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Mathematical Methods II, PHAS0009
- Course Outline and Lecture Notes (Table of Contents)
Chapter1:
Differential Vector Operators |
- Scalar and Vector Fields
- Partial Derivatives of Fields
- Directional Derivative and Gradient
- The Total Differential of Fields
- Divergence and Curl of Vector Fields
- Product Rules
- 2nd Order Variations of Fields, Laplace Operator
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Chapter2:
Multidimensional Integration
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- Line Integrals
- Area Integrals
- Polar Coordinates
- Volume Integrals
- Cylindrical and Spherical Coordinates
- Surface Integrals
- Gauss's Divergence Theorem
- Stokes's Theorem
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Chapter3:
Ordinary Differential
Equations (ODEs)
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- Examples of ODEs in Physics
- Fixing the Arbitrary Constants
- Separable First-Order ODEs
- Linear First-Order ODEs
- Perfect Differential Method
- Second-Order Linear ODEs with Constant Coefficients
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Chapter4:
Linear Alegbra
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- Formal Definition of Complex Vector Spaces
- Linear Dependence and Independence of Vectors
- Matrices and linear transformations
- Matrix addition and multiplication
- Determinants
- Trace of a matrix
- Properties of matrices (symmetric, hermitian, unitary)
- Inverse of a matrix
- Solving coupled linear equations
- Eigenvalues and Eigenvectors
- Matrix Diagonalisation
- Quadratic Forms
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- Books recommended as core/background reading
- Mathematical Methods in the Physical Sciences, Mary L. Boas, John Wiley & Sons
- Mathematical Methods for Physics and Engineering: A Comprehensive Guide,
K.F. Riley, M.P. Hobson, S.J. Bence, Cambridge University Press
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