MANE 3351
Lecture 17
Classroom Management
Agenda
- Numerical Differentiation
- Homework 4 (due 10/29/2025)
- Homework 5 (due November 3 - no late work)
- Lab 7 after lecture (due 11/3/2025)
Resources
Handouts
- Lecture 17 slides
Lecture 17 slides marked- Test 2 - Fall 2024
Calendar
| Week | Monday Lecture | Wednesday Lecture |
|---|---|---|
| 9 | 10/27: Gaussian Quadrature | 10/29: Numerical Differentiation (not on Test 2) |
| 10 | 11/3: Linear Algebra | 11/5: Test 2 (Root Finding and Numerical Integration) |
Test 2
- Content
- Lectures 8 - 16 (9/29 - 10/27)
- Homeworks 3 - 5
- You are allowed one 4 inch by 6 inch notecard
- Calculator needed
- Previous test provided above
Lecture Topics
- Lecture 8 - Root Finding, Bisection lecture
- Lecture 9 - Bisection Method Error Analysis, False Position Method
- Lecture 10 - No lecture - Test 1
- Lecture 11 - Newton's Method
- Lecture 12 - Secant Method
- Lecture 13 - Numerical Integration, Trapezoid Rule
- Lecture 14 - Simpson's 1/3 Rule, Simpson's 3/8 Rule
- Lecture 15 - Romberg Integration
- Lecture 16 - Gaussian Integration
Derivatives
You are responsible for calculating the following derivatives:
- Polynomial: \(ax^3+bx^2+cx+d\) (arbitrary power)
- \(a\sin(bx)\)
- \(a\cos(bx)\)
- \(ae^{bx}\)
- \(a\ln(bx)\)
- Product Rule: \(\frac{d}{dx}f(x)g(x)=f(x)g^\prime(x)+f^\prime(x)g(x)\)
Lecture 17
The topic for Lecture 17 is numerical differentiation. This topic will NOT be on Test 2 and the material is taken from the Chapra and Canale textbook
Forward finite-divided-difference formulas
Backward finite-divided-difference formulas
Centered finite-divided-difference formulas
Example Problem
