Good Books for Numerical Analysis & Mathematica for Learning

[MidgetDwarf]

I am currently working through Spivak, and have finished Geometry by Moise. I wanted to learn numerical analysis on my own. I could take it at the university, but I rather use the elective for differential geometry.

What are good books on Numerical Analysis?

I have completed 2 books in Linear Algebra (Axler and Friedberg). Differential Equations ( Terrebaun/Ross).

I have access to Mathematica for free. Is Mathematica a good program to use for Numerical Analysis?

My goal was to learn programming, by motivating the learning with Numerical Analysis.

 

[MathematicalPhysicist]

For my BSc studies I used both the books by de-Boor and Conte called: "Elementary numerical analysis: an algorithmic approach" and Arieh Iserles book called:"A first course in the numerical differential equations" it was a course that combined numerical methods in integration and differentiation, splines B-splines etc and numerical methods for solving DEs such as Runga-Kutta.

I am not sure what's better at numerical calculations: matlab,mathematica or maple?
people say that MATLAB is better at numerical simulations and stuff in engineering while at symbolic stuff not so good like maple and mathematica.

 

[MidgetDwarf]

Thanks for the suggestions. Will check them out. What program did you have to use for your course? Did you find the program easy to use, or was it hard? Any good suggestions on a book for one of these programs? I know web sources exist, but I prefer to have a book.

 

[MathematicalPhysicist]

Well the course I took was mainly theoretical, besides one lecture which was dedicated to introduce us to MATLAB there weren't any numerical questions to use matlab, the final grade was given by the final exam.

For doing numerical exercises you can use either mathematica or matlab, just use the help in mathematica or use google to type for the specific commands you need.
It's not hard to use mathematica or MATLAB or maple it's just different syntax, if you have taken a course in a programming language you would see that these are similar).

 

[MidgetDwarf]

Well the course I took was mainly theoretical, besides one lecture which was dedicated to introduce us to MATLAB there weren't any numerical questions to use matlab, the final grade was given by the final exam.

For doing numerical exercises you can use either mathematica or matlab, just use the help in mathematica or use google to type for the specific commands you need.
It's not hard to use mathematica or MATLAB or maple it's just different syntax, if you have taken a course in a programming language you would see that these are similar).

Great, thanks. I am majoring in Pure Math. Just ordered the books.

 

[MathematicalPhysicist]

I hope you don't mind me asking, but what type of school let you pick a first course in numerical analysis as an elective course?
In my country in BSc studies in either Engineering or Natural Sciences they have one course in numerical analysis mandatory.

What are the mandatory courses that you are supposed to take in your BSc studies?

 

[MidgetDwarf]

I am a pure math major. The school is in the States. We need to take a course in Probability, Analysis/Complex, and Abstract Algebra. My electives can be from either applied math/pure math, or a combination of both.

I can choose from Topology, Number Theory, Differential Analysis, Partial Diff Equations, Diff Eq, Linear Algebra just to name a few.

 

[bacte2013]

Just curious, what are some major differences of the approximation theory and numerical analysis? My impression about NA is that it creates the algorithms and theorems regarding to approximating the unknown functions, but I am not sure.