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t.BA.XXM4.AN2.19HS (Analysis 2)

Module: Analysis 2

This information was generated on: 18 May 2024

No.

t.BA.XXM4.AN2.19HS

Title

Analysis 2

Organised by

T IAMP

Credits

4

Description

Version: 4.0 start 01 August 2022

Short description

Advanced calculus

Module coordinator

Robbiani Marcello (roma)

Learning objectives (competencies)

Objectives

Competences

Taxonomy levels

You know the basical elements of functional thougth and are able to translate it in applications on exponential and logarithmical functions on hyperbolic functions and on area functions, on trigonometric functions and on arcus functions. In particular you know the role of the trigonometric additions theorems for the analysis of oscillations.

F, M

K2, K3

You know the fundamental concepts of differential and integral calculus. In particular you know the central role of the fundamental theorem of calculus.

You are able to calculate derivatives and to apply them among others to the solution of extremal problems.

You are able to use integration methods to calculate definite and indefinite integrals. You are able to apply integrals in geometry, science and technology.

F, M

K2, K3

You know the concept of a differential equation and the corresponding vocabulary. You know the concept of the solution to a differential equation.

F, M

K2, K3

You know the consept of the approximation of functions by Taylor polynomials and are able to estimate the approximation error. You are able to develop analytical functions in Taylor series

F, M

K2, K3

Module contents

Elementary functions

power and root functions, exponential and logarithmic functions

trigonometrix and hyperbolic function and their inverses

elementary theory of oscillations

Differential calculus in one real variable

derivation rules and methods

applications of differential calculus - extremal problems

power series, Taylor polynomials and series

Introduction to differential equations

Integral calculus in one real variable

definite and indefinite integrals

fundamental theorem of calculus

rules and methods of integration, imprper integrals

applications of integral calculus in geometry, science and technology

Teaching materials

scripts, exercises

Supplementary literature

Papula, Lothar: Mathematik für Ingenieure und Naturwissenschaftler

The module description is part of the legal basis in addition to the general academic regulations. It is binding. During the first week of the semester a written and communicated supplement can specify the module description in more detail.