LINEAR ALGEBRA: M340L EE, 54300, Fall 2017
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1 LINEAR ALGEBRA: M340L EE, 54300, Fall 2017 TTh 3:30 5:00pm Room: EER Click for printable PDF Version Click for Very Basic Matlab Pre requisite M427J Instructor: John E Gilbert E mail: gilbert@math.utexas.edu Office: RLM Office Hours: T, W 1:00 3:00pm, (and by appointment) There is no required text for the course Learning Modules covering each lecture can be found on QUEST at You will be expected to have read each Learning Module carefully before the corresponding in class lecture. If you wish to consult a textbook (cheapest copy/edition is fine!) or online notes, try: RECOMMENDED COURSE TEXTS APPLIED LINEAR ALGEBRA by P. J. Olver & C. Shakiban RYAN: Linear Algebra, Signal Processing. A unified approach Click for PDF COURSE GRADE Your course grade will be determined by Quest Homework (16%): Multiple Choice Homework assignments will be set weekly via Quest, but only the highest 12 homework scores will be counted. Exams (48%): 3 exams will be set as announced in the day by day timetable. These will be in Multiple Choice format and will be held in class. All exam scores will be counted. Final (36%): a 3 hour comprehensive Final in Multiple Choice format will be set. Time: TBA. Room: TBA. All Homework, Exam and Final scores will be posted on Quest only. Your grade will be one of GRADE CUT OFFS WILL NOT BE ANNOUNCED UNTIL AFTER THE FINAL EXAM. NO CALCULATORS ON EXAMS OR FINAL!!
2 SEMESTER SYLLABUS HW 01: Review: (briefly covered in class) LM 00a Vectors and Matrices LM 00b Gauss Elimination LM 00c Reduced Row Echelon Form LM 00d Matrix Inverses LM 00e Determinants LM 01a Matrix Algebra HW 02: LM 01b Linear Systems LM 01c Factorizations HW 03: LM 02 Vector Spaces LM 03 Subspaces, Span HW 04: LM 04 Linear Independence, Bases LM 05 Fundamental Matrix Subspaces HW 05: LM 06 Inner Products, Orthogonal Bases LM 07 Inequalities, Norms HW 06: LM 08 Complex Numbers LM 09 Complex Spaces HW 07: LM 10 Linear Functions LM 11 Linear Transformations HW 08: LM 12 Continuous Time Fourier Series LM 13 Gram Schmidt HW 09: LM 14 Orthogonal and Unitary Matrices LM 15 QR Factorization HW 10: LM 16 Orthogonal Subspaces LM 17 Discrete Time Fourier Series HW 11: Review: LM 18a Eigenvalues, Eigenvectors LM 18b Diagonalization LM 19 Differential Equations HW 12: LM 20 Linear, Time Invariant (LTI) Systems LM 21 Fast Fourier Transform HW 13: LM 22 Diagonalization of Symmetric Matrices LM 23 Spectral Thm, Positive Definite Matrices HW 14: LM 24 Singular Value Decomposition LM 25 Image Compression, PCA HW 15: Review FINAL EXAM: Dec 16, 2:00 5:00pm, Room: EER 1.516
3 VECTOR SPACES introduced: real polynomials of degree at most. Real or complex valued periodic trigonometric polynomials of degree at most. complex polynomials of degree at most, and positive and negative degree at most respectively. Continuous time signals (real or complex valued) periodic Continuoustime signals (real or complex valued). Discrete time signals (real or complex valued) period Discrete time signals (real or complexvalued). Spaces of Linear Functions, Transformations, Operators between vector spaces. real or complex valued continuous functions defined on the periodic real or complex valued continuous functions defined on. Context should make clear whether the functions are assumed to be real valued or complex valued. BASES introduced: Standard Basis for. Standard Basis for. Standard (real) Monomial Basis for. Standard (complex) Monomial Basis for. Standard (complex) Monomial Basis for. Fourier Cosine Sine basis for real. Complex Exponential basis for complex.
4 Frequency basis for where LINEAR TRANSFORM PAIRS introduced: Continuous Time Complex Fourier Series: (DFT) Discrete Fourier Transform: with,
5 The syllabus below is for Prof Robert Heath's EE313 course. The chapters and sections refer to the ''Systems and Signals'' (2nd Edn) text by Oppenheim and Willsky.
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8 M427J Syllabus: Differential Equations with Linear Algebra TEXT: Differential Equations and their Applications, by Martin Braun. Chap 1: First Order Differential Equations (4 hours) 1.1 Introduction 1.2 First Order linear Differential Equations 1.4 Separable Equations 1.9 Exact Equations 1.10 Existence Uniqueness Theorem; Picard Iteration Chap 2: Second Order Linear Diff. Eqts. (11 12 hours) 2.1 Algebraic Properties of Solutions 2.2 Linear Equations with Constant Coefficients Complex Roots Equal Roots; Reduction of Order 2.3 Non Homogeneous Equations 2.4 Variation of Parameters 2.5 Judicious Guessing 2.6 Mechanical Vibrations 2.8 Series Solutions Singular Points, Euler Equations Regular Singular Points, Frobenius Method Chap 3: Systems of Differential Equations (15 hours) 3.1 Algebraic Properties of Solutions of Linear Systems 3.2 Vector Spaces 3.3 Dimension of a Vector Space 3.4 Application of Linear Algebra to Diff. Eqts. 3.5 Theory of Determinants 3.6 Solutions of Simultaneous Equations 3.7 Linear Transformations 3.8 Eigenvalue Eigenvector Method 3.9 Complex Roots 3.10 Equal Roots 3.11 Fundamental Matrix Solutions; Chapter 3 Supplement: 3.A Matrix Vector Multiplication 3.B Vectors as Arrows in 3.C Null and Column Spaces 3.D Complete Solution Set of Systems (RREF) Chap 4: (Optional) Qualitative Theory (3 hours) 4.1 Introduction 4.2 Stability of Linear Systems 4.4 Phase Plane 4.7 Phase Portraits of Linear Systems Chap 5: Separation of Variables, Fourier Series (6 7 hours) 5.1 Two Point Boundary Value Problems 5.2 Introduction to Partial Diff. Eqts. 5.3 Heat Equation; Separation of Variables 5.4 Fourier Series 5.5 Even and Odd Functions 5.6 Return to the Heat Equation Chap 6: (Optional) Sturm Liouville Problems (3 hours) 6.1 Introduction 6.2 Inner Product Spaces 6.3 Orthogonal Bases, Hermitian Operators 6.4 Sturm Liouville Theory
9 OTHER INFORMATION Quest Charge: this course makes use of the web based Quest content delivery and homework server system maintained by the College of Natural Sciences. This homework service requires a $30 charge per student for its use, which goes towards the maintenance and operation of the resource. After the 12th day of class, when you log into Quest you will be asked to pay by credit card on a secure payment site. You have the option to wait up to 30 days to pay while still continuing to use Quest for your assignments. If you are taking more than one course using Quest, you will not have to pay more than $60 per semester. Quest provides mandatory instructional material for this course. For payment questions, questfees@cns.utexas.edu. Students with disabilities: the University of Texas provides appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at , TTY. If you plan on using such accommodations, you need to notify me early in the semester. Religious Holidays: by UT Austin policy, you must notify me of your absence at least 14 days prior to the observance of a religious holiday. If you must miss a class, examination, or assignment in order to observe a religious holiday, you will be given an opportunity to complete the missed work within a reasonable time after the absence. Emergencies: the following recommendations regarding emergency evacuation are from the Office of Campus Safety and Security: Occupants of buildings on The University of Texas at Austin campus are required to evacuate buildings when a fire alarm is activated. Alarm activation or announcement requires exiting and assembling outside. Familiarize yourself with all exit doors of each classroom and building you may occupy. Remember that the nearest exit door may not be the one you used when entering the building. Students requiring assistance in evacuation shall inform their instructor in writing during the first week of class. In the event of an evacuation, follow the instruction of faculty or class instructors. Do not re enter a building unless given instructions by the following: Austin Fire Department, The University of Texas at Austin Police Department, or Fire Prevention Services office. Behavior Concerns Advice Line (BCAL): For information on emergency evacuation routes and emergency procedures click on:
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