Mathematical methods for Physics I

Course Code :1001WETWMF
Study domain:Mathematics
Academic year:2017-2018
Semester:1st semester
Contact hours:105
Credits:9
Study load (hours):252
Contract restrictions: No contract restriction
Language of instruction:Dutch
Exam period:exam in the 1st semester
Lecturer(s)David Eelbode

3. Course contents *

The following topics will be covered in this course:

- Functions of one real variable and their properties (boundedness, injectivity/surjectivity/bijectivity, continuity, limits)

- Differentiability in one variable (with a short excursion to partial derivatives) and applications (mean value theorems, extremal problems, graph sketching)

- Primitives (basic formulae and indefinite integrals of the first/second/third kind)

- Definite integrals (Riemann integration) and applications (volume, arc length, surface area)

- Taylor-polynomials and -series (with applications)

- Differential equations (survey of techniques: seperation of variables, homogeneous equations, exact equations, integrating factors, linear equations of n-th order, reduction of the order, variation of parameters, method of unknown coefficients)

- Linear algebra (vector spaces, generating set, basis and dimension)

- Matrix calculus (elementary structure, trace and determinant)

- Linear systems of equations in several variables

- Scalar and vector product

- Eigenvalues/eigenvectors and diagonalization

In short, this is classical one variable calculus as developed by Newton and Leibniz, together with the standard applications (appearing in almost all branches of natural science), and an introduction to basic linear algebra (which is, in some sense, an introduction to more advanced courses such as quantum mechanics, in which concepts such as 'diagonalization' and 'eigenvalues' play a dominant role).