Študijska smer Study field. Samost. delo Individ. work Klinične vaje work. Vaje / Tutorial: Slovensko/Slovene
|
|
- Felicia Clarke
- 5 years ago
- Views:
Transcription
1 UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Matematika 2 Course title: Mathematics 2 Študijski program in stopnja Study programme and level Univerzitetni študijski program 1.stopnje Fizika First cycle academic study program Physics Študijska smer Study field Letnik Acade mic year Semester Semester vse 1 drugi all 1 second Vrsta predmeta / Course type Univerzitetna koda predmeta / University course code: obvezni predmet/core course??? Predavan ja Lectures Seminar Seminar Vaje Tutorial Klinične vaje work Druge oblike študija Samost. delo Individ. work ECTS Nosilec predmeta / Lecturer: Prof. dr. Peter Legiša, prof. dr. Bojan Magajna, prof. dr. Janez Mrčun Jeziki / Languages : Predavanja / Slovensko/Slovene Lectures: Vaje / Tutorial: Slovensko/Slovene Pogoji za vključitev v delo oz. za opravljanje študijskih obveznosti: Vpis v letnik. Opravljen izpit iz vaj je pogoj za pristop k izpitu iz teorije. Prerequisits: Enrolment into the first year of the program. Positively graded exercises are necessary for the admittion to the theoretical part of the exam. 44
2 Vsebina: Vektorski prostori: linearna odvisnost, baza, razsežnost, podprostori. Skalarni produkt na vektorskem prostoru: pravokotnost, ortonormirane baze, ortogonalni komplementi, Gram-Schmidtova ortogonalizacija. Matrike: operacije med matrikami, transponirana matrika, kvadratne matrike, grupa obrnljivih matrik, Gaussova eliminacijska metoda, vrstična kanonična oblika matrike, rang, sistemi linearnih enačb, inverzna matrika. Determinante: lastnosti, razvoj po vrstici ali stolpcu, determinanta produkta, Cramerjevo pravilo. Linearni operatorji: matrika linearnega operatorja, lastne vrednosti in vektorji, karakteristični in minimalni polinom, diagonalizabilnost, Cayley-Hamiltonov izrek, invariantni podprostori. Operatorji na prostorih s skalarnim produktom: adjungirani operator, unitarni,, sebi adjungirani in pozitivni operatorji, diagonalizacija sebiadjungiranega operatorja. Bilinearne in kvadratne forme: kanonična oblika za linearne in za ortogonalne transformacije, ploskve drugega reda. Content (Syllabus outline): Vector spaces: linear dependence, basis, dimension, subspaces. Inner product spaces: orthogonality, orthonormal basis, orthogonal complements, Gram-Schmidt orthogonalization Matrices: operations with matrices, transpose matrix, square matrices, invertible matrices, Gauss elimination, systems of linear equations, the row canonical form, rang, inverse. Determinants: properties, computation by expansion over rows or columns, determinant of the product of matrices, Cramer s rule. Linear operators: matrix of a linear operator, eigenvalues and eigenvectors, characteristic and minimal polynomial, diagonalizability, Cayley-Hamilton theorem, invariant subspaces. Operators on inner product spaces: the adjoint, unitary, self-adjoint and positive operators, diagonalization of selfadjoint operators. Bilinear and quadratic forms: canonical form for linear and for orthogonal transformations, quadratic surfaces. 45
3 Metrični prostori: odprte in zaprte množice, notranjost in rob, stekališča in limite zaporedij, kompaktnost, kompaktnost v evklidskih prostorih, zvezne preslikave. Vektorske funkcije več spremenljivk: diferenciabilnost in Jacobijeva matrika, verižno pravilo, ekstremi funkcij več spremenljivk, Hessejeva matrika, izrek o inverzni in implicitni funkciji, vezani ekstremi in Lagrangeva metoda množiteljev. Metric spaces: open and closed sets, interior, closure and boundary, limit points, compactness, compactness in euclidean spaces, continuous maps. Vector functions of several variables: differentiability and the Jacobian, the chain rule, extrema, Hessian, the inverse and the implicit function theorem, constrained extrema and Lagrange multipliers. Temeljni literatura in viri / Readings: 1. S. I. Grossman, Elementary linear algebra. Saunders College Publishing, Orlando, P. R. Halmos, Finite-dimensional vector spaces. Springer-Verlag, New York-Heidelberg, F. Križanič, Temelji realne matematične analize. Državna založba Slovenije, Ljubljana, F. Križanič, Linearna algebra in linearna analiza. Državna založba Slovenije, Ljubljana, D. C. Lay, Linear algebra and its applications. Addison-Wesley, Reading, B. Magajna, Linearna algebra, metrični prostor in funkcije več spremenljivk, DMFA, Ljubljana, M. Dobovišek, B. Magajna in D. Kobal, Naloge iz algebre I, DMFA, Ljubljana, M. H. Protter, C. B. Morrey, Intermediate Calculus. Springer-Verlag, New York-Heidelberg,
4 9. I. Vidav, Višja matematika I. Društvo matematikov, fizikov in astronomov Slovenije, Ljubljana, Cilji in kompetence: Študent spozna osnovne pojme linearne algebre ter pojem in uporabo odvoda vektorske funkcije več realnih spremenljivk. Matematika 2 sodi med temeljne predmete pri študiju fizike. Objectives and competences: Objectives: to familiarize students with basic concepts of linear algebra, metric spaces and with the derivative of a vector function in several variables. Competences: students should be able to apply the methods of linear algebra and calculus in several varibles to problems in physics. Predvideni študijski rezultati: Znanje in razumevanje: Poznavanje in razumevanje osnovnih pojmov in definicij. Uporaba: Uporaba teorije pri reševanju problemov. Refleksija: Razumevanje teorije na podlagi uporabe. Prenosljive spretnosti - niso vezane le na en predmet: Spretnosti uporabe domače in tuje literature in drugih virov, identifikacija in reševanje problemov, kritična analiza. Intended learning outcomes: Knowledge and understanding: understanding of basic concepts and definitions. Application: there are numerous applications of linear algebra and several variable calculus to physics (and other disciplines) Reflection: this part of mathematics is basic for understanding classical and modern physics. Transferable skills: ability to apply mathematical methods. Identification of problems and critical analysis. 47
5 Metode poučevanja in učenja: Predavanja in vaje. Opravljen izpit iz vaj je pogoj za pristop k izpitu iz teorije. Learning and teaching methods: Lectures and exercises. Positively graded exercises are the condition for admittance to the theoretical part of the exame. Načini ocenjevanja: 2 kolokvija namesto izpita iz vaj, izpit iz vaj, Delež (v %) / Weight (in %) 50 Assessment: Written exam or two midterm exams. Izpit iz teorije, domače naloge (niso obvezne) (pozitivno), in 1-5 (negativno) (po Statutu UL). 50 Theoretical exam, homework (optional). Reference nosilca / Lecturer's references: prof. dr. P.Legiša: 1. P.Legiša, Adjacency preserving mappings on real symmetric matrices, Math. commun., Croat. Math. Soc., Divis. Osijek, 2011, vol. 16, no. 2, P.Legiša, Automorphisms of Mn, partially ordered by the star order, Linear multilinear algebra, 2006, vol. 54, no. 3, P.Legiša, Automorphisms of Mn, partially ordered by rank subtractivity ordering, Linear algebra appl. 2004, vol. 389, prof. dr. Bojan Magajna: 1. B. Magajna, Linearna algebra, metrični prostor in funkcije več spremenljivk, DMFA, Ljubljana, 2011 (247 strani). 2. B. Magajna, Fixed points of normal completely positive maps on B(H), J. Math. Anal. Appl. 389 (2012) B. Magajna, The Haagerup norm on the tensor product of operator 48
6 modules, J. Funct. Anal 129 (1995) prof. dr. J. Mrčun: 1. I. Moerdijk, J. Mrčun, On the developability of Lie subalgebroid, Adv. Math. 210 (2007), J. Mrčun, On isomorphisms of algebras of smooth functions, Proc. Amer. Math. Soc. 133 (2005), I. Moerdijk, J. Mrčun, On integrability of infinitesimal actions, Amer. J. Math. 124 (2002),
UČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Predmet: Algebra 1 Course title: Algebra 1. Študijska smer Study field ECTS
UČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Predmet: Algebra 1 Course title: Algebra 1 Študijski program in stopnja Study programme and level Univerzitetni študijski program Matematika
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Analiza 1 Course title: Analysis 1. Študijska smer Study field. Samost. delo Individ.
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Analiza 1 Course title: Analysis 1 Študijski program in stopnja Study programme and level Univerzitetni študijski program Finančna matematika First cycle
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Študijska smer Study field ECTS Vaje / Tutorial: slovenski / Slovene
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Linearna algebra Linear algebra Študijski program in stopnja Study programme and level Visokošolski strokovni študijski
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS. Študijska smer Study field. Samost. delo Individ. work Klinične vaje work
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS Linearna algebra Linear algebra Študijski program in stopnja Study programme and level Visokošolski strokovni študijski program Praktična matematika
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Parcialne diferencialne enačbe Partial differential equations. Študijska smer Study field
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Parcialne diferencialne enačbe Partial differential equations Študijski program in stopnja Study programme and level Magistrski
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Predmet: Analiza 3 Course title: Analysis 3. Študijska smer Study field ECTS
UČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Predmet: Analiza 3 Course title: Analysis 3 Študijski program in stopnja Study programme and level Univerzitetni študijski program Matematika
More informationŠtudijska smer Study field. Klinične vaje work. Nosilec predmeta / prof. dr. Peter Legiša, prof. dr. Bojan Magajna, prof. dr.
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Matematika 1 Course title: Mathematics 1 Študijski program in stopnja Study programme and level Univerzitetni študijski program 1.stopnje Fizika First cycle
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Študijska smer Study field ECTS
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Numerične metode Numerical methods Študijski program in stopnja Study programme and level Interdisciplinarni univerzitetni
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS Numerical linear algebra. Študijska smer Study field. Samost. delo Individ. work Klinične vaje work
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS Numerična linearna algebra Numerical linear algebra Študijski program in stopnja Study programme and level Univerzitetni študijski program Matematika
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Predmet: Optimizacija 1 Course title: Optimization 1. Študijska smer Study field
UČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Predmet: Optimizacija 1 Course title: Optimization 1 Študijski program in stopnja Study programme and level Univerzitetni študijski program Matematika
More informationŠtudijska smer Study field. Samost. delo Individ. work Klinične vaje work. Vaje / Tutorial: Slovensko/Slovene
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Kvantna mehanika Course title: Quantum mechanics Študijski program in stopnja Study programme and level Univerzitetni študijski program 1.stopnje Fizika First
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Diferencialne enačbe. Študijska smer Study field ECTS
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Diferencialne enačbe Differential equations Študijski program in stopnja Study programme and level Visokošolski strokovni
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS. Študijska smer Study field. Samost. delo Individ. work Klinične vaje work
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS Statistika Statistics Študijski program in stopnja Study programme and level Univerzitetni študijski program Matematika First cycle academic
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2016/17) Diferencialne enačbe. Študijska smer Study field ECTS
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2016/17) Diferencialne enačbe Differential equations Študijski program in stopnja Study programme and level Visokošolski strokovni
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS. Študijska smer Study field. Samost. delo Individ. work Klinične vaje work
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS Teorija grafov Graph theory Študijski program in stopnja Study programme and level Magistrski študijski program Matematika Master's study
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS. Študijska smer Study field
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Course title: Teorija umeritvenih polj Gauge field theory Študijski program in stopnja Study programme and level Študijska smer Study field Letnik Academ
More informationŠtudijska smer Study field. Samost. delo Individ. work Klinične vaje work. Vaje / Tutorial: Slovensko/Slovene
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Matematika III Course title: Mathematics III Študijski program in stopnja Study programme and level Univerzitetni študijski program 1.stopnje Fizika First
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS. Študijska smer Study field. Samost. delo Individ. work Klinične vaje work
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS Optimizacija Optimization Študijski program in stopnja Study programme and level Visokošolski strokovni študijski program Praktična matematika
More informationŠtudijska smer Study field. Samost. delo Individ. work Klinične vaje work. Vaje / Tutorial: Slovensko/Slovene
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Numerične metode Course title: Numerical methods Študijski program in stopnja Study programme and level Univerzitetni študijski program 1.stopnje Fizika First
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Numerične metode 1 Course title: Numerical methods 1. Študijska smer Study field
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Numerične metode 1 Course title: Numerical methods 1 Študijski program in stopnja Study programme and level Visokošolski strokovni študijski program Praktična
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Študijska smer Study field ECTS
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Kompleksna analiza Complex analysis Študijski program in stopnja Study programme and level Magistrski študijski program
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Študijska smer Study field ECTS
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Teorija števil Number theory Študijski program in stopnja Study programme and level Magistrski študijski program Matematika
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS
UČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Predmet: Izbrana poglavja iz diskretne matematike 1 Course title: Topics in discrete mathematics 1 Študijski program in stopnja Study programme
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Predmet: Statistika 2 Course title: Statistics 2. Študijska smer Study field
UČNI NAČRT PREDMETA / COURSE SYLLABUS (leto / year 2017/18) Predmet: Statistika 2 Course title: Statistics 2 Študijski program in stopnja Study programme and level Magistrski študijski program Matematika
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS. Študijska smer Study field
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Course title: Analiza in prognoza vremena Weather analysis and forecasting Študijski program in stopnja Study programme and level Študijska smer Study field
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS. Študijska smer Study field
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Course title: Fizika laserjev Laser physics Študijski program in stopnja Study programme and level Študijska smer Study field Letnik Academ ic year Semester
More informationHOSTOS COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS
HOSTOS COMMUNITY COLLEGE DEPARTMENT OF MATHEMATICS MAT 217 Linear Algebra CREDIT HOURS: 4.0 EQUATED HOURS: 4.0 CLASS HOURS: 4.0 PREREQUISITE: PRE/COREQUISITE: MAT 210 Calculus I MAT 220 Calculus II RECOMMENDED
More informationColumbus State Community College Mathematics Department Public Syllabus
Columbus State Community College Mathematics Department Public Syllabus Course and Number: MATH 2568 Elementary Linear Algebra Credits: 4 Class Hours Per Week: 4 Prerequisites: MATH 2153 with a C or higher
More informationMULTIVARIABLE CALCULUS, LINEAR ALGEBRA, AND DIFFERENTIAL EQUATIONS
T H I R D E D I T I O N MULTIVARIABLE CALCULUS, LINEAR ALGEBRA, AND DIFFERENTIAL EQUATIONS STANLEY I. GROSSMAN University of Montana and University College London SAUNDERS COLLEGE PUBLISHING HARCOURT BRACE
More informationLAKELAND COMMUNITY COLLEGE COURSE OUTLINE FORM
LAKELAND COMMUNITY COLLEGE COURSE OUTLINE FORM ORIGINATION DATE: 8/2/99 APPROVAL DATE: 3/22/12 LAST MODIFICATION DATE: 3/28/12 EFFECTIVE TERM/YEAR: FALL/ 12 COURSE ID: COURSE TITLE: MATH2800 Linear Algebra
More informationModule name Calculus and Linear Algebra (Maths 2) To provide additional mathematical tools required for core statistical and actuarial modules
MODULE SPECIFICATION UNDERGRADUATE PROGRAMMES KEY FACTS Module name and Linear Algebra (Maths 2) Module code AS2051 School Cass Business School Department or equivalent UG Programme UK credits 20 ECTS
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS. Študijska smer Study field
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Course title: Fizika kondenzirane snovi Condensed Matter Physics Študijski program in stopnja Study programme and level Študijska smer Study field Letnik
More informationLinear Algebra Done Wrong. Sergei Treil. Department of Mathematics, Brown University
Linear Algebra Done Wrong Sergei Treil Department of Mathematics, Brown University Copyright c Sergei Treil, 2004, 2009 Preface The title of the book sounds a bit mysterious. Why should anyone read this
More informationMATHEMATICS COMPREHENSIVE EXAM: IN-CLASS COMPONENT
MATHEMATICS COMPREHENSIVE EXAM: IN-CLASS COMPONENT The following is the list of questions for the oral exam. At the same time, these questions represent all topics for the written exam. The procedure for
More informationHONORS LINEAR ALGEBRA (MATH V 2020) SPRING 2013
HONORS LINEAR ALGEBRA (MATH V 2020) SPRING 2013 PROFESSOR HENRY C. PINKHAM 1. Prerequisites The only prerequisite is Calculus III (Math 1201) or the equivalent: the first semester of multivariable calculus.
More informationAlgebra and Geometry (250101)
Algebra and Geometry (250101) General information School: ETSECCPB Departments: 751 - Departament d'enginyeria Civil i Ambiental Credits: 6.0 ECTS Programs: 1305 - GRAU EN ENGINYERIA CIVIL (2017), 790
More informationALGGEOM - Algebra and Geometry
Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2017 250 - ETSECCPB - Barcelona School of Civil Engineering 751 - DECA - Department of Civil and Environmental Engineering BACHELOR'S
More informationMAT188H1S LINEAR ALGEBRA: Course Information as of February 2, Calendar Description:
MAT188H1S LINEAR ALGEBRA: Course Information as of February 2, 2019 2018-2019 Calendar Description: This course covers systems of linear equations and Gaussian elimination, applications; vectors in R n,
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS. Študijska smer Study field
UČNI NAČRT PREDMETA / COURSE SYLLABUS Predmet: Course title: Molekularna biofizika Molceular biophysics Študijski program in stopnja Study programme and level Študijska smer Study field Letnik Academ ic
More informationDetailed Assessment Report MATH Outcomes, with Any Associations and Related Measures, Targets, Findings, and Action Plans
Detailed Assessment Report 2015-2016 MATH 3401 As of: 8/15/2016 10:01 AM EDT (Includes those Action Plans with Budget Amounts marked One-Time, Recurring, No Request.) Course Description Theory and applications
More informationMATRIX AND LINEAR ALGEBR A Aided with MATLAB
Second Edition (Revised) MATRIX AND LINEAR ALGEBR A Aided with MATLAB Kanti Bhushan Datta Matrix and Linear Algebra Aided with MATLAB Second Edition KANTI BHUSHAN DATTA Former Professor Department of Electrical
More informationReduction to the associated homogeneous system via a particular solution
June PURDUE UNIVERSITY Study Guide for the Credit Exam in (MA 5) Linear Algebra This study guide describes briefly the course materials to be covered in MA 5. In order to be qualified for the credit, one
More informationMATH 23a, FALL 2002 THEORETICAL LINEAR ALGEBRA AND MULTIVARIABLE CALCULUS Solutions to Final Exam (in-class portion) January 22, 2003
MATH 23a, FALL 2002 THEORETICAL LINEAR ALGEBRA AND MULTIVARIABLE CALCULUS Solutions to Final Exam (in-class portion) January 22, 2003 1. True or False (28 points, 2 each) T or F If V is a vector space
More informationŠtudijska smer Study field Konstrukcijsko mehanske inženirske znanosti Constructional and Mechanical Engineering Sciences. Vrsta predmeta Course type
UČNI NAČRT PREDMETA COURSE SYLLABUS Predmet Course title AKUSTIČNA EMISIJA IN HRUP ACOUSTICAL EMISSION AND NOISE Študijski program in stopnja Study programme and level Doktorski študijski program STROJNIŠTVO
More informationhomogeneous 71 hyperplane 10 hyperplane 34 hyperplane 69 identity map 171 identity map 186 identity map 206 identity matrix 110 identity matrix 45
address 12 adjoint matrix 118 alternating 112 alternating 203 angle 159 angle 33 angle 60 area 120 associative 180 augmented matrix 11 axes 5 Axiom of Choice 153 basis 178 basis 210 basis 74 basis test
More information(Refer Slide Time: 2:04)
Linear Algebra By Professor K. C. Sivakumar Department of Mathematics Indian Institute of Technology, Madras Module 1 Lecture 1 Introduction to the Course Contents Good morning, let me welcome you to this
More informationLinear Algebra. Min Yan
Linear Algebra Min Yan January 2, 2018 2 Contents 1 Vector Space 7 1.1 Definition................................. 7 1.1.1 Axioms of Vector Space..................... 7 1.1.2 Consequence of Axiom......................
More informationCENTRAL TEXAS COLLEGE SYLLABUS FOR MATH 2318 Linear Algebra. Semester Hours Credit: 3
CENTRAL TEXAS COLLEGE SYLLABUS FOR MATH 2318 Linear Algebra Semester Hours Credit: 3 I. INTRODUCTION A. Linear Algebra is a three semester-hour course. This course introduces and provides models for application
More informationSYLLABUS. 1 Linear maps and matrices
Dr. K. Bellová Mathematics 2 (10-PHY-BIPMA2) SYLLABUS 1 Linear maps and matrices Operations with linear maps. Prop 1.1.1: 1) sum, scalar multiple, composition of linear maps are linear maps; 2) L(U, V
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS Analiza varnosti in tveganja v medicinski fiziki Evaluation of safety and risk in medical physics
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS Analiza varnosti in tveganja v medicinski fiziki Evaluation of safety and risk in medical physics Študijski program in stopnja Study programme
More informationContents. Preface for the Instructor. Preface for the Student. xvii. Acknowledgments. 1 Vector Spaces 1 1.A R n and C n 2
Contents Preface for the Instructor xi Preface for the Student xv Acknowledgments xvii 1 Vector Spaces 1 1.A R n and C n 2 Complex Numbers 2 Lists 5 F n 6 Digression on Fields 10 Exercises 1.A 11 1.B Definition
More informationThe value of a problem is not so much coming up with the answer as in the ideas and attempted ideas it forces on the would be solver I.N.
Math 410 Homework Problems In the following pages you will find all of the homework problems for the semester. Homework should be written out neatly and stapled and turned in at the beginning of class
More informationLINEAR ALGEBRA 1, 2012-I PARTIAL EXAM 3 SOLUTIONS TO PRACTICE PROBLEMS
LINEAR ALGEBRA, -I PARTIAL EXAM SOLUTIONS TO PRACTICE PROBLEMS Problem (a) For each of the two matrices below, (i) determine whether it is diagonalizable, (ii) determine whether it is orthogonally diagonalizable,
More informationSyllabus for the course «Linear Algebra» (Линейная алгебра)
Government of Russian Federation Federal State Autonomous Educational Institution of High Professional Education «National Research University Higher School of Economics» National Research University High
More informationReview problems for MA 54, Fall 2004.
Review problems for MA 54, Fall 2004. Below are the review problems for the final. They are mostly homework problems, or very similar. If you are comfortable doing these problems, you should be fine on
More informationMath 410 Linear Algebra Summer Session American River College
Course Information Instructor: Kristin Lui Email: luik@arc.losrios.edu Office Hours: By appointment Location: Liberal Arts 163 ARC Main Campus Meet Times: Tuesday/Thursday 6:30 pm 9:40 pm Dates: June 16,
More informationELEMENTARY MATRIX ALGEBRA
ELEMENTARY MATRIX ALGEBRA Third Edition FRANZ E. HOHN DOVER PUBLICATIONS, INC. Mineola, New York CONTENTS CHAPTER \ Introduction to Matrix Algebra 1.1 Matrices 1 1.2 Equality of Matrices 2 13 Addition
More informationMATH 240 Spring, Chapter 1: Linear Equations and Matrices
MATH 240 Spring, 2006 Chapter Summaries for Kolman / Hill, Elementary Linear Algebra, 8th Ed. Sections 1.1 1.6, 2.1 2.2, 3.2 3.8, 4.3 4.5, 5.1 5.3, 5.5, 6.1 6.5, 7.1 7.2, 7.4 DEFINITIONS Chapter 1: Linear
More informationMobile Robotics 1. A Compact Course on Linear Algebra. Giorgio Grisetti
Mobile Robotics 1 A Compact Course on Linear Algebra Giorgio Grisetti SA-1 Vectors Arrays of numbers They represent a point in a n dimensional space 2 Vectors: Scalar Product Scalar-Vector Product Changes
More informationABSTRACT ALGEBRA WITH APPLICATIONS
ABSTRACT ALGEBRA WITH APPLICATIONS IN TWO VOLUMES VOLUME I VECTOR SPACES AND GROUPS KARLHEINZ SPINDLER Darmstadt, Germany Marcel Dekker, Inc. New York Basel Hong Kong Contents f Volume I Preface v VECTOR
More informationMath 4153 Exam 3 Review. The syllabus for Exam 3 is Chapter 6 (pages ), Chapter 7 through page 137, and Chapter 8 through page 182 in Axler.
Math 453 Exam 3 Review The syllabus for Exam 3 is Chapter 6 (pages -2), Chapter 7 through page 37, and Chapter 8 through page 82 in Axler.. You should be sure to know precise definition of the terms we
More informationSpecial Two-Semester Linear Algebra Course (Fall 2012 and Spring 2013)
Special Two-Semester Linear Algebra Course (Fall 2012 and Spring 2013) The first semester will concentrate on basic matrix skills as described in MA 205, and the student should have one semester of calculus.
More informationASSIGNMENT BOOKLET. Bachelor's Degree Programme LINEAR ALGEBRA. It is compulsory to submit the assignment before filling in the exam form.
ASSIGNMENT BOOKLET MTE- Bachelor's Degree Programme LINEAR ALGEBRA (Valid from st January, to st December, ) It is compulsory to submit the assignment before filling in the exam form. School of Sciences
More informationCOURSE SYLLABUS (Formally the CIS)
COURSE SYLLABUS (Formally the CIS) COURSE NUMBER AND TITLE: MATH 2318.01 - Linear algebra COURSE (CATALOG) DESCRIPTION: An introductory course in linear algebra. Topics include system of linear equations,
More informationMath 302 Outcome Statements Winter 2013
Math 302 Outcome Statements Winter 2013 1 Rectangular Space Coordinates; Vectors in the Three-Dimensional Space (a) Cartesian coordinates of a point (b) sphere (c) symmetry about a point, a line, and a
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS Analiza varnosti in tveganja v medicinski fiziki Evaluation of safety and risk in medical physics
Predmet: Course title: UČNI NAČRT PREDMETA / COURSE SYLLABUS Analiza varnosti in tveganja v medicinski fiziki Evaluation of safety and risk in medical physics Študijski program in stopnja Study programme
More informationSection Instructors: by now you should be scheduled into one of the following Sections:
MAT188H1F LINEAR ALGEBRA: Syllabus for Fall 2018 as of October 26, 2018 2018-2019 Calendar Description: This course covers systems of linear equations and Gaussian elimination, applications; vectors in
More informationLinear algebra II Homework #1 due Thursday, Feb. 2 A =. 2 5 A = When writing up solutions, write legibly and coherently.
Homework #1 due Thursday, Feb. 2 1. Find the eigenvalues and the eigenvectors of the matrix [ ] 4 6 A =. 2 5 2. Find the eigenvalues and the eigenvectors of the matrix 3 3 1 A = 1 1 1. 3 9 5 3. The following
More informationkemijsko tehnologijo Kemija UČNI NAČRT PREDMETA / COURSE SYLLABUS ANALIZNA KEMIJA I ANALYTICAL CHEMISTRY I Študijska smer Study Field
Predmet: Course Title: UČNI NAČRT PREDMETA / COURSE SYLLABUS ANALIZNA KEMIJA I ANALYTICAL CHEMISTRY I Študijski program in stopnja Study Programme and Level Študijska smer Study Field Letnik Academic Year
More informationACM - Algebra and Multivariable Calculus
Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2018 295 - EEBE - Barcelona East School of Engineering 749 - MAT - Department of Mathematics BACHELOR'S DEGREE IN ELECTRICAL ENGINEERING
More informationMath 102, Winter Final Exam Review. Chapter 1. Matrices and Gaussian Elimination
Math 0, Winter 07 Final Exam Review Chapter. Matrices and Gaussian Elimination { x + x =,. Different forms of a system of linear equations. Example: The x + 4x = 4. [ ] [ ] [ ] vector form (or the column
More informationMATH 215 LINEAR ALGEBRA ASSIGNMENT SHEET odd, 14, 25, 27, 29, 37, 41, 45, 47, 49, 51, 55, 61, 63, 65, 67, 77, 79, 81
MATH 215 LINEAR ALGEBRA ASSIGNMENT SHEET TEXTBOOK: Elementary Linear Algebra, 7 th Edition, by Ron Larson 2013, Brooks/Cole Cengage Learning ISBN-13: 978-1-133-11087-3 Chapter 1: Systems of Linear Equations
More informationALG - Algebra
Coordinating unit: Teaching unit: Academic year: Degree: ECTS credits: 2018 270 - FIB - Barcelona School of Informatics 749 - MAT - Department of Mathematics BACHELOR'S DEGREE IN DATA SCIENCE AND ENGINEERING
More informationLast name: First name: Signature: Student number:
MAT 2141 The final exam Instructor: K. Zaynullin Last name: First name: Signature: Student number: Do not detach the pages of this examination. You may use the back of the pages as scrap paper for calculations,
More informationANSWERS. E k E 2 E 1 A = B
MATH 7- Final Exam Spring ANSWERS Essay Questions points Define an Elementary Matrix Display the fundamental matrix multiply equation which summarizes a sequence of swap, combination and multiply operations,
More informationFinal Exam, Linear Algebra, Fall, 2003, W. Stephen Wilson
Final Exam, Linear Algebra, Fall, 2003, W. Stephen Wilson Name: TA Name and section: NO CALCULATORS, SHOW ALL WORK, NO OTHER PAPERS ON DESK. There is very little actual work to be done on this exam if
More informationComprehensive Introduction to Linear Algebra
Comprehensive Introduction to Linear Algebra WEB VERSION Joel G Broida S Gill Williamson N = a 11 a 12 a 1n a 21 a 22 a 2n C = a 11 a 12 a 1n a 21 a 22 a 2n a m1 a m2 a mn a m1 a m2 a mn Comprehensive
More informationMath 18, Linear Algebra, Lecture C00, Spring 2017 Review and Practice Problems for Final Exam
Math 8, Linear Algebra, Lecture C, Spring 7 Review and Practice Problems for Final Exam. The augmentedmatrix of a linear system has been transformed by row operations into 5 4 8. Determine if the system
More informationColumbus State Community College Mathematics Department. CREDITS: 5 CLASS HOURS PER WEEK: 5 PREREQUISITES: MATH 2173 with a C or higher
Columbus State Community College Mathematics Department Course and Number: MATH 2174 - Linear Algebra and Differential Equations for Engineering CREDITS: 5 CLASS HOURS PER WEEK: 5 PREREQUISITES: MATH 2173
More informationMAT 211, Spring 2015, Introduction to Linear Algebra.
MAT 211, Spring 2015, Introduction to Linear Algebra. Lecture 04, 53103: MWF 10-10:53 AM. Location: Library W4535 Contact: mtehrani@scgp.stonybrook.edu Final Exam: Monday 5/18/15 8:00 AM-10:45 AM The aim
More informationCourse description. Syllabus for MATHEMATICS FOR ECONOMISTS
Syllabus for MATHEMATICS FOR ECONOMISTS Lecturers: Kirill Bukin, Dmitri Pervouchine, Boris Demeshev Class teachers: Boris Demeshev, Daniil Esaulov, Pavel Zhukov, Petr Lukianchenko, Vasily Bogdan, Ayana
More informationMATH 20F: LINEAR ALGEBRA LECTURE B00 (T. KEMP)
MATH 20F: LINEAR ALGEBRA LECTURE B00 (T KEMP) Definition 01 If T (x) = Ax is a linear transformation from R n to R m then Nul (T ) = {x R n : T (x) = 0} = Nul (A) Ran (T ) = {Ax R m : x R n } = {b R m
More informationConceptual Questions for Review
Conceptual Questions for Review Chapter 1 1.1 Which vectors are linear combinations of v = (3, 1) and w = (4, 3)? 1.2 Compare the dot product of v = (3, 1) and w = (4, 3) to the product of their lengths.
More informationMATH 1120 (LINEAR ALGEBRA 1), FINAL EXAM FALL 2011 SOLUTIONS TO PRACTICE VERSION
MATH (LINEAR ALGEBRA ) FINAL EXAM FALL SOLUTIONS TO PRACTICE VERSION Problem (a) For each matrix below (i) find a basis for its column space (ii) find a basis for its row space (iii) determine whether
More informationoblika število ur število KT izvaja Predavanja 45 1,5 učitelj Seminar 30 1 učitelj, sodelavec SKUPAJ 75 2,5
UČNI NAČRT: Analiza IV Realna analiza Osnovni podatki o predmetu 1. Ime predmeta: Analiza IV Realna analiza 2. Število KT (seštevek iz tabel spodaj): 6 3. Učni jezik: slovenski Podatki o umeščenosti predmeta
More informationMath 200 A and B: Linear Algebra Spring Term 2007 Course Description
Math 200 A and B: Linear Algebra Spring Term 2007 Course Description February 25, 2007 Instructor: John Schmitt Warner 311, Ext. 5952 jschmitt@middlebury.edu Office Hours: Monday, Wednesday 11am-12pm,
More information22m:033 Notes: 7.1 Diagonalization of Symmetric Matrices
m:33 Notes: 7. Diagonalization of Symmetric Matrices Dennis Roseman University of Iowa Iowa City, IA http://www.math.uiowa.edu/ roseman May 3, Symmetric matrices Definition. A symmetric matrix is a matrix
More informationUČNI NAČRT PREDMETA / COURSE SYLLABUS. Študijska smer Study Field
Predmet: Course Title: UČNI NAČRT PREDMETA / COURSE SYLLABUS ORGANSKA KEMIJA I ORGANIC CHEMISTRY I Študijski program in stopnja Study Programme and Level Študijska smer Study Field Letnik Academic Year
More informationSUMMARY OF MATH 1600
SUMMARY OF MATH 1600 Note: The following list is intended as a study guide for the final exam. It is a continuation of the study guide for the midterm. It does not claim to be a comprehensive list. You
More informationLinear Algebra. and
Instructions Please answer the six problems on your own paper. These are essay questions: you should write in complete sentences. 1. Are the two matrices 1 2 2 1 3 5 2 7 and 1 1 1 4 4 2 5 5 2 row equivalent?
More informationMATHEMATICS. Course Syllabus. Section A: Linear Algebra. Subject Code: MA. Course Structure. Ordinary Differential Equations
MATHEMATICS Subject Code: MA Course Structure Sections/Units Section A Section B Section C Linear Algebra Complex Analysis Real Analysis Topics Section D Section E Section F Section G Section H Section
More informationALN - Linear Algebra
Coordinating unit: 230 - ETSETB - Barcelona School of Telecommunications Engineering Teaching unit: 749 - MAT - Department of Mathematics Academic year: ECTS credits: 2018 6 Teaching languages: Catalan,
More informationArchive of past papers, solutions and homeworks for. MATH 224, Linear Algebra 2, Spring 2013, Laurence Barker
Archive of past papers, solutions and homeworks for MATH 224, Linear Algebra 2, Spring 213, Laurence Barker version: 4 June 213 Source file: archfall99.tex page 2: Homeworks. page 3: Quizzes. page 4: Midterm
More informationMath 307 Learning Goals
Math 307 Learning Goals May 14, 2018 Chapter 1 Linear Equations 1.1 Solving Linear Equations Write a system of linear equations using matrix notation. Use Gaussian elimination to bring a system of linear
More informationPreface. Figures Figures appearing in the text were prepared using MATLAB R. For product information, please contact:
Linear algebra forms the basis for much of modern mathematics theoretical, applied, and computational. The purpose of this book is to provide a broad and solid foundation for the study of advanced mathematics.
More informationMath 520 Exam 2 Topic Outline Sections 1 3 (Xiao/Dumas/Liaw) Spring 2008
Math 520 Exam 2 Topic Outline Sections 1 3 (Xiao/Dumas/Liaw) Spring 2008 Exam 2 will be held on Tuesday, April 8, 7-8pm in 117 MacMillan What will be covered The exam will cover material from the lectures
More informationUpon successful completion of MATH 220, the student will be able to:
MATH 220 Matrices Upon successful completion of MATH 220, the student will be able to: 1. Identify a system of linear equations (or linear system) and describe its solution set 2. Write down the coefficient
More informationAMS526: Numerical Analysis I (Numerical Linear Algebra for Computational and Data Sciences)
AMS526: Numerical Analysis I (Numerical Linear Algebra for Computational and Data Sciences) Lecture 1: Course Overview; Matrix Multiplication Xiangmin Jiao Stony Brook University Xiangmin Jiao Numerical
More informationServicepart. References 379. Index 381
377 Servicepart References 379 Index 381 Springer International Publishing AG 2017 B. Said-Houari, Linear Algebra, Compact Textbooks in Mathematics, DOI 10.1007/978-3-319-63793-8 379 References 1. H. Anton,
More informationUNIVERSITY OF NORTH ALABAMA MA 110 FINITE MATHEMATICS
MA 110 FINITE MATHEMATICS Course Description. This course is intended to give an overview of topics in finite mathematics together with their applications and is taken primarily by students who are not
More information