|
chapter |
topics |
|
ch7c.pdf |
PDE’s, seperation of variables, Lagrangian method |
|
ch7b.pdf |
Position, velocity and acc in different coordinates. Gradient, Curl and Div. |
|
ch7a.pdf |
Multivariable calculus. Jacobian. Gravitional field for shell, Pressure and energy of gas |
|
ch6b.pdf |
First order ODE’s. Second order Constant coefficients. under,over and critical damping |
|
ch6a.pdf |
Second order ODE’s. Variable coefficient. Power series methods. Hermite ODE. |
|
ch5c.pdf |
Function spaces. Hermitian operators. Complex Fourier series. Fourier transform. Deep well probem |
|
ch5b.pdf |
Linear vector spaces and QM. Probability when making measurements. Commutation. Schrodinger equation. Spin operators \(S_x,S_y,S_z\). Pauli matrices. Time evolution of spin state. Solving mass/spring problem using normal modes. |
|
ch5a.pdf |
Linear vector spaces. Linear independence. Gram-Schmidt. Linear operators. Finding eigenvalues and eigenvectors for matrices. Coordinates transformation between orthonormal basis. |
|
ch4.pdf |
Matrices and Determinants. 2D rotation matrix. Lorentz transformation. Pauli matrices. Levi-civita. Properties of determinants. Solution to linear equations. Cramer rule. Dimensional analysis. |
|
ch3.pdf |
Complex numbers. Taylor series expansion. Solving \(x^n=1\). Integrals. Completing the squares for \(\int _{-\infty }^{\infty } e^{(x+ia)^2}\,dx\). Gaussian integral, N slit intererence. Single slit diffraction. |
|
ch2.pdf |
Gaussian and exponential integrals. Evaluating Gaussian integral. Evaluating \(\int _{0}^{\infty } x^n e^{-x}\, dx = n!\). Zeta function. Gamma function. Sterling formula. |
|
ch1.pdf |
Taylor series. Convergence test. Taylor series of common functions. Using Taylor series to find equilibrium point for small oscillations. Pendulum. |
|
|
|
|
|
|