For the electronics part, after this module the student should be able to:
Mathematics C1 Cayley : Educational Targets
- Know how to model a diode and analyze circuits using the large signal behavior of diodes, rectifiers, clamping circuits and voltage multipliers.
- Know how to bias a BJT and a MOSFET and understand the limitations of the different bias circuits with respect to variations in temperature and component properties.
- Know the small signal equivalent circuit of a diode, BJT and MOSFET.
- Be able to transform a transistor circuit to its small signal equivalent form, analyze its behavior and make a bode plot of small signal properties like gain and in- and output impedances.
- Know the basic one transistor stages and their gain and input- and output impedances, and use this knowledge to choose and combine appropriate stages.
- Know and be able to analyze the effect of feedback on circuit properties like gain, bandwidth, distortion, input impedance and output impedance.
- Be able to analyze the stability of feedback circuits by Nyquist plots and bode plots of the loop gain.
- Understand the workings of an oscillator and determine its oscillation criteria.
- Know and be able to analyze the various building blocks inside an opamp like differential pair, current mirror and amplifier stages.
- Know the basic workings of an antenna and be able to match it to a circuit.
- Be able to design, simulate, build and measure circuits with transistors and opamps according to a given set of specifications.
- Work in a scientific way by comparing calculations, simulations and measurements
The student is able to:
1. work with systems of linear equations, vectors, matrices, subspaces of Rn and explain the connections between these concepts
- determine an echelon form and the reduced echelon form of a matrix
- write a linear system in the form Ax = b
- determine if a linear system is (in)consistent
- determine the solution set of a linear system
- perform operations with vectors and matrices (addition, scalar multiplication, multiplication, transpose, linear combinations
- apply properties of operations with vectors and matrices
- de ne the concept of inverse of a matrix
- apply properties of an invertible matrix
- calculate the inverse of a regular matrix
- characterize an invertible matrix in terms of its echelon form, its columns (rows), linear systems
- interrelate the solution sets of Ax = b and Ax = 0
- examine the linear (in)dependency of a set of vectors
- explain the concepts of subspace and basis
- determine (a basis for) a subspace (e.g. column space, null space of a matrix)
- compute coordinate vectors w.r.t. a basis
- determine the dimension of a subspace
2. work with determinants, eigenvalues, eigenvectors, linear transformations and connect them with the previous concepts
- explain the concept of determinant of a matrix
- compute the determinant of a matrix using cofactor expansion
- apply properties of determinants (w.r.t. row- and column operations and multiplication)
- characterize an invertible matrix in terms of its determinant
- calculate the area of a parallelogram or volume of a parallelepiped using determinants
- explain the concepts of eigenvalue and eigenvector of a matrix
- compute the eigenvalues and eigenvectors of a matrix, using the characteristic equation
- determine if a matrix is diagonalizable
- write a diagonalizable matrix as A = PDP��1
- explain the concept of linear transformation (domain, codomain, images)
- calculate the standard matrix of a linear transformation
- examine properties of linear transformations (one-to-one, onto)