Mathematical Techniques provides a complete course in mathematics, covering all the essential topics with which a physical sciences or engineering student should be familiar. It introduces and builds on concepts in a progressive, carefully-layered way, and features over 2000 end of chapter problems, plus additional self-check questions.
Mathematical Techniques provides a complete course in mathematics, covering all the essential topics with which a physical sciences or engineering student should be familiar. It introduces and builds on concepts in a progressive, carefully-layered way, and features over 2000 end of chapter problems, plus additional self-check questions.
Dominic Jordan is formerly of the Mathematics Department, Keele University, UK. Peter Smith is Emeritus Professor in the School of Computing and Mathematics, Keele University, UK.
Inhaltsangabe
PART 1. ELEMENTARY METHODS, DIFFERENTIATION, COMPLEX NUMBERS 1: Standard functions and techniques 2: Differentiation 3: Further techniques for differentiation 4: Applications of differentiation 5: Taylor series and approximations 6: Complex numbers PART 2. MATRIX AND VECTOR ALGEBRA 7: Matrix algebra 8: Determinants 9: Elementary operations with vectors 10: The scalar product 11: Vector product 12: Linear algebraic equations 13: Eigenvalues and eigenvectors PART 3. INTEGRATION AND DIFFERENTIAL EQUATIONS 14: Antidifferentiation and area 15: The definite and indefinite integral 16: Applications involving the integral as a sum 17: Systematic techniques for integration 18: Unforced linear differential equations with constant coefficients 19: Forced linear differential equations 20: Harmonic functions and the harmonic oscillator 21: Steady forced oscillations: phasors, impedance, transfer functions 22: Graphical, numerical, and other aspects of first-order equations 23: Nonlinear differential equations and the phase plane PART 4. TRANSFORMS AND FOURIER SERIES 24: The Laplace transform 25: Laplace and z transforms: applications 26: Fourier series 27: Fourier transforms PART 5. MULTIVARIABLE CALCULUS 28: Differentiation of functions of two variables 29: Functions of two variables: geometry and formulae 30: Chain rules, restricted maxima, coordinate systems 31: Functions of any number of variables 32: Double integration 33: Line integrals 34: Vector fields: divergence and curl PART 6. DISCRETE MATHEMATICS 35: Sets 36: Boolean algebra: logic gates and switching functions 37: Graph theory and its applications 38: Difference equations PART 7. PROBABILITY AND STATISTICS 39: Probability 40: Random variables and probability distributions 41: Descriptive statistics PART 8. PROJECTS 42: Applications projects using symbolic computing Self-tests: selected answers Answers to selected problems Appendices Further reading Index
PART 1. ELEMENTARY METHODS, DIFFERENTIATION, COMPLEX NUMBERS 1: Standard functions and techniques 2: Differentiation 3: Further techniques for differentiation 4: Applications of differentiation 5: Taylor series and approximations 6: Complex numbers PART 2. MATRIX AND VECTOR ALGEBRA 7: Matrix algebra 8: Determinants 9: Elementary operations with vectors 10: The scalar product 11: Vector product 12: Linear algebraic equations 13: Eigenvalues and eigenvectors PART 3. INTEGRATION AND DIFFERENTIAL EQUATIONS 14: Antidifferentiation and area 15: The definite and indefinite integral 16: Applications involving the integral as a sum 17: Systematic techniques for integration 18: Unforced linear differential equations with constant coefficients 19: Forced linear differential equations 20: Harmonic functions and the harmonic oscillator 21: Steady forced oscillations: phasors, impedance, transfer functions 22: Graphical, numerical, and other aspects of first-order equations 23: Nonlinear differential equations and the phase plane PART 4. TRANSFORMS AND FOURIER SERIES 24: The Laplace transform 25: Laplace and z transforms: applications 26: Fourier series 27: Fourier transforms PART 5. MULTIVARIABLE CALCULUS 28: Differentiation of functions of two variables 29: Functions of two variables: geometry and formulae 30: Chain rules, restricted maxima, coordinate systems 31: Functions of any number of variables 32: Double integration 33: Line integrals 34: Vector fields: divergence and curl PART 6. DISCRETE MATHEMATICS 35: Sets 36: Boolean algebra: logic gates and switching functions 37: Graph theory and its applications 38: Difference equations PART 7. PROBABILITY AND STATISTICS 39: Probability 40: Random variables and probability distributions 41: Descriptive statistics PART 8. PROJECTS 42: Applications projects using symbolic computing Self-tests: selected answers Answers to selected problems Appendices Further reading Index
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