Mathematical methods in the physical sciences - Boas, Mary L. (Hoboken, NJ : Wiley, 2006)
Now in its third edition, Mathematical Concepts in the Physical Sciences provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.
1. Infinite Series, Power Series. The Geometric Series. Definitions and Notation. Applications of Series. Convergent and Divergent Series. Convergence Tests. Convergence Tests for Series of Positive Terms. Alternating Series. Conditionally Convergent Series. Useful Facts about Series. Power Series; Interval of Convergence. Theorems about Power Series. Expanding Functions in Power Series. Expansion Techniques. Accuracy of Series Approximations. Some Uses of Series. 2. Complex Numbers. Introduction. Real and Imaginary Parts of a Complex Number. The Complex Plane. Terminology and Notation. Complex Algebra. Complex Infinite Series. Complex Power Series; Disk of Convergence. Elementary Functions of Complex Numbers. Euler's Formula. Powers and Roots of Complex Numbers. The Exponential and Trigonometric Functions. Hyperbolic Functions. Logarithms. Complex Roots and Powers. Inverse Trigonometric and Hyperbolic Functions. Some Applications. 3. Linear Algebra. Introduction. Matrices; Row Reduction. Determinants; Cramer's Rule. Vectors. Lines and Planes. Matrix Operations. Linear Combinations, Functions, Operators. Linear Dependence and Independence. Special Matrices and Formulas. Linear Vector Spaces. Eigenvalues and Eigenvectors. Applications of Diagonalization. A Brief Introduction to Groups. General Vector Spaces. 4. Partial Differentiation. Introduction and Notation. Power Series in Two Variables. Total Differentials. Approximations using Differentials. Chain Rule. Implicit Differentiation. More Chain Rule. Maximum and Minimum Problems. Constraints; Lagrange Multipliers. Endpoint or Boundary Point Problems. Change of Variables. Differentiation of Integrals. 5. Multiple Integrals. Introduction. Double and Triple Integrals. Applications of Integration. Change of Variables in Integrals; Jacobians. Surface Integrals. 6. Vector Analysis. Intro
Includes index.
Keywords: Mathematics