65926 - Mathematical Institutions 1

Academic Year 2018/2019

  • Teaching Mode: Traditional lectures
  • Campus: Ravenna
  • Corso: First cycle degree programme (L) in Environmental Sciences (cod. 8011)

Learning outcomes

The student knows the basic tools of calculus in one variable (limits, derivatives, intergral computations), and linear algebra. The student can use these tools for studying other disciplines.

Course contents

Premises: Sets. Relations. Maxima, minima, extreme inferior and superior. Functions. Two-way functions. Inverse functions.

- Vector subspaces and analytical geometry: Vector spaces. Linear addiction. Base of a vector space.

- Complex numbers: Trigonometric representation. Nth roots.

- Real variable functions: Limit and properties. Continuity'. Properties of continuous functions; Continuity and derivability (*).

- Differential calculus: Derivative. Rules for calculating derivatives. Fermat's theorem. Rolle's theorem (*). Monotonicity test (*). Maximum and Minimum. Theorem of de l'Hopital-Bernoulli. Derivatives of higher order.

- Integral according to Riemann: Integrability and Integral. Fundamental theorem of integral calculus (*). Integration methods: integration by parts (*), change of variable. Integration of elementary functions, simple fractions.

- Analytic Geometric: Equation of the line, of the plane. Orthogonality and parallelism. - Linear Algebra: Arrays and their operations. Reduction method (elimination of Gauss) for the solution of linear systems with a square matrix. Singular systems and homogeneous systems.

Readings/Bibliography

"Istituzioni di Matematica", Avantaggiati, ed. CEA "Istituzioni di Matematica", Bertsch, ed. Bollati Boringhieri "Istituzioni di Matematica I", Zwirner, ed. CEDAM

Teaching methods

Classroom lectures and exercises. Available class notes with solved exercised.

Assessment methods

Written exam. Possible additional oral exam (optional)

Teaching tools

Selected basic textbooks from the library. Classroom notes.

Links to further information

http://www.dm.unibo.it/~simoncin/Ist_I.html

Office hours

See the website of Valeria Simoncini