# 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 |

### 1. Prerequisites *

- competences corresponding the final attainment level of secondary school

an active knowledge of

- Dutch

For most of the topics in this course, no explicit prerequisites are required, in view of the fact that they will be built up from scratch. However, it is desired that the student has a certain familiarity with the mathematical notions and concepts that were taught at secondary school (8 or 6 hours of mathematics, and - taking into account an extra effort - also 4 hours). In particular, students are required to exhibit specific skills related to the following mathematical methods that were considered at secondary level:

- Logic and the systematics of a mathematical proof

- Being able to calculate with real numbers, and to deal with polynomials in a finite number of variables

- Factoring polynomials

- Solving elementary equations and inequalities

- Being able to handle functions of first and second degree

- Newton's binomial formula

- Solving linear systems of equations (in 2 and 3 variables)

- Trigonometry

### 2. Learning outcomes *

- The student is supposed to get familiar with the notions and concepts that will be presented throughout this course, and knows what their precise meaning is.
- The student is able to situate these properties in the framework of the course and - where possible - in the framework of the natural sciences (physics) as a whole. This way the student comes to understand that the basic mathematical tools are indeed applied in other sciences, and sometimes even inspired by practical questions.
- The student is able to understand and reproduce an abstract reasoning (e.g. a theorem), and succeeds in exhibiting his understanding of the logic behind this reasoning.
- The student is able to obtain a mathematical formulation for a given problem, using sound logic deductive arguments, and is also able to formulate the answer to this question. Essentially, he is able to use mathematics as a formal language in which both the problem and the solution can be formulated.
- The student is able to apply techniques (considered in the course notes) on both typical examples and practical exercises.
- The student is able to approach specific bits of information from a pragmatic point of view, and knows where and when to apply certain properties/theorems/etc.

### 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).

### 4 International dimension*

### 5. Teaching method and planned learning activities

### 6. Assessment method and criteria

Continuous assessment

### 7. Study material *

#### 7.1 Required reading

Course notes will be availaible, and the slides that will be projected during the classes are available through Blackboard.

**7.2 Optional reading**

The following study material can be studied voluntarily :### 8. Contact information *

David Eelbode (CM, G.312)

david.eelbode@ua.ac.be