Mathematical Methods in Physics 1
- Offered bySwayam
Mathematical Methods in Physics 1 at Swayam Overview
Duration | 8 weeks |
Mode of learning | Online |
Official Website | Go to Website  |
Credential | Certificate |
Mathematical Methods in Physics 1 at Swayam Highlights
- Earn a certificate from Swayam
- Learn from industry experts
Mathematical Methods in Physics 1 at Swayam Course details
- For individuals who want to enhance their knowledge & skills in the field
- Gain a solid understanding of foundational mathematical concepts such as calculus, linear algebra, differential equations, and complex analysis, and their relevance to physics
- Master techniques of calculus including differentiation, integration, multivariable calculus, and vector calculus, and understand their applications in physics problems such as motion, forces, and energy
- Acquire proficiency in linear algebra concepts such as vector spaces, matrices, determinants, eigenvalues, and eigenvectors, and their application in solving problems related to quantum mechanics, electromagnetism, and classical mechanics
- Learn to solve ordinary and partial differential equations relevant to physics problems, including those arising in classical mechanics, electromagnetism, and quantum mechanics
- Understand special functions such as Bessel functions, Legendre polynomials, and Hermite polynomials, and develop skills in using series solutions to solve differential equations
- This would be the first of a two-part series on Mathematical Methods in Physics
- The aim here is to provide a solid mathematical foundation for the budding Physicist eager to climb the ladder of self-learning
- This course is designed to cater to an undergraduate student who excitedly embarks on a study of Physics, but is obstructed by the mathematics which appears so forbidding
- The approach we will follow is one of showing many examples, and weaving the theory around examples
- When possible, we will show how Mathematica can be used to offer extra insight
- The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres
- The exam is optional for a fee of Rs 1000/- (Rupees one thousand only)
Mathematical Methods in Physics 1 at Swayam Curriculum
Week 1:Linear Algebra 1 : vectors, linear vector spaces, inner product, C-S inequality, linear independence, row-reduction
Week 2:Linear Algebra 2 : Matrices, determinants, span, basis, orthonormal basis, subspaces, linear operators
Week 3: Linear Algebra 3: Direct sum, eigenvalues and eigenvectors, unitary, Hermitian, normal operators, transformations, defective matrices, diagonalization
Week 4: Fourier Series and Transforms: periodic functions, series expansion, Fourier coefficients, Completeness relation, Fourier transforms
Week 5: Ordinary Differential Equations 1: Introduction, Separable variables, orthogonal trajectories, linear first-order ODEs, Wronksian, exact ODEs, auxiliary equation
Week 6: Ordinary Differential Equations 2: Inhomogeneous second order ODEs, method of undetermined coefficients, vibrations in mechanical systems, forced vibrations, resonance, linear superposition
Week 7: Ordinary Differential Equations 3: Laplace transforms, Solving ODEs using Laplace transforms, Dirac Delta function
Week 8: Ordinary Differential Equations 4: Green's function method, power series method, Frobenius method
Mathematical Methods in Physics 1 at Swayam Entry Requirements
- Education: Graduate
- Not mentioned
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