Perspectives
Perspectives
Which contents do you have to study during your first year of math lectures?
Principally the curricula of the departments define the contents.
As an example we provide a possible setup for a first-year course in mathematics for electrical engineering in keywords;
we divided it into two semesters.
1. Semester
- Mathematical Induction, Sums, Binomial Theorem
- Sequences and Infinite Series, Limits
- Continuous Functions and their Properties
- Elementary Functions, for example
ex = |
¥ å
k = 0
|
|
xk
k!
|
, ex + y = ex ey, ln(x), cos(x), arccos(x) etc. |
|
and their properties
- Complex Numbers and Complex Functions, for example
ejx = cos(x) + j sin(x) mit j2 = -1, |
|
ln(x + j y) = ln(|x + j y|) + j arg(x + j y) + 2pk j with x + j y Ï R0-, k Î Z. |
|
Polynomials, The Fundamental Theorem of Algebra
- Differential Calculus for Functions of a Single Variable
Linear Approximation, Rules for Derivatives, Mean Value Theorem and
Taylor Formula
f(x) = |
N å
k = 0
|
|
f(k)(x0)
k!
|
(x - x0)k + error(N, x0, x) (f suitably differentiable) |
|
Application Examples
- Integrals for Functions of a Single Variable
Primitives, Integration Methods, Mean Values, Numerical Integration,
Application Examples.
Time Budget
About 13 weeks, six 45-minute classes and two 45-minute exercises, altogether 58 - 60 hours of classes
and 20 hours of exercises.
2. Semester
- Linear Algebra
Vectors, Vector Spaces, Basis, Dimension, ¼
Linear Mappings, Matrices,
Determinants, Systems of Linear Equations, Eigenvalue Problems,
Approximation in Vector Spaces.
- Differential Calculus for Functions of Several Variables
Partial Derivatives, Mean Value Theorem and Taylor Formula,
Local
Extrema with or without Restrictions, Error Estimation and further
Application Examples
- Integral Calculus for Functions of Several Variables
Integrals and Their Properties, Integration with Respect to Cartesian,
Polar, Cylindrical and Spherical Coordinates, Application Examples.
- Ordinary Differential Equations
Basic Theorems on Ordinary Differential Equations,
Solvability and Solution Methods,
specially for Linear
Differential Equations, Laplace Transform,
Applications in Electrical Engineering.
Time Budget
As in 1. Semester
For other fields, e.g. Computer Science, there are of course other focusses.
In Computer Science for example you have more topics on Algebra and
Discrete Mathematics. This page wants to give you an impression
of the contents and the time budget only.