This is an online textbook written by Evans M. Harrell II and James V. Herod, both of Georgia Tech. It is suitable for a first course on partial differential equations, Fourier series and special functions, and integral equations. Readers are expected to have completed two years of calculus and an introduction to ordinary differential equations and vector spaces.
This text is suitable for students who are quite comfortable with calculus and are mainly interested in problem solving. For that reason, this text does not stress proofs, although it tries to give careful statements of theorems and to discuss the technical assumptions. Also, it does not spend much time with material like methods to calculate the integrals arising in Fourier analysis, choosing instead to appeal to software to do some calculations.
Currently, the calculations are usually done with Mathematica
, although some parts of the text are also available using Maple
. It is not at all necessary to have previous experience with mathematical software, since the calculations in the text are self-explanatory. On the other hand, there are links to many more detailed calculations done in Mathematica notebooks, which will be useful for those who are familiar with Mathematica or who are learning it. Many Georgia Tech
students have also found Matlab
to be useful for calculations like those in this text.