Math 32800 Methods of Numerical Analysis
Exam Schedule
Exam 1: Tuesday 10 March
Exam 2: Tuesday 21 April
Office Hours
Mondays 3-4pm
Matlab
CCNY students can download matlab free of charge from this download Matlab page . Just install standard matlab. You need not install any add-on products. (You may also try to use Matlab through the CUNY Virtual Desktop.)
Matlab Tutorials
Matlab Onramp. Get started quickly with the basics of Matlab in less than 2 hours.
Kelly Black's MATLAB Tutorial is a solid introduction to the basic code we will study in our course. In particular she includes code for a Gaussian elimination algorithm and code for Euler's method. These are two of the most important algorithms we will study.
Textbook
Follow these instructions to receive a 20% discount when purchasing our textbook, "A First Course in Numerical Methods", by Ascher and Greif, Siam, 2011. There is a digital version as well. You must get access to this text. I will place a copy on reserve in the Science library in Marshak.
Flipped Classroom
Here is some good advice: Read assigned sections from our textbook before class. Learning how to read a math textbook will be helpful in this course as well as in all your future math courses. Read the section we will cover in class before coming to class. You will not fully understand the topic after a first reading. Do not worry. You will pick up enough of the idea to make your time in class more productive. After class you will then most likely need to reread the section multiple times to become comfortable with the material.
Exercise Sets
The best way to learn the material is to consistently do many exercises on your own, or with a group of classmates. It is better to spend a couple hours every day doing problems rather than spending the weekend before the exam cramming for eight hours a day. Consider the final exam like running a marathon and the problems as your training sessions. If you consistently do problems (train) then you will be well-prepared for the final exam. However if you have long gaps between working on problems you will always have difficulty getting back into the math mindset necessary to complete the problems. The first day of training is always the most painful.
Getting Help
Final piece of good advice: Form study groups and go to office hours or tutoring when you inevitably get stuck. I will be available for 30 minutes after each class for office hours. A quick conversation with me or with a group of students after class sometimes clears up a confusing point. Do not spend more than a day or two being stuck on a problem or try to master a concept from class or our textbook. There is not enough time in the semester to remain stuck and not practicing. Ask for help instead. If you cannot make office hours there is free CCNY.
Grading Factors
HW Average: 4% of course grade.
Quiz Average: 12% of course grade.
Midterm Exam 1: 22% of course grade.
Midterm Exam 2: 22% of course grade.
Final exam 40% of course grade
There will be no make-up quizzes. If you miss one of our two in-class exams, your final exam will serve as your make-up in-class exam. All topics covered on the in-class exams will be covered on the final exam. There will be a make-up final exam if you are ill on the final exam day.
Moreover, at the end of the course if your final exam average is superior to your in-class exam 1 grade or your in-class exam 2 grade, then you can use your final exam grade to replace all lower in-class exam average(s). For instance, if your hw grade is 100, quiz average is 85, midterm 1 grade 86, midterm 2 grade 77, and final exam grade 79 then your course grade will be computed as 4% * 100 + 12% * 85 + 22% * 86 + 62% * 79 = 82.1 course grade.
Quiz and exam questions will be similar to the assigned textbook homework questions, exact replicas sometimes. You should attempt all the assigned homework problems to learn the material and prepare for quizzes and exams. If you have done all assigned hw problems, there should be no surprises on quizzes and exams.
Assignments from "A First Course in Numerical Methods", by Ascher and Greif
Chapter 1 and partial solutions
Chapter 3 and partial solutions
Chapter 4 and partial solutions
Chapter 5 and partial solutions
Chapter 6 and partial solutions
Chapter 7 and partial solutions
Chapter 8 and partial solutions
Chapter 9 and partial solutions
Chapter 10 and partial solutions
Chapters 14, 15, 16 and partial solutions
Class Slides from "A First Course in Numerical Methods", by Ascher and Greif
Practice Final Exam
HW Quizzes
Here are some hw quiz questions I've used in past semesters as well as some solutions, solutions2.
Review of Linear Algebra
Many students struggle with the numerical linear algebra component of this course because their linear algebra skills are weak. Most students need to review linear algebra while taking 328. I will place a few copies of a linear algebra textbook You should be familiar with chapters 1,2,3,5,6,7, and 8 and the exercises from those sections.
Review of Calculus
There are a few copies of Thomas' Calculus Early Transcendentals (14th Edition) You should be familiar with sections 2.5 Intermediate Value Theorem, 4.1 Extreme Values, 4.2 The Mean Value Theorem, 8.7 Numerical Integration , 9.1 Euler's Method, 9.2 First order linear, 10.1 Sequences, 10.2 Series, 10.7 Power Series, 10.8 Taylor Series, 10.9 Convergence of Taylor Series, 10.10 Applications of Taylor Series as well as the included exercises from those sections.
Review of Differential Equations
It is important to understand the difference between exact solutions and approximate solutions to IVPs. We will study approximate solutions in this course while exact solutions are the focus of math 391.
Watch the first three videos of Arthur Mattuck Differential Equations Lecture Videos provide solid geometric motivation of Euler's method, as well as explanations of some higher order methods we will study at the end of our course. Please watch these three videos.
The notes and exercises linked below will help you better appreciate the videos.
Graphical and Numerical Methods (Notes)
