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Description: From best-selling author Donald McQuarrie comes his newest text, Mathematical Methods for Scientists and Engineers. Intended for upper-level undergraduate and graduate courses in chemistry, physics, math and engineering, this book will also become a must-have for the personal library of all advanced students in the physical sciences. Comprised of more than 2000 problems and 700 worked examples that detail every single step, this text is exceptionally well adapted for self study as well as for course use. Famous for his clear writing, careful pedagogy, and wonderful problems and examples, McQuarrie has crafted yet another tour de force.
As the author of landmark chemistry books and textbooks, Donald McQuarrie’s name is synonymous with excellence in chemical education. From his classic text on Statistical Mechanics to his recent quantum-first tour de force on Physical Chemistry, McQuarrie’s best selling textbooks are highly acclaimed by chemistry community. McQuarrie received his PhD from the University of Oregon, and is Professor Emeritus from the Department of Chemistry at the University of California, Davis. He makes his home at The Sea Ranch in California with his wife Carole, where he continues to write.
Contents: CHAPTER 1 Functions of a Single Variable: Functions • Limits • Continuity • Differentiation • Differentials • Mean Value Theorems • Integration • Improper Integrals • Uniform Convergence of Integrals • References
CHAPTER 2 Infinite Series: Infinite Sequences • Convergence and Divergence of Infinite Series • Tests for Convergence • Alternating Series • Uniform • Convergence • Power Series • Taylor Series • Applications of Taylor Series • Asymptotic Expansions • References
CHAPTER 3 Functions Defined As Integrals: The Gamma Function • The Beta Function • The Error Function • The Exponential Integral • Elliptic Integrals The Dirac Delta Function • Bernoulli Numbers and Bernoulli Polynomials • References CHAPTER 4 Complex Numbers and Complex Functions: Complex Numbers and the Complex Plane • Functions of a Complex Variable • Euler’s Formula and the Polar Form of Complex Numbers • Trigonometric and Hyperbolic Functions • The Logarithms of Complex Numbers • Powers of Complex Numbers • References
CHAPTER 5 Vectors: Vectors in Two Dimensions • Vector Functions in Two Dimensions • Vectors in Three Dimensions • Vector Functions in Three Dimensions • Lines and Planes in Space • References
CHAPTER 6 Functions of Several Variables: Functions • Limits and Continuity • Partial Derivatives • Chain Rules for Partial Differentiation • Differentials and the Total Differential • The Directional Derivative and the Gradient • Taylor’s Formula in Several Variables • Maxima and Minima • The Method of Lagrange Multipliers • Multiple Integrals • References
CHAPTER 7 Vector Calculus: Vector Fields • Line Integrals • Surface Integrals • The Divergence • Theorem • Stokes’s Theorem • References
CHAPTER 8 Curvilinear Coordinates: Plane Polar Coordinates • Vectors in Plane Polar Coordinates • Cylindrical Coordinates • Spherical Coordinates• Curvilinear Coordinates • Some Other Coordinate Systems • References
CHAPTER 9 Linear Algebra and Vector Spaces: Determinants • Gaussian Elimination • Matrices • Rank of a Matrix • Vector Spaces • Inner Product Spaces • Complex Inner Product Spaces • References
CHAPTER 10 Matrices and Eigenvalue Problems: • Orthogonal and Unitary Transformations • Eigenvalues and Eigenvectors • Some Applied Eigenvalue Problems • Change of Basis • Diagonalization of Matrices • Quadratic Forms • References
CHAPTER 11 Ordinary Differential Equations: Differential Equations of First Order and First Degree • Linear First-Order Differential Equations • Homogeneous Linear Differential Equations with Constant Coefficients • No homogeneous Linear Differential Equations with Constant Coefficients • Some Other Types of Higher-Order Differential Equations • Systems of Linear Differential Equations • Two Invaluable Resources for Solutions to Differential Equations • References
CHAPTER 12 Series Solutions of Differential Equations: The Power Series Method • Ordinary Points and Singular • Points of Differential Equations • Series Solutions Near an Ordinary Point: Legendre’s Equation • Solutions Near Regular Singular Points • Bessel’s Equation • Bessel Functions • ReferencesCHAPTER 13 Qualitative Methods for Nonlinear Differential Equations: The Phase Plane • Critical Points in the Phase Plane • Stability of Critical Points • Nonlinear Oscillators • Population Dynamics • References
CHAPTER 14 Orthogonal Polynomials and Sturm-Liouville Problems: Legendre Polynomials • Orthogonal Polynomials • Sturm-Liouville Theory • Eigenfunction Expansions • Green’s Functions • References
CHAPTER 15 Fourier Series: Fourier series as Eigenfunction Expansions • Sine and Cosine Series • Convergence of Fourier series • Fourier series and Ordinary Differential Equations • References
CHAPTER 16 Partial Differential Equations: Some Examples of Partial Differential Equations • Laplace’s Equation • The One-Dimensional Wave Equation • The Two-Dimensional Wave Equation • The Heat Equation The Schrodinger Equation • The Classification of Partial Differential Equations • References
CHAPTER 17 Integral Transforms: The Laplace Transform • The Inversion of Laplace Transforms • Laplace Transforms and Ordinary Differential Equations • Laplace Transforms and Partial Differential Equations • Fourier Transforms • Fourier Transforms and Partial Differential Equations • The Inversion Formula for Laplace Transforms • References
CHAPTER 18 Functions of a Complex Variable: Theory: Functions, Limits, and Continuity • Differentiation: The Cauchy-Riemann Equations • Complex Integration: Cauchy’s Theorem • Cauchy’s Integral Formula • Taylor Series and Laurent Series • Residues and the Residue Theorem • References
CHAPTER 19 Functions of a Complex Variable: Applications: The Inversion Formula for Laplace Transforms • Evaluation of Real, Definite Integrals • Summation of Series • Location of Zeros • Conformal Mapping • Conformal Mapping and Boundary Value Problems • Conformal Mapping and Fluid Flow • References
CHAPTER 20 Calculus of Variations: The Euler Equation Two Laws of Physics in Variational Form • Variational Problems with Constraints • Variational Formulation of Eigenvalue Problems • Multidimensional Variational Problems • References
CHAPTER 21 Probability Theory and Stochastic Processes: Discrete Random Variables • Continuous Random Variables • Characteristic Functions • Stochastic Processes—General • Stochastic Processes—Examples • References
CHAPTER 22 Mathematical Statistics: Estimation of Parameters • Three Key Distributions Used in Statistical Tests • Confidence Intervals • Goodness of Fit • Regression and Correlation • Answers to Selected Problems • Illustration Credits • Index ISBN - 9788130909974
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Pages : 1176
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