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Studies in theoretical physics. Volume 1, Fundamental mathematical methods
Author
Title
Studies in theoretical physics. Volume 1, Fundamental mathematical methods / Daniel Erenso, Victor Montemayor.
ISBN
9780750331357
9780750331340
9780750331333
9780750331364
Publication
Bristol [England] (Temple Circus, Temple Way, Bristol BS1 6HG, UK) : IOP Publishing, [2022]
Physical Description
1 online resource : illustrations (some color).
Local Notes
Access is available to the Yale community.
Notes
"Version: 20220701"--Title page verso.
Access and use
Access restricted by licensing agreement.
Biographical / Historical Note
Dr. Daniel Erenso has been working as a professor of physics at Middle Tennessee State University (MTSU) since 2003. Dr. Victor Montemayor teaches Physics and Advanced Mathematics at Germantown Academy (GA) in Fort Washington, PA. He retired from Middle Tennessee State University (MTSU) in 2015 after serving for 25 years as Professor of Physics.
Summary
Studies in Theoretical Physics, Volume 1: Fundamental mathematical methods is the first of the six-volume series in theoretical physics. It provides the mathematical methods that any physical sciences and engineering undergraduate might need in upper-division courses in classical mechanics, quantum mechanics, and electricity and magnetism.
Variant and related titles
IOP ebooks.
Other formats
Also available in print.
Print version:
Format
Books / Online
Language
English
Added to Catalog
August 25, 2022
Series
[IOP release $release]
IOP ebooks. [2022 collection]
Bibliography
Includes bibliographical references.
Audience
Students globally at the upper undergraduate level in physics and engineering required to take Mathematical Methods courses.
Contents
1. Series and convergence
1.1. Sequence and series
1.2. Testing series for convergence
1.3. Series representations of real functions
1.4. Sequence, series and Mathematica
1.5. Homework assignment
2. Complex numbers, functions, and series
2.1. Complex numbers
2.2. Complex infinite series
2.3. Powers and roots of complex numbers
2.4. Algebraic versus transcendental functions
2.5. Complex numbers, functions and Mathematica
2.6. Homework assignment
3. Vectors
3.1. Vector fundamentals
3.2. Vector addition
3.3. Vector multiplication
3.4. Vectors and equations of a line and a plane
3.5. Vectors and Mathematica
3.6. Homework assignment
4. Matrices and determinants
4.1. Important terminologies
4.2. Matrix arithmetic and manipulation
4.3. Matrix representation of a set of linear equations
4.4. Solving a set of linear equations using matrices
4.5. Determinant of a square matrix
4.6. Cramer's rule
4.7. The adjoint and inverse of a matrix
4.8. Orthogonal matrices and the rotation matrix
4.9. Linear dependence and independence
4.10. Gram-Schmidt orthogonalization
4.11. Matrices and Mathematica
4.12. Homework assignment
5. Introduction to differential calculus I
5.1. Partial differentiation
5.2. Total differential
5.3. The multivariable form of the chain rule
5.4. Extremum (max/min) problems
5.5. The method of Lagrangian multipliers
5.6. Change of variables
5.7. Partial differentiation and Mathematica
5.8. Homework assignments
6. Introduction to differential calculus II
6.1. First-order ordinary DE
6.2. The first-order ODE and exact total differential
6.3. First-order ODE and non-exact total differential
6.4. Higher-order ODE
6.5. The particular solution and the method of superposition
6.6. The method of successive integration
6.7. Introduction to partial differential equations
6.8. Linear differential equations and Mathematica
6.9. Homework assignment
7. Integral calculus-scalar functions
7.1. Integration in Cartesian coordinates
7.2. Physical applications
7.3. 1-D and 2-D curvilinear coordinates
7.4. 3-D curvilinear coordinates : cylindrical
7.5. 3-D curvilinear coordinate : spherical
7.6. Scalar integrals and Mathematica
7.7. Homework assignment
8. Vector calculus
8.1. Review of vector products
8.2. Vectors product physical applications
8.3. Vectors derivatives
8.4. The gradient operator and directional derivative
8.5. The divergence, the curl, and the Laplacian
8.6. Line vector integrals
8.7. Conservative vectors and exact differentials
8.8. Double integral and Green's theorem
8.9. The Stokes' theorem
8.10. The divergence theorem
8.11. Vector calculus and Mathematica
8.12. Homework assignment
9. Introduction to the calculus of variations
9.1. Stationary points and geodesic
9.2. The general problem of the calculus of variations
9.3. The Brachistochrone problem
9.4. The Euler-Lagrange equation in classical mechanics
9.5. The calculus of variations and Mathematica
9.6. Homework assignment
10. Introduction to the eigenvalue problem
10.1. Eigenvalue problem in physics
10.2. Matrix review
10.3. Orthogonal transformations and Dirac's notation
10.4. Eigenvalues and eigenvectors
10.5. Eigenvalue equation and Hermitian matrices
10.6. The similarity transformation
10.7. Eigenvalue equation and Mathematica
10.8. Homework assignment
11. Special functions
11.1. The factorial, the gamma function, and Stirling's formula
11.2. The beta function
11.3. The error function
11.4. Elliptic integrals
11.5. The Dirac delta function
11.6. Mathematica and special functions
11.7. Homework assignments
12. Power series and differential equations
12.1. Power series substitution
12.2. Orthonormal set of vectors and functions
12.3. Complete set of functions
12.4. The Legendre differential equation
12.5. The Legendre polynomials
12.6. The generating function for the Legendre polynomials
12.7. Legendre series
12.8. The associated Legendre differential equation
12.9. Spherical harmonics and the addition theorem
12.10. The method of Frobenius and the Bessel equation
12.11. The orthogonality of the Bessel functions
12.12. Fuch's theorem
12.13. Mathematica and serious substitution method
12.14. Homework assignments
13. Partial differential equation
13.1. PDE in physics
13.2. Laplace's equation in Cartesian coordinates
13.3. Laplace's equation in spherical coordinates
13.4. Laplace's equation in cylindrical coordinates
13.5. Poisson's equation
13.6. Homework assignment
14. Functions of complex variables
14.1. Review of complex numbers
14.2. Analytic functions
14.3. Essential terminologies
14.4. Contour integration and Cauchy's theorem
14.5. Cauchy's integral formula
14.6. Laurent's theorem
14.7. The residue theorem
14.8. Methods of finding residues
14.9. Applications of the residue theorem
14.10. The modified residue theorem
14.11. Mathematica and complex functions
14.12. Homework assignment
15. Laplace transform
15.1. Integral transform
15.2. The Laplace transform
15.3. Inverse Laplace transform
15.4. Applications of Laplace transforms
15.5. Mathematica and Laplace transform
15.6. Homework assignment
16. Fourier series and transform
16.1. Average and root-mean-square values
16.2. The Fourier series
16.3. Dirichlet conditions
16.4. Fourier series with spatial and temporal arguments
16.5. The Fourier transform and inverse transform
16.6. The Dirac delta function and the Fourier inverse transform
16.7. Applications of the Fourier transform
16.8. Fourier transform and convolution
16.9. Mathematica, Fourier series, transform, and inverse transform.
Subjects
Also listed under
Institute of Physics (Great Britain), publisher.
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