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Week 1 (Lecture 1)
Sept 2015 S M Tu W Th F S 30 31 1 2 3 4 5Reading:
- Course Outline
- Introduction
Overton: Chap 1; Cheney and Kincaid: 1.1Week 2 (Lectures 2)
Sept 2015 S M Tu W Th F S 6 7 8 9 10 11 12Reading:
- Decimal and binary representation
- Computer representation of numbers
Overton: Chapters 2-3.Week 3 (Lectures 3-4)
Sept 2015 S M Tu W Th F S 13 14 15 16 17 18 19Reading:
- IEEE floating point representation
- Rounding
- Floating point operations
- Exceptional situations
Overton: Chapters 4-7; Cheney and Kincaid: 1.3Week 4 (Lectures 6-7)
Sept 2015 S M Tu W Th F S 20 21 22 23 24 25 26Reading:
- Floating point in C
- Taylor series
- Approximating a derivative
- Numerical cancellation
- MATLAB demo
- Solving a linear system of equations
- Gaussian elimination with no pivoting
- Overton: Chapters 10-11. Cheney and Kincaid: 1.2, 1.4, 2.1
Week 5 (Lectures 8-9)
Sept, Oct 2015 S M Tu W Th F S 27 28 29 30 1 2 3Solving a linear system of equations
Reading:
- Gaussian elimination with partial pivoting
- Some theoretical results about GEPP
- Solving tridiagonal systems by GENP
Cheney and Kincaid: 2.2 & 2.3
Week 6 (Lectures 10-11)
October 2015 S M Tu W Th F S 4 5 6 7 8 9 10Solving a nonlinear equation:Reading:
- Introduction
- The bisection method
- Newton's method
Cheney and Kincaid: 3.1, 3.2Week 7 (Midterm)
October 2015 S M Tu W Th F S 11 12 13 14 15 16 17
- In class Midterm on Oct 14.
Week 8 (Lectures 12-13)
October 2015 S M Tu W Th F S 18 19 20 21 22 23 24Solving a nonlinear equation:Reading:
- Newton's method
- The secant method
- Comparsions of the three methods.
Cheney and Kincaid: 3.2, 3.3
Week 9 (Lectures 14-15)
October, Novemebr 2015 S M Tu W Th F S 25 26 27 28 29 30 31Polynomial interpolation:Reading:
- Vandermonde form
- Lagrange form
- Newton form
Cheney and Kincaid: 4.1, 4.2
Week 10 (Lectures 16-17)
November 2015 S M Tu W Th F S 1 2 3 4 5 6 7Reading:
- Polynomial interpolation: Newton form, contd.
- Spline interpolation:
- Linear spline
- Cubic spline
Cheney and Kincaid: 6.1, 6.2Week 11 (Lectures 18-19)
November 2015 S M Tu W Th F S 8 9 10 11 12 13 14Reading:
- Cubic spline
- Least squares approximation
Cheney and Kincaid: 6.3, 9.1Week 12 (Lectures 20-21)
November 2015 S M Tu W Th F S 15 16 17 18 19 20 21Numerical integration:Reading:
- Rectangle rule
- Midpoint rule
- Trapezoid rule
- Simpson's rule
- Adaptive Simpson's rule
Cheney and Kincaid: 5.1, 5.3.
Week 13 (Lectures 22-23)
November 2015 S M Tu W Th F S 22 23 24 25 26 27 28Numerical solutions of ordinary differential equations:
- Gaussian quadrature rules
Reading:
- Introduction
- Euler's method
- Types of errors
- Trapezoid-Euler method and Midpoint-Euler method
Cheney and Kincaid: 5.4, 7.1Week 14 (Lectures 24-25)
November, December 2015 S M Tu W Th F S 29 30 1 2 3 4 5Reading:
- General Taylor series methods
- Runge Kutta Methods
- Review
Cheney and Kincaid: 7.2Week 15 (Lectures 26)
December 2015 S M Tu W Th F S 6 7 8 9 10 11 12Class time will be office hours