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Guide to essential math : a review for physics, chemistry and engineering students

Author: S M Blinder
Publisher: Amsterdam ; Boston : Academic Press, 2008.
Series: Complementary science series.
Edition/Format:   Print book : English : 1st edView all editions and formats
Summary:
Presents a review of mathematics used in physics, chemistry, and engineering.
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Document Type: Book
All Authors / Contributors: S M Blinder
ISBN: 9780123742643 0123742641
OCLC Number: 176924777
Notes: Includes index.
Description: xiii, 286 pages : illustrations ; 23 cm.
Contents: 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. 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.
Series Title: Complementary science series.
Responsibility: S.M. Blinder.

Abstract:

Reminds students in junior, senior and graduate level courses in physics, chemistry and engineering of the math they may have forgotten (or learned imperfectly) which is needed to succeed in science  Read more...

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