WEEK 1
Chapter 1 Mathematical Preliminaries
Quiz 1
Definition of limit, continuity, and differentiable
Fundamental Theorem of Calculus
Rolle's Theorem
Mean Value Theorem
Weighted Mean Value Theorem
Taylor's Theorem
Taylor series for exp(x), cos(x), sin(x)
Example 3 (page 10) Taylor series for cos(x) of degree 2 and degree 3
Quiz 2
Problem 1.9
Maple worksheet for Example 3
Maple worksheet for Problem 1.9

WEEK 2
Quiz 3
Taylor series for arctan(x), sin(x)/x
Quiz 4
Alternating series test
Integral test
Nested form for polynomials
Homework Problems
 
WEEK 3
Compute the infinite sum of 1/n from n=1 to infinity
Maple worksheet for the sum of 1/n from n=1 to infinity
Computing pi
Internal representation of integers
Two's complement
Internal representation of real numbers
Quiz 5

WEEK 4
Hidden bit, largest real number, smallest positive number, machine epsilon
Maple worksheets for largest integer, largest real, smallest positive real, machine epsilon
Absolute and relative errors
Solving a quadratic polynomial
Maple worksheet for solving a quadratic
Surface measure problem
Homework Problems
Test #1 on Chapter 1

WEEK 5
Chapter 2 Solutions of Equations in One Variable
Bisection method
Maple worksheet for Bisection Method
Bisection method error has linear convergence
Fixed point method
Maple worksheet for Fixed Point Method
Chord and secant problem
Error analysis for fixed point method
Fixed point method has linear convergence
Newton's method
Maple worksheet for Newton's Method
Secant method
Maple worksheet for the Secant Method
False position method
Maple worksheet for  the False Positon Method

WEEK 6
Maple worksheet comparing the root finding methods
Homework Problems
Aitken accelerated convergence
Steffensen's Method
Maple Worksheet for Accelerated Convergence
Horner's Rule and synthetic division
Muller's Method
Maple Worksheet for Muller's Method
Parabolic extrapolation
Maple Worksheet for Parabolic Extrapolation

WEEK 7
Homework Problems
Error Analysis for Newton's Method
Error Analysis for the Secant Method
Secant error is super linear
How computers calculate square roots
How computers divide
Chapter 3 Interpolation and Polynomial Approximation
Sequences: polynomial, exponential, second order difference equations
Method I: Matrix algebra solution
Method II: Lagrange polynomials

WEEK 8
Neville's Algorithm
Maple worksheet for Neville's Algorithm
Inverse Interpolation
Proof of Taylor's Theorem
Proof of Lagrange's Theorem
Vandermonde Determinant
Newton's Divided Difference

WEEK 9
Hermite interpolation
Homework Problems
Maple worksheet for interpolation

WEEK 10
Homework Problems
Maple worksheet for Runge's function and splines
Chapter 8.3 Chebyshev Polynomials
Maple worksheet for the Chebyshev Polynomials
Chapter 8.4 Rational Function Approximation
Maple worksheet for Pade' apprroximations
Homework Problems

WEEK 11
Homework Problems
Chapter 5 Initial Value Problems for Ordinary Differential Equations
Euler's Method
Taylor Method
Runge-Kutta Method
Adam-Bashforth Method
Adam-Moulton Method
Adam-Bashforth-Moulton predictor-corrector method
Maple worksheets for ODE

WEEK 12
Test #2
Homework Problems
Chapter 4 Numerical Integration and Integration
Numerical Differentiation
Composite Trapezoid rule and error bound and error estimate by extrapolation
Romberg Method

WEEK 13
Composite Trapezoid rule and error bound and error estimate by extrapolation
Romberg Method
Composite Simpson's rule and error bound and error estimate by extrapolation
Multiple Integrals
Gaussian Quadrature
Review