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. Comprising 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.

Table of Contents:
Chapter 1: Functions of a Single Variable 1-1 Functions 1-2 Limits 1-3 Continuity 1-4 Differentiation 1-5 Differentials 1-6 Mean Value Theorems 1-7 Integration 1-8 Improper Integrals 1-9 Uniform Convergence of Integrals Chapter 2: Infinite Series 2-1 Infinite Sequences 2-2 Convergence and Divergence of Infinite Series 2-3 Tests for Convergence 2-4 Alternating Series 2-5 Uniform Convergence 2-6 Power Series 2-7 Taylor Series 2-8 Applications of Taylor Series 2-9 Asymptotic Expansions Chapter 3: Functions Defined As Integrals 3-1 The Gamma Function 3-2 The Beta Function 3-3 The Error Function 3-4 The Exponential Integral 3-5 Elliptic Integrals 3-6 The Dirac Delta Function 3-7 Bernoulli Numbers and Bernoulli Polynomials Chapter 4: Complex Numbers and Complex Functions 4-1 Complex Numbers and the Complex Plane 4-2 Functions of a Complex Variable 4-3 Euler’s Formula and the Polar Form of Complex Numbers 4-4 Trigonometric and Hyperbolic Functions 4-5 The Logarithms of Complex Numbers 4-6 Powers of Complex Numbers Chapter 5: Vectors 5-1 Vectors in Two Dimensions 5-2 Vector Functions in Two Dimensions 5-3 Vectors in Three Dimensions 5-4 Vector Functions in Three Dimensions 5-5 Lines and Planes in Space Chapter 6: Functions of Several Variables 6-1 Functions 6-2 Limits and Continuity 6-3 Partial Derivatives 6-4 Chain Rules for Partial Differentiation 6-5 Differentials and the Total Differential 6-6 The Directional Derivative and the Gradient 6-7 Taylor’s Formula in Several Variables 6-8 Maxima and Minima 6-9 The Method of Lagrange Multipliers 6-10 Multiple Integrals Chapter 7: Vector Calculus 7-1 Vector Fields 7-2 Line Integrals 7-3 Surface Integrals 7-4 The Divergence Theorem 7-5 Stokes’s Theorem Chapter 8: Curvilinear Coordinates 8-1 Plane Polar Coordinates 8-2 Vectors in Plane Polar Coordinates 8-3 Cylindrical Coordinates 8-4 Spherical Coordinates 8-5 Curvilinear Coordinates 8-6 Some Other Coordinate Systems Chapter 9: Linear Algebra and Vector Spaces 9-1 Determinants 9-2 Gaussian Elimination 9-3 Matrices 9-4 Rank of a Matrix 9-5 Vector Spaces 9-6 Inner Product Spaces 9-7 Complex Inner Product Spaces Chapter 10: Matrices and Eigenvalue Problems 10-1 Orthogonal and Unitary Transformations 10-2 Eigenvalues and Eigenvectors 10-3 Some Applied Eigenvalue Problems 10-4 Change of Basis 10-5 Diagonalization of Matrices 10-6 Quadratic Forms Chapter 11: Ordinary Differential Equations 11-1 Differential Equations of First Order and First Degree 11-2 Linear First-Order Differential Equations 11-3 Homogeneous Linear Differential Equations with Constant Coefficients 11-4 Nonhomogeneous Linear Differential Equations with Constant Coefficients 11-5 Some Other Types of Higher-Order Differential Equations 11-6 Systems of First-Order Differential Equations 11-7 Two Invaluable Resources for Solutions to Differential Equations Chapter 12: Series Solutions of Differential Equations 12-1 The Power Series Method 12-2 Ordinary Points and Singular Points of Differential Equations 12-3 Series Solutions Near an Ordinary Point: Legendre’s Equation 12-4 Solutions Near Regular Singular Points 12-5 Bessel’s Equation 12-6 Bessel Functions Chapter 13: Qualitative Methods for Nonlinear Differential Equations 13-1 The Phase Plane 13-2 Critical Points in the Phase Plane 13-3 Stability of Critical Points 13-4 Nonlinear Oscillators 13-5 Population Dynamics Chapter 14: Orthogonal Polynomials and Sturm–Liouville Problems 14-1 Legendre Polynomials 14-2 Orthogonal Polynomials 14-3 Sturm–Liouville Theory 14-4 Eigenfunction Expansions 14-5 Green’s Functions Chapter 15: Fourier Series 15-1 Fourier Series as Eigenfunction Expansions 15-2 Sine and Cosine Series 15-3 Convergence of Fourier Series 15-4 Fourier Series and Ordinary Differential Equations Chapter 16: Partial Differential Equations 16-1 Some Examples of Partial Differential Equations 16-2 Laplace’s Equation 16-3 The One-Dimensional Wave Equation 16-4 The Two-Dimensional Wave Equation 16-5 The Heat Equation 16-6 The Schrödinger Equation a. Particle in a Box b. A Rigid Rotor c. The Electron in a Hydrogen Atom 16-7 The Classification of Partial Differential Equations Chapter 17: Integral Transforms 17-1 The Laplace Transform 17-2 The Inversion of Laplace Transforms 17-3 Laplace Transforms and Ordinary Differential Equations 17-4 Laplace Transforms and Partial Differential Equations 17-5 Fourier Transforms 17-6 Fourier Transforms and Partial Differential Equations 17-7 The Inversion Formula for Laplace Transforms Chapter 18: Functions of a Complex Variable: Theory 18-1 Functions, Limits, and Continuity 18-2 Differentiation. The Cauchy–Riemann Equations 18-3 Complex Integration. Cauchy’s Theorem 18-4 Cauchy’s Integral Formula 18-5 Taylor Series and Laurent Series 18-6 Residues and the Residue Theorem Chapter 19: Functions of a Complex Variable: Applications 19-1 The Inversion Formula for Laplace Transforms 19-2 Evaluation of Real, Definite Integrals 19-3 Summation of Series 19-4 Location of Zeros 19-5 Conformal Mapping 19-6 Conformal Mapping and Boundary Value Problems 19-7 Conformal Mapping and Fluid Flow Chapter 20: Calculus of Variations 20-1 The Euler’s Equation 20-2 Two Laws of Physics in Variational Form 20-3 Variational Problems with Constraints 20-4 Variational Formulation of Eigenvalue Problems 20-5 Multidimensional Variational Problems Chapter 21: Probability Theory and Stochastic Processes 21-1 Discrete Random Variables 21-2 Continuous Random Variables 21-3 Characteristic Functions 21-4 Stochastic Processes—General 21-5 Stochastic Processes—Examples a. Poisson Process b. The Shot Effect Chapter 22: Mathematical Statistics 22-1 Estimation of Parameters 22-2 Three Key Distributions Used in Statistical Tests a. The Normal Distribution b. The Chi–Square Distribution c. Student t-Distribution 22-3 Confidence Intervals a. Confidence Intervals for the Mean of a Normal Distribution Whose Variance is Known b. Confidence Intervals for the Mean of a Normal Distribution with Unknown Variance c. Confidence Intervals for the Variance of a Normal Distribution 22-4 Goodness of Fit 22-5 Regression and Correlation  Index