the partial derivative 48; 3.1.2 Total derivatives 51; 3.1.3 Some relations 53; 3.1.4 Change of variables 55; 3.1.5 Mechanics again 56; 3.1.6 Exact differentials and thermodynamics 58; 3.2 Extrema under constraint 60; 3.3 Multiple Integrals 62; 3.3.1 Triple Integrals 66; 3.3.2 Change of variables 67; 3.4 Problems 69; ; 4 Vectors in R3 72; 4.1 Basic operation 72; 4.1.1 scalar triple product 79; 4.1.2 Vector equations of lines and planes 80; 4.2 Kinematics in three dimensions 81; 4.2.1 Differentiation 81; 4.2.2 Motion in a uniform magnetic field 81; 4.3 Coordinate systems 83; 4.3.1 Polar coordinates 83; 4.4 Central Forces 84; 4.5 Rotating Frames 88; 4.5.1 Larmor Effect 91; 4.6 Problems 93; ; 5 Vector fields and operators 96; 5.1 The gradient operator 96; 5.1.1 Coordinate Systems 97; 5.2 Work and energy in vectorial mechanics 101; 5.2.1 Line integrals 104; 5.3 A little fluid dynamics 107; 5.3.1 Rotational motion 111; 5.3.2 Fields 114; 5.3.3 Surface integrals 115; 5.4 The divergence theorem 118; 5.5 Stokes' Theorem 121; 5.5.1 Conservative Forces 123; 5.6 Problems 126; ; 6 Generalized Functions. 130; 6.1 The Dirac delta function 130; 6.2 Problems 139; ; 7 Vector Spaces 140; 7.1 Formal Definition of a vector space 140; 7.2 Fourier Series 145; 7.3 Linear Operators 148; 7.4 Change of basis 160; 7.5 Problems 163; ; Part II: Physics 168; ; 8 Maxwell's Equations: A very short Introduction 169; 8.1 Electrostatic: Gauss's Law 169; 8.2 Gauss's Law for a magnetic field 173; 8.3 Ampere's Law 173; 8.3.1 Gauge conditions 174; 8.4 Problems 177; ; 9 Special Relativity:4-vector formalism 179; 9.1 Lorentz transformation 179; 9.1.1 Inertial frames 179; 9.1.2 Properties and consequences of the Lorentz transformation; 182; 9.2 Minkowski space 183; 9.2.1 Four vectors 183; 9.2.2 Time Dilation 189; 9.3 Four velocity 190; 9.3.1 Four momentum 191; 9.4 Electrodynamics 197; 9.4.1 Maxwell's equations in 4-vector form 197; 9.4.2 Field of a moving point charge 200; 9.5 Problems 202; ; 10 Quantum Theory 205; 10.1 Formalism 205; 10.1.1 Dirac notation 206; 10.2 Probabilistic interpretation 207; 10.2.1 Commutator relations 208; 10.2.2 Functions of observables 210; 10.3 The Stern-Gerlach experiment 210; 10.3.1 Spin space 210; viii Contents; 10.3.2 Explicit matrix representation 210; 10.3.3 EPR paradox 210; 10.3.4 Bell's Theorem 210; 10.4 Quantization 210; 10.4.1 Time evolution 210; 10.4.2 The harmonic oscillator, coherent states 210; 10.5 Problems 212; ; 11 Atoms, molecules, solids, wave mechanics in one dimension; 216; 11.1 Atom 217; 11.1.1 The square well 218; 11.1.2 The delta function potential 219; 11.2 Molecules 221; 11.3 Solids 223; 11.3.1 Block's Theorem 224; 11.3.2 Band structure 226; 12 An informal treatment of variational principles and their; history 229; ; Appendix 1 Conic Sections 230; Appendix 2 Vector Relations 232; Index 237;
• Edition: 1st
• Publisher Details: Weinheim : Wiley-VCH
• Publication Date: 2016
• Extent: 1 online resource
• Subjects: 530.15; Mathematical physics
• Languages: English
• ISBNs: 9783527687152; 9783527687138; 9783527687145
• Related ISBNs: 9783527413331
• Notes: Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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