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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. 'McQuarrie's Mathematical Methods for Scientists and Engineers is a well-written, carefully conceived panorama of an extensive mathematical landscape. From asymptotic analysis to linear algebra to partial differential equations and complex variables, McQuarrie provides relevant background, physical and mathematical intuition and motivation, and just the right dose of mathematical rigor to get the ideas across effectively. The large collection of examples and exercises will prove indispensable for teaching and learning the material.' - Dennis DeTurck, University of Pennsylvania, USA 'McQuarrie has produced a masterpiece that anyone would want to have handy when confronted with the need to perform serious mathematical analyses. It's destined to become a classic reference text...beautifully illustrated with two-color graphical side bars that emphasize the principles presented in the text. It includes vignettes of the lives of various mathematicians that almost make them seem human...as appealing as any reference work you might imagine on this topic...The text is authoritative and comprehensive...what every undergraduate student should master to become mathematically adept.' - Richard N Zare, Stanford University, USA, Chemical and Engineering News

Mathematical Methods for Scientists and Engineers

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 Schroedinger 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