"Version: 20220701"--Title page verso.

Includes bibliographical references.

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.

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.

Students globally at the upper undergraduate level in physics and engineering required to take Mathematical Methods courses.

Also available in print.

Mode of access: World Wide Web.

System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.

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.

Title from PDF title page (viewed on August 5, 2022).