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Duration
LevelCalculus and Analysis (B-KUL-I0O64A)
Cannot be taken as part of an examination contractAims
The concrete objectives for this course Calculus and Analysis are the following:
- Impart and teach to use the students a number of basical concepts and techniques, in concrete applications;
- Convince the students of the necessity to use the mathematical language carefully to formulate problems accurately and teach them how to use this language;
- Let students get acquainted with the power of the abstract mathematical approach of problems by showing that very diverse problems often can be solved with the same mathematical techniques;
- Teach students to reason, analyse and impart techniques to prove a statement.
Previous knowledge
Have had at least six hours of mathematics in high school
Content
See Teaching activities
Course material
Syllabus
Slides, transparencies, courseware
Toledo / e-platform
Order of Enrolment
This course unit is a prerequisite for taking the following course units:
I0N34A : Thermodynamics
Activities
4.0 ects. Calculus (B-KUL-I0O65a)
Content
Calculus covers the analysis of real functions of a real variable and consists of:
- Real numbers (absolute value and topological terms)
- Functions, rows, continuity and limits
- Derivatives and mean value theorems + applications (averages, course of functions and optimalisation problems)
- Rows and power series
- Transcendent functions (exp, ln, log, sin, cos, tg, cotg): properties, calculationrules, inverses, etc.
- Graphs of functions and equations (convexity, inflection points, asymptotes, conic section, parametrised curves)
- Integrals (definition, geometrical interpretation, properties and calculation rules), integration techniques, improper integrals and applications (lengths of curves, surfaces and volumes)
- Series expansions (Taylor- and Maclaurin series) and applications (calculation limits, defined integrals, zero points of functions)
Aims
See Course
Description of learning activities
- Follow lectures: listen actively, make assngments now and then and answer questions.
Course material
- Own course text Calculus and Analysis (Parts 1 and 2), available at Acco) contains exercises after each chapter
- Slides and extra information - see Toledo
2.0 ects. Analysis (B-KUL-I0O66a)
Content
The course module Analysis covers real analysis concerning functions of multiple variables:
- Derivatives and integrals, formulas of Taylor-Maclaurin, functions of Euler, vectoranalysis
- Differential-equations: first order: exact equations, linear equations, equations of Bernoulli; higher order: homogeneous and non-homogeneous linear equations.
Aims
See Course
Description of learning activities
Follow lectures: listen actively, make assignments every now and then and answer questions.
Course material
- Own course Calculus and Analysis (Parts 1 and 2), available at Acco, contains exercises after each chapter.
- Slides and extra information - see Toledo
1.0 ects. Calculus: Exercises (B-KUL-I0O73a)
Content
The practical exercises consist of exercises linked to the lecture Calculus.
Aims
Students learnt to apply mathematical concepts and techniques from the thearetical classes (lectures). By participating actively during the exercise sessions, students get the chance to get more insight and additional explanation concerning exercises and problems, ensuing from the subject matter from the lectures.
Description of learning activities
- Exercise sessions (groups of 25 students)
- Making exercises with guidance
- Discuss solutions and solution-strategies.
- Doing homework.
Course material
- Own course text Calculus and Analysis (Parts 1 and 2), available at ACCO, contains exercises after each chapter.
- Slides and extra information - see Toledo
1.0 ects. Analysis: Exercises (B-KUL-I0O74a)
Content
The practical exercises contain exercises that are linked to the lecture Analysis.
Aims
Students learnt to apply mathematical concepts and techniques from the thearetical classes (lectures). By participating actively during the exercise sessions, students get the chance to get more insight and additional explanation concerning exercises and problems, ensuing from the subject matter from the lectures.
Description of learning activities
- Exercise sessions (groups of 25 students)
- Making exercises with guidance
- Discuss solutions and solution strategies
- Doing homework
Course material
- Own course text Calculus and Analysis (Parts 1 and 2), available with ACCO, contains exercises after each chapter.
- Slides and extra information - see Toledo
Evaluation
Evaluation : Calculus and Analysis (B-KUL-I2O64a)
Explanation
The Teaching activities Calculus and Analysis are interrogated together in one written final exam. It consists of 2 parts:
- A theoretical part (takes 1h20min at most, counts for 50% of the marks): closed book, a combination of open questions (60%) and multiple-choice questions (40%) (with correction for guessing).
- An exercise part (takes 2h30min at most, counts for 50% of the marks): typically three or four exercises, students can use on the exam: the course text, an own handwritten portfolio and own handwritten notes, made during the exercise sessions.
