Lab Exercises:
Programming: Review of basic python programming techniques –conditionals, branching and looping, arrays, functions, printing and saving. (Ref. 1) [2 weeks]
Differential Equations: Program to solve elementary differential equations using first order forward Euler method: Projectile motion or simple harmonic oscillations. [2 weeks]
Linear Algebra and Array Operations:
One and higher dimensional arrays, indexing; column and row vectors, transposition; vector and matrix operations using for loops and built-in vector operations (a selection from): addition, scalar multiplication; inner product of vectors, orthogonality, angle between vectors, norm, unit vectors, multiplication of matrices, unit matrix. [2 weeks]
Further array operations: submatrices – slicing, reshaping, rearranging, and resizing, conversion of 1D to 2D arrays and vice versa; selected examples from symmetric matrices, transposition and index switching operations. [1 week]
Determinants, determinants of matrices of given set column or row vectors using built-in functions, volume of a parallelopiped, other properties. [1 week]
Solution to simultaneous linear equation using row reductions and built-in functions. [1 week]
Special matrices, Orthogonal matrices in 2D, rotations in 2D and their properties; rotation of a vector in 2D; general transformation of a vector. Instructor demonstrations of transformation of a square: rotations, general deformation, demonstrations of pure compression and pure elongation in certain directions – the idea of eigenvectors. [1 week]
Finding eigenvalues and eigenvectors of a matrix using built-in functions, properties of eigenvectors; non-degenerate and degenerate cases for 3×3 matrices. [1 week]
