Content, progress and pedagogy of the module

Purpose:
Calculus is the branch of mathematics that studies differential equations and operations such as integration. Differential equations, in turn, describe (among other things) how signals in electric circuits behave

Learning objectives

Knowledge

• Must have knowledge on real functions of two or more variables.
• Must have knowledge of the trigonometric functions and their inverse functions
• Most have knowledge of Taylors formula and Taylor series
• Must have knowledge of complex numbers and roots in polynomials
• Must have knowledge of the complex exponential function, its characteristics and its connection with trigonometric functions
• Must have knowledge of curves in the plane (both rectangular and polar coordinates) and spatial parameterisations, tangent vectors and curvatures of such curves
• Must have knowledge of the Laplace transform and its use in relation to solving differential equations.

Skills

• Must be able to approximate functions via Taylor series
• Must be able to carry out differentiation of functions of more variables, and have a geometric understanding that allows solution of inhomogeneous second order linear differential equations.

Competences

• Must be able to solve linear differential equations with constant parameters
• Must be able to solve coupled first order linear differential equations and inhomogeneous second order linear differential equations
• Must be able to give a geometric description of real functions in 2 and 3 variables

Type of instruction

See the general description of the types of instruction described in the introduction to Chapter 3.

Exam

Exams