Course Outline, Homework, Reading, and Exam Dates²

• 6 Direct Methods for Solving Linear Systems
  • Lecture 1 (Aug. 23) 6.1 Linear Systems of Equations, 6.2 Pivoting Strategies
  • Lecture 2 (Aug. 25) 6.3 Linear Algebra and Matrix Inversion, 6.4 The Determinant of a Matrix
• Assignment 1 (Aug. 30) 6.1 (5.a, 9, 12, 15, 16); 6.2 (1.b, 3.b, 9.a, 13.a); 6.3 (8th ed:1.b, 8.(a,d), 14$\Vert$9th ed:5.b, 12.(a,d), 18); 6.4 (7, 9, 11, 13)
  • Lecture 3 (Aug. 30) 6.5 Matrix Factorization
  • Lecture 4 (Sept. 1) 6.6 Special Types of Matrices
• Assignment 2 (Sept. 6) 6.5 (1.a, 3.b, 5.a, 9.a, 10.(a,b,c), 11); 6.6 (3.a, 5.a, 12.a, 17, 19, 20)
• Review and Test 1 (Sept. 6)
• 7 Iterative Techniques in Matrix Algebra
  • Lecture 5 (Sept. 8) 7.1 Norms of Vectors and Matrices, 7.2 Eigenvalues and Eigenvectors, 7.3 The Jacobi and Gauss-Siedel Iterative Techniques
  • Lecture 6 (Sept. 13) 7.4 Relaxation Techniques for Solving Linear Systems
• Assignment 3 (Sept. 15) 7.1 (2.a, 6.d, 11, 13); 7.2 (8th ed:1.d, 3.d, 12.a||9th ed:1.d, 5.d, 14.a); 7.3 (1.a, 3,a); 8th ed:7.3(9.a)||9th ed:7.4(3.a)
• • Lecture 7 (Sept. 15) 7.5 Error Bounds and Iterative Refinement
  • Lecture 8 (Sept. 20) 7.6 The Conjugate Gradient Method
• Assignment 4 (Sept. 22) 8th ed:7.4(2.d,4.d,9,10)||9th ed:7.5(2.d,4.d,9,10); 8th ed:7.5(3,14)||9th ed:7.6(3,14)
• Review and Test 2 (Sept. 22)
• 9 Approximating Eigenvalues
  • Lecture 9 (Sept. 27) 9.1 Linear Algebra and Eigenvalues, 9.2 Orthogonal Matrices and Similarity Transformations
  • Lecture 10 (Sept. 29) 9.3 The Power Method
• Assignment 5 (Oct. 4) 9.1 (1.a, 6.d, 11, 13); 8th ed:9.2(1.a,3.a,5.a,20)||9th ed:9.3(1.a,3.a,5.a,20)
• • Lecture 11 (Oct. 4) 9.4 Householder's Method, 9.5 The QR Algorithm
  • Lecture 12 (Oct. 6) 9.6 Singular Value Decomposition
• Assignment 6 (Oct. 11) 8th ed:9.3(1.a)||9th ed:9.4(1.a); 8th ed:9.4(1.a,8.11)||9th ed:9.5(1.a,8.11); 9th ed:9.6(1.b, 3.b)
• Review and Test 3 (Oct. 11)
• EXAM I (Oct. 13)
• Review (Oct. 18): 1 Mathematical Preliminaries and Error Analysis
• 2 Solutions of Equations in One Variable
  • Lecture 13 (Oct. 20) 2.1 The Bisection Method, 2.2 Fixed-Point Iteration
  • Lecture 14 (Oct. 25) 2.3 Newton's Method and Its Extensions
• Assignment 7 (Oct. 27) 1.1(1.d,2.c,4.a,9,14); 1.2(5.e,9.a,12,15.c,21); 1.3(3.a,8,15); 2.1(1,2.a,11,14); 2.2(3,9,12.c,19.a); 2.3(1,3,5.c,7.c,9.c,16,19,23)
• • Lecture 15 (Oct. 27) 2.4 Error Analysis for Iterative Methods, 2.5 Accelerating Convergence
  • Lecture 16 (Nov. 1) 2.6 Zeros of Polynomials and Muller's Method
• Assignment 8 (Nov. 3) No Homework for Week 8! Happy Halloween!
• Review and Test 4 (Nov. 3)
• 10 Numerical Solutions of Nonlinear Systems of Equations
  • Lecture 17 (Nov. 8) 10.1 Fixed Points for Functions of Several Variables
  • Lecture 18 (Nov. 10) 10.2 Newton's Method
• Assignment 9 (Nov. 15) 10.1(4,5,12); 10.2(2.b,3.c,5.c,12)
• • Lecture 19 (Nov. 15) 10.3 Quasi-Newton Methods, 10.4 Steepest Descent Techniques
  • Lecture 20 (Nov. 17) 10.5 Homotopy and Continuation Methods
• Assignment 10 (Nov. 22) 10.3(2.b,9,10.a); 10.4(1.a); 10.5(3.a,10)
• Review and Test 5 (Nov. 22)
• Review (Nov. 29)
• EXAM II (Dec. 1)