MATHEMATICAL ANALYSIS I
Academic year and teacher
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- FAUSTO SEGALA
- Credits
- 12
- Didactic period
- Primo Semestre
- SSD
- MAT/05
Training objectives
- The aim ofthe course for first-year students in physics is to give the basic knowledges of differential and integral calculus.
After passing the analysis I exam,the student will be able to graph functions of a real variable,evaluate non-elementary integrals,solve ordinary differential equations with constant coefficients,understand and solve typical physics problems such as harmonic oscillator,damped oscillations (car suspension systems),falling bodies in earth's atmosphere.
A special role is played by the deduction of the law of universal gravitation,by following original ideas of Newton,during the annus mirabilis 1666. Prerequisites
- Basic algebra,analytic geometry,trigonometry.
Course programme
- the set of real numbers(4 hours)
elementary functions,limits and continous functions, basics theorems about continous functions (16 hours)
differential calculus,max and min,Taylor's formula, cartesian graphs of simple functions (24 hours)
areas.,primitive functions,Riemann's integral (20 hours)
The set of complex numbers (10 hours)
ordinary differential equations with constant coefficients (22 hours)
some non linear equations (2 hours)
introduction to Lebesgue integral (4 hours)
some remarkable problems of physical interest (6 hours) Didactic methods
- Frontal lessons.
Learning assessment procedures
- Written/oral examination.
The final mark is the mean value between written test and oral exam.
About written exam,the student can be choose wether to sit a final test,or three intermediate tests,during period lesson.
Written exams are devoted to solutions of basic exercises,in order to test the knowledge of technicalities.
The oral exam mainly concern in the proof of a list of theorems.
In order to improve final score,non standard can be proposed Reference texts
- R.ADAMS,CALCOLO DIFFERENZIALE I,CEA,MILANO
E.FISCHER,INTERMEDIATE REAL ANALYSIS,SPRINGER VERLAG
http://www.themathpage.com/
