1. |
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Infinite series_0304 |
Convergence tests |
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2. |
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Series expansion of functions_0306 |
Uniform convergence, Taylor expansion |
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3. |
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Partial differentiation 1_0311 |
Basics of differentiation |
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Partial differentiation 2_0313 |
Finding maximum and minimum |
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4. |
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Lagrange multiplier method_0318 |
Finding extrema with Lagrange multiplier |
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5. |
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Minimum and maximum near the boundary_0320 |
Endpoint problems in finding extrema |
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6. |
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Double and triple integrals_0325 |
Techniques in computing multiple integrals |
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7. |
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Jacobian_0327 |
Integrals changing coordinate systems |
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8. |
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Vector_0401 |
Properties of vectors |
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9. |
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Vector operation_0408 |
Triple products |
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10. |
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Differential operators 1_0410 |
Gradient, divergence |
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Differential operators 2_0415 |
Curl, composite operators |
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11. |
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Integral theorems_0418 |
Green’s theorem, divergence theorem |
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Integral theorems 2_0422 |
Divergence and Stokes’ theorems |
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12. |
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Curvilinear coordinates_0424 |
Curvilinear coordinates |
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13. |
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Linear algebra 1_0429 |
Linear equations and determinants |
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Linear algebra 2_0501 |
Linear transformations |
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Linear algebra 3_0508 |
Linear algebra 3 |
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14. |
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Eigenvalue problem_0513 |
Eigenvalue problem and diagonalization of matrices |
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15. |
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Diagonalization of matrices_0520 |
Diagonalization of hermitian matrices |
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Application of diagonalization_0522 |
Small oscillation using eigenvalue problem |
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Linear space and Fourier series_0527 |
Linear space and Fourier series |
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Fourier sine and cosine series_0529 |
Fourier sine and cosine series |
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Fourier transform_0603 |
Fourier transform and its properties |
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Delta functions_0605 |
Properties of delta functions |
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