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" Guide to essential math : "
S.M. Blinder
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BL
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| Record Number
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622217
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dltt
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| Main Entry
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Blinder, S. M.,1932-
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| Title & Author
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Guide to essential math : : a review for physics, chemistry and engineering students /\ S.M. Blinder
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| Edition Statement
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1st ed
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| Publication Statement
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Amsterdam ;Boston :: Academic Press,, 2008
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| Series Statement
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Complementary science series
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| Page. NO
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xiii, 286 p. :: ill. ;; 23 cm
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| ISBN
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9780123742643 (hbk.)
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: 0123742641 (hbk.)
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| Notes
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Includes index
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| Contents
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To the reader -- 1. Mathematical thinking -- 1.1. NCAA March Madness problem -- 1.2. Gauss and the arithmetic series -- 1.3. Pythagorean theorem -- 1.4. Torus area and volume -- 1.5. Einstein's Velocity Addition Law -- 1.6. Birthday problem -- 1.7. Fibonacci numbers and the golden ratio -- 1.8. [pi] in the Gaussian Integral -- 1.9. Function equal to its derivative -- 1.10. Log of N factorial for Large N -- 1.11. Potential and kinetic energies -- 1.12. Riemann Zeta Function and prime numbers -- 1.13. How to solve it -- 1.14. Note on mathematical rigor -- 2. Numbers -- 2.1. Integers -- 2.2. Primes -- 2.3. Divisibility -- 2.4. Rational Numbers -- 2.5. Exponential notation -- 2.6. Powers of 10 -- 2.7. Binary number system -- 2.8. Infinity -- 3. Algebra -- 3.1. Symbolic variables -- 3.2. Legal and illegal algebraic manipulations -- 3.3. Factor-label method -- 3.4. Powers and roots -- 3.5. Logarithms -- 3.6. Quadratic formula -- 3.7. Imagining i -- 3.8. Factorials, permutations, and combinations -- 3.9 Binomial theorem -- 3.10. e Is for Euler -- 4. Trigonometry -- 4.1. What use is trigonometry? -- 4.2. Pythagorean theorem -- 4.3. [pi] in the Sky -- 4.4. Sine and cosine -- 4.5. Tangent and secant -- 4.6. Trigonometry in the complex plane -- 4.7. de Moivre's Theorem -- 4.8. Euler's theorem -- 4.9. Hyperbolic functions -- 5. Analytic geometry -- 5.1. Functions and graphs -- 5.2. Linear functions -- 5.3. Conic sections -- 5.4. Conic sections in polar coordinates -- 6. Calculus -- 6.1. Little road trip -- 6.2. Speedboat ride -- 6.3. Differential and integral calculus -- 6.4. Basic formulas of differential calculus -- 6.5. More on derivatives -- 6.6. Indefinite integrals -- 6.7. Techniques of integration -- 6.8. Curvature, maxima, and minima -- 6.9. The gamma function -- 6.10. Gaussian and error functions --
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7. Series and integrals -- 7.1. Some elementary series -- 7.2. Power series -- 7.3. Convergence of series -- 7.4. Taylor series -- 7.5. L'Hôpital's Rule -- 7.6. Fourier series -- 7.7. Dirac deltafunction -- 7.8. Fourier integrals -- 7.9. Generalized Fourier expansions -- 7.10. Asymptotic series -- 8. Differential equations -- 8.1. First-order differential equations -- 8.2. AC circuits -- 8.3. Second-order differential equations -- 8.4. Some examples from physics -- 8.5. Boundary conditions -- 8.6. Series solutions -- 8.7. Bessel functions -- 8.8. Second solution -- 9. Matrix algebra -- 9.1. Matrix multiplication -- 9.2. Further properties of matrices -- 9.3. Determinants -- 9.4. Matrix inverse -- 9.5. Wronskian determinant -- 9.6. Special matrices -- 9.7. Similarity transformations -- 9.8. Eigenvalue problems -- 9.9. Group theory -- 9.10. Minkowski spacetime -- 10. Multivariable calculus -- 10.1. Partial derivatives -- 10.2. Multiple integration -- 10.3. Polar coordinates -- 10.4. Cylindrical coordinates -- 10.5. Spherical polar coordinates -- 10.6. Differential expressions -- 10.7. Line integrals -- 10.8. Green's theorem -- 11. Vector analysis -- 11.1. Scalars and vectors -- 11.2. Scalar or Dot product -- 11.3. Vector or cross product -- 11.4. Triple products of vectors -- 11.5. Vector velocity and acceleration -- 11.6. Circular motion -- 11.7. angular momentum -- 11.8. Gradient of a scalar field -- 11.9. Divergence of a vector field -- 11.10. Curl of a vector field -- 11.11. Maxwell's equations -- 11.12. Covariant electrodynamics -- 11.13. Curvilinear coordinates -- 11.14. Vector identities -- 12. Partial differential equations and special functions -- 12.1. Partial differential equations -- 12.2. Separation of variables -- 12.3. Special functions -- 12.4. Leibniz's formula -- 12.5. Vibration of a circular membrane -- 12.6. Bessel functions -- 12.7. Laplace's equation in spherical coordinates -- 12.8. Legendre polynomials -- 12.9. Spherical harmonics -- 12.10. Spherical Bessel functions -- 12.11. Hermite polynomials -- 12.12. Laguerre polynomials -- 13. Complex variables -- 13.1. Analytic functions -- 13.2. Derivative of an analytic function -- 13.3. Contour integrals -- 13.4. Cauchy's theorem -- 13.5. Cauchy's integral formula -- 13.6. Taylor series -- 13.7. Laurent expansions -- 13.8. Calculus of residues -- 13.9. Multivalued functions -- 13.10. Integral representations for special functions
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| Abstract
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Presents a review of mathematics used in physics, chemistry, and engineering
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Mathematics
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Mathematical physics
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Chemistry-- Mathematics
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| Subject
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Engineering mathematics
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| LC Classification
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QA39.3.B55 2008
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