- C. F. Gerald and P. O. Wheatley,
*Applied Numerical Analysis*, 5th Ed., Addison-Wesley, 1994.

- Lecture 1: Introduction to MCS 471 Numerical Analysis
- Lecture 2: Examples of Numerical Errors; Floating Point Representation (GW0.5)
- Lecture 3: Finite Single and Double Precision Differences (GW0.5)
- Lecture 4: Holiday Allowance
- Lecture 5: Machine Epsilon; Significant Digits; Catastrophic Cancellation (GW0.5)
- Lecture 6: Method of Bisection (GW1.2)
- Lecture 7: Secant Method (skip False Position) (GW1.3)
- Lecture 8: Newton-Raphson's Method (GW1.4)
- Lecture 9: More Newton's, Unstable Examples; Quadratic Convergence Rate (GW1.4, 1.11)
- Lecture 10: Maple for Nonlinear Equations; Secant Method Convergence (GW1.11)
- Lecture 11: Fixed Point Method (GW1.6); Muller's Method (GW1.5)
- Lecture 12: Application of Inverse Quadratic Interpolation to Muller Root; Optimization Using Golden Section Search
- Lecture 13: Introduction to Linear Algebra (GW2.2)
- Lecture 14: Show Computational Complexity Cramer's Rule O(e*(n+1)!)
- Lecture 15: Forward Gaussian Elimination and Backward Substitution (GW2.3-4)
- Lecture 16: Computational Complexity of FGE & BS, also Gauss-Jordan Elimination (GW2.4)
- Lecture 17: Computational Complexity of Inverse and Determinants by FGE (GW2.4,2.7); (Emphasize Efficiency by Correcting Inefficient Notions Taught in Linear Algebra Courses)
- Lecture 18: First Hour Exam on Precision and Nonlinear Equations
- Lecture 19: Review First Hour Exam; Problem of Small Pivots (GW2.6)
- Lecture 20: FGE with Virtual Row Pivoting and Virtual Row Scaling; Algorithm (GW2.4); (Emphasize Computational Accuracy with Ill-Conditioned Examples)
- Lecture 21: FGE with Virtual Full Pivoting (GW2.4)
- Lecture 22: LU Decomposition (Doolittle Version using FGE with Saved Multipliers); Maple and Octave for Computational Linear Algebra (GW2.5)
- Lecture 23: Norms (GW2.8); Condition Numbers (GW2.9)
- Lecture 24: Error Propagation through Condition Numbers (GW2.9)
- Lecture 25: Iterative (Jacobi Only, Save rest for MCS 571) Methods (GW2.10)
- Lecture 26: Multidimensional Newton's Method; Jacobians (GW2.12); Mention Eigenvalue Problems; begin Lagrange Polynomial Interpolation
- Lecture 27: Introduction to Interpolation; Newton-Horner's Method of Fast Polynomial Computation (GW3.1,3.2); Calculus of Finite Differences
- Lecture 28: Finite Difference and Divided Difference Tables; Newton-Gregory Polynomial Form (GW3.3, 3.4)
- Lecture 29: Second Hour Exam on Computational Linear Algebra
- Lecture 30: Review Second Exam
- Lecture 31: Theoretical Errors in Interpolation (GW3.9);
- Lecture 32: Computational Complexity of Polynomial Interpolation: Lagrange versus Newton; Mention Splines If Time Permits; Dispel Notion of High Degree Polynomial Approximation with Problems of Nonuniform Convergence
- Lecture 33: Discrete Approximation of Coordinates, Ordinates and Derivatives (GW4.2,4.3) (Caution: Text is Overly Complicated Here as Elsewhere, Emphasize Forward, Backward and Central Finite Difference Forms, Using Central Only for Second Order)
- Lecture 34: Numerical Integration, Simple Newton-Cotes Rules and Local Theoretical Errors: Rectangular (LRR1, RRR1, MPRR1), Trapezoidal (TR2) and Simpson's (1/3: SR3) Rules (GW4.4, 4.5, 4.6)
- Lecture 35: Composite Rules and Global Theoretical Errors (GW4.5-4.7); (Emphasize Efficient Algorithms Saving Floating Point Operations and Function Evaluations)
- Lecture 36: More Composite Rules ; Use of Global Theoretical Error Estimates to Estimate Minimal Step Size or Number of Nodes; Extrapolation To The Limit Techniques (GW4.4.4-4.7); Use of Maple int and student Package for TRN and SRN
- Lecture 37: Gaussian Quadrature Rules: GR1=MPRR1, GR2, GR3, MXGRN (Gauss-Legendre); Briefly Mention Gauss-Laguerre, -Hermite, -Chebychev for Singular Integrals (GW4.9); Briefly Explain Idea of Adaptive Quadrature and Relation to Extrapolation (GW4.10)
- Lecture 38: Theoretical versus Truncation (Rounding/Chopping) Errors (Dispel Pure Math Silly Notion of Taking Step Size as Small as You Please: If Global Theoretical Error = O(h^{q+1}) and Global Truncation Error = O(MacEps/h), where StepSize = h, MacEps = O(b^{1-p}), and p = Digits of Precision in Base = b, Then There Exists Finite Optimal Step Size h* = O(MacEps^{1/(q+1)}/q)); Begin Euler's Method for Numerical Solution of ODEs (GW5.3)
- Lecture 39: More Numerical Solution of ODEs, Euler's Method, Local Theoretical Error, Modified Euler's Method (Approximate TR2 via Predication and Correction) (GW5.3, some 5.10?); (Motivate by Equivalence of EM to LRR1 and Calculus Tangent Line Approximation)
- Lecture 40: Runge-Kutta Method (RK4: Approximate Simpson's Rule SR3; Notion Helps to Remember Form); Algorithm (GW5.4); Start Multistep (GW5.5); Use of Maple and Octave
- Lecture 41: More Predictor-Corrector Multistep Methods (Emphasize Adams-Moulton Method Only; Text is Over Done Here; Skip Milne's Method) (GW5.5, 5.7); Global Discretization Error for Euler's Method (GW5.10); (Caution: Global Estimate Apply Only to Unstable Case)
- Lecture 42: More Euler Global Theoretical Error but with GLobal Truncation (Rounding/Chopping) Error (If Global Theoretical Euler Error = O(h) and Global Roundoff Error = O(MacEps/h), Then There Exists Finite Optimal Step Size h* = O(\sqrt{MacEps})) (GW5.9-5.10, poorly)
- Lecture 43: Boundary Value Problems and Shooting Method (GW6.1) (Caution: Motivate by Nonlinear Example, like y"(x) = -y^2(x), since Method Most Useful for Nonlinear Problems, Unlike Text Example)
- Lecture 44: Boundary Value Problems and Linear Algebra Methods (GW6.2) (Emphasize Thomas Elimination Algorithm for Tridiagonal System, noting the Importance of Tridiagonal Form Efficiency in Numerics; Caution: Do Nontrivial, Nonconstant Coefficient, Second Order, Linear Boundary Value Problem Example)
- Lecture 45: General Form of Thomas Tridiagonal Algorithm; Review for Final Examination; Mention Eigenvalue Problems if Time Permits.

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