Rosanna MANZO | Mathematics III
Rosanna MANZO Mathematics III
cod. 0612700003
MATHEMATICS III
| 0612700003 | |
| DIPARTIMENTO DI INGEGNERIA DELL'INFORMAZIONE ED ELETTRICA E MATEMATICA APPLICATA | |
| COMPUTER ENGINEERING | |
| 2014/2015 |
| OBBLIGATORIO | |
| YEAR OF COURSE 2 | |
| YEAR OF DIDACTIC SYSTEM 2012 | |
| PRIMO SEMESTRE |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/05 | 6 | 60 | LESSONS |
| Objectives | |
|---|---|
| THE COURSE AIMS AT ACQUIRING ELEMENTS OF MATHEMATICAL ANALYSIS AND COMPLEX ANALYSIS: COMPLEX FUNCTIONS OF COMPLEX VARIABLES, FOURIER SERIES, FOURIER TRANSFORMS, LAPLACE TRANSFORMS, PARTIAL DIFFERENTIAL EQUATIONS. LEARNING OUTCOMES OF COURSE CONSIST IN THE ACHIEVEMENT OF RESULTS AND PROOF TECHNIQUES, AS WELL AS THE ABILITY TO USE THE RELATED COMPUTATIONAL TOOLS. THE THEORETICAL PART OF THE COURSE WILL BE PRESENTED IN A RIGOROUS BUT CONCISE WAY AND IT WILL BE SUPPORTED BY PARALLEL EXERCISE SESSIONS DESIGNED TO PROMOTE MEANINGFUL UNDERSTANDING OF CONCEPTS. KNOWLEDGE AND UNDERSTANDING KNOWLEDGE OF THE FUNDAMENTALS CONCEPTS OF COMPLEX ANALYSIS. FOURIER SERIES. FOURIER TRANSFORMS. LAPLACE AND INVERSE LAPLACE TRANSFORMS. BASICS ON PARTIAL DIFFERENTIAL EQUATIONS AND BOUNDARY PROBLEMS. APPLYING KNOWLEDGE AND UNDERSTANDING BEING ABLE TO APPLY THEOREMS AND RULES IN PROBLEMS SOLVING. BEING ABLE TO CONSISTENTLY BUILD PROOFS. BEING ABLE TO BUILD METHODS AND PROCEDURES FOR THE PROBLEMS RESOLUTION. MAKING JUDGEMENTS TO IDENTIFY THE BEST AND EFFICIENT METHOD TO SOLVE A MATHEMATICAL PROBLEM. COMMUNICATION SKILLS BEING ABLE TO EXPLAIN VERBALLY A TOPIC OF THE COURSE. BEING ABLE TO WORK IN GROUPS IN SOLVING EXERCISES. LEARNING SKILLS BEING ABLE TO APPLY THE ACQUIRED KNOWLEDGE TO DIFFERENT CONTEXTS FROM THOSE PRESENTED DURING THE COURSE. SKILL TO DEEPEN THE TOPICS DEALT WITH BY USING MATERIALS DIFFERENT FROM THOSE PRESENTED IN THE COURSE. |
| Prerequisites | |
|---|---|
| FOR THE SUCCESSFUL ACHIEVEMENT OF THE GOALS, STUDENTS ARE REQUIRED TO MASTER THE FOLLOWING PREREQUISITES: - KNOWLEDGE OF THE INTEGRAL CALCULUS, WITH PARTICULAR REFERENCE TO INTEGRATION OF FUNCTIONS OF ONE VARIABLE, INTEGRALS ON CURVES, INTEGRALS OF DIFFERENTIAL FORMS; - KNOWLEDGE OF SERIES EXPANSIONS, WITH PARTICULAR REFERENCE TO NUMERICAL SERIES AND FUNCTIONS ONES; - KNOWLEDGE OF THE FUNCTIONS IN SEVERAL VARIABLES AND ORDINARY DIFFERENTIAL EQUATIONS. |
| Contents | |
|---|---|
| COMPLEX ANALYSIS (HOURS LECTURE / PRACTICE / LABORATORY 10/6/-) COMPLEX DIFFERENTIATION, HOLOMORPHIC FUNCTIONS AND THEIR PROPERTIES. THE CAUCHY-RIEMANN CONDITIONS. ELEMENTARY FUNCTIONS IN THE COMPLEX FIELD. SINGULAR POINTS. COMPLEX INTEGRATION. CAUCHY'S THEOREM AND CAUCHY'S INTEGRAL FORMULAS. LIOUVILLE THEOREM. MEAN VALUE THEOREM. MORERA THEOREM. FUNDAMENTAL ALGEBRA THEOREM. TAYLOR'S AND LAURENT SERIES. CLASSIFICATION OF SINGULAR POINTS. RESIDUES, THE RESIDUE THEOREM AND ITS APPLICATION TO THE EVALUATION OF INTEGRALS OF REAL FUNCTIONS. FOURIER SERIES (HOURS 6/5/-) DEFINITIONS. EXAMPLES. BESSEL INEQUALITY. PUNCTUAL CONVERGENCE THEOREM. UNIFORM CONVERGENCE THEOREM. SERIES INTEGRATION. SERIES DERIVATION. FOURIER TRANSFORM (HOURS 6/4/-) DEFINITION AND PROPERTIES. THE RELATIONSHIP BETWEEN DERIVATION AND MULTIPLICATION BY MONOMIALS. CONVOLUTION TRANSFORM. INVERSION FORMULA. LAPLACE TRANSFORM (HOURS 8/6/-) DEFINITION AND PROPERTIES. LAPLACE TRANSFORMS OF DERIVATIVES. MULTIPLICATION BY POWERS OF T. LAPLACE TRANSFORM OF INTEGRALS. DIVISION BY T. PERIODIC FUNCTIONS. BEHAVIOUR OF LAPLACE TRANSFORM AT INFINITY. INITIAL AND FINAL VALUE THEOREM. CONVOLUTION TRANSFORM. INVERSE LAPLACE TRANSFORM. INVERSION FORMULAS. LAPLACE TRANSFORM AND INVERSE LAPLACE TRANSFORM CALCULATIONS. APPLICATION TO ORDINARY DIFFERENTIAL EQUATIONS. PARTIAL DIFFERENTIAL EQUATIONS (HOURS 4/5/-) INTRODUCTION TO PARTIAL DIFFERENTIAL EQUATIONS (PDE). HEAT, WAVE AND LAPLACE EQUATIONS. BOUNDARY PROBLEMS. SOLUTIONS OF LINEAR PDE USING SEPARATION OF VARIABLES AND LAPLACE TRANSFORMS. TOTAL HOURS 34/26/- |
| Teaching Methods | |
|---|---|
| THE COURSE COVERS: LECTURES, DURING WHICH ALL COURSE CONTENTS WILL BE PRESENTED BY LECTURES AND CLASSROOM EXERCISES, DURING WHICH THE MAIN TOOLS NECESSARY FOR THE RESOLUTION OF EXERCISES RELATED TO TEACHING CONTENTS WILL BE PROVIDED. |
| Verification of learning | |
|---|---|
| THE FINAL EXAM IS DESIGNED TO EVALUATE AS A WHOLE: •THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED DURING THE COURSE; •THE MASTERY OF THE MATHEMATICAL LANGUAGE IN THE WRITTEN AND ORAL PROOFS; •THE SKILL OF PROVING THEOREMS; •THE SKILL OF SOLVING EXERCISES; •THE SKILL TO IDENTIFY AND APPLY THE BEST AND EFFICIENT METHOD IN EXERCISES SOLVING; •THE ABILITY TO APPLY THE ACQUIRED KNOWLEDGE TO DIFFERENT CONTEXTS FROM THOSE PRESENTED DURING THE COURSE. THE EXAM CONSISTS OF A WRITTEN PROOF AND AN ORAL INTERVIEW. WRITTEN PROOF: THE WRITTEN PROOF CONSISTS IN SOLVING TYPICAL PROBLEMS PRESENTED IN THE COURSE. IN THE CASE OF A SUFFICIENT PROOF, IT WILL BE EVALUATED BY THREE SCALES. ORAL INTERVIEW: THE INTERVIEW IS DEVOTED TO EVALUATE THE DEGREE OF KNOWLEDGE OF ALL THE TOPICS OF THE COURSE, AND COVERS DEFINITIONS, THEOREMS PROOFS, EXERCISES SOLVING. FINAL EVALUATION: THE FINAL MARK, EXPRESSED IN THIRTIETHS (EVENTUALLY CUM LAUDE), DEPENDS ON THE MARK OF THE WRITTEN PROOF, WITH CORRECTIONS IN EXCESS OR DEFECT ON THE BASIS OF THE ORAL INTERVIEW. |
| Texts | |
|---|---|
| MURRAY R. SPIEGEL, SEYMOUR LIPSCHUTZ, JOHN SCHILLER, DENNIS SPELLMAN: COMPLEX VARIABLES, SCHAUM’S OUTLINES SERIES. MURRAY R. SPIEGEL: FOURIER ANALYSIS, SCHAUM’S OUTLINES SERIES. MURRAY R. SPIEGEL: LAPLACE TRANSFORMS, SCHAUM’S OUTLINES SERIES. PAUL DUCHATEAU, D. ZACHMANN: PARTIAL DIFFERENTIAL EQUATIONS, SCHAUM’S OUTLINES SERIES. C. D'APICE, R. MANZO: VERSO L’ESAME DI MATEMATICA III, CUES, 2011. EDUCATIONAL CONTENTS ON E-LEARNING PLATFORM IWT AND LECTURE NOTES. |
| More Information | |
|---|---|
| COMPULSORY ATTENDANCE. TEACHING IN ITALIAN. |
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