318 Willamette Hall,
TuTh, 8:30-9:50
Instructor: James N. Imamura
Office: 444 Willamette Hall (or 441 Willamette Hall)
E-mail: imamura@uoregon.edu
Phone: 541-346-5212
Office Hours: TBA, 444 (or 441) Willamette Hall
Course: Physics 410: Mathematical Methods
Course CRN:
Text: Mathematical Methods in the Physical Science, 3rd Ed., Mary L. Boas
Class: TuTh, 8:30-9:50
Room: 318 Willamette Hall
Material:
Grading:
Tests:
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Chapters 2 and 14, Complex Numbers and Functions of a Complex Variable; Introduction to imaginary numbers and Complex numbers. Properties of complex numbers, algebraic equations, series. |
Set 1 |
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Chapters 14, Complex Functions: Euler's formula, de Moivre's formula, functions of a complex variable, amd applications, limits, analytic functions, derivatives of complex functions, conformal mapping, contour integration, Cauchy-Riemann equations. |
Set 2 |
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Chapters 14, Complex Functions: mapping, Conformal maps, contour integration, Cauchy-Riemann equations, Cauchy's Theorem, Cauchy's Integral Theorem, Laurent Series, simple poles, regular points, residue, evaluation of integrals using contour integration, residue theorem, Principal Value, Bromwich Intgeral (inverse Laplace transforms). |
Set 3 |
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Chapter 14: Residue Theorem, contour integration, and Inverse Laplace Transforms (Bromwich Integrals). Chapters 3: Linear Algebra, linear vector spaces, vectors, vector properties, vector operations and their properties. |
Set 4 |
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Chapters 3: Linear Algebra, linear vector spaces, dot product, norm, inner product, scalar product, matrices, properties of matrices, matrix operations and their properties, special matrices, transpose, conjugate, conjugate transpose, Hermitian transpose, adjoint, inverse, meaning of A dagger where A is a matrix, Hermitian conjugate, determinants, cofactors, solution of systems of linear algebraic equations, Cramer's rule. matrices, properties of matrices, matrix operations and their properties, special matrices, transpose, cojugate, conjugate transpose, Hermitian transpose, adjoint, inverse, meaning of A dagger where A is a matrix, Hermitian conjugate, determinants, cofactors, solution of systems of linear algebraic equations, Cramer's rule. |
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Chapters 3: Linear Algebra, matrices, matrix operations and properties, some special matrices, transpose, conjugate, conjugate transpose, Hermitian transpose, adjoint, inverse, meaning of A dagger where A is a matrix, Hermitian conjugate, orthogonal transformations and matrices, symmetric and skew-symmetric matrices, determinants, cofactors, solution of systems of linear algebraic equations, Cramer's rule, elimination of variables, row reduction, similarity transformations. |
Set 5 |
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Chapter 3: Linear Algebra. Matrix Operations, linear combinations, linear functions, linear opperators, linear independence and linear dependence of vectors and functions, Wronskian, characteristic value problems (eigenvalues and eigenvectors). |
Set 6 |
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Chapter 3: Linear Algebra. Characteristic value problems (eigenvalues and eigenvectors), diagonalization of matrices (meaning of diagonalization), similarity transformations, Hamilton's Principle, Action, Lagrangian, Calculus of Variations (Chapter 9), Euler-Lagrange equation, Properties of unitary matrices, Hermitian matrices, eigenvalues of Hermitian matrices, diagonalizing Hermitian matrices. |
Set 7 |
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Matrices and applications ot matrix mechanics: Hermitian and unitary matrices and Hermitan and unitary operators, |
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Hermitian and unitary matrices and Hermitan and unitary operators, Hamiltonian and momentum operators, Dirac's bra and ket notation, state vectors, representations, the inner product, the outer product, and tensor product, Lagrange ad Hamilton dynamics and their relationship to Heisenberg's matrix mechanics, relationship of the Schrodinger and Heisenberg approaches. |
Set 8 |
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