• Man pages.
• Preprocessing, compiling, linking, and execution of a C-program.
• C program: global structure.
• C data types for numbers, also complex numbers.
• Arithmetic and comparison C operators.
• C mathematical functions; type generic functions; libm.

• Arithmetic, comparison, and compound assignment operators from the list of operators in C and C++.
• Ternary conditional operator (in the same list).
• C iteration statements (loops); and the C selection statements.
• Scope of variables.

• Pointers in computer programming (in particular, C-pointers and C-arrays);
• C syntax→Arrays (including dynamic arrays);
• C syntax→Pointers;
• C dynamic memory allocation.

• C syntax → Structures and Unions (concentrate on structures, we won't be using unions).
• C syntax → Functions → Global Structure → main invocation.
• C syntax → Miscellaneous → Command-line arguments.
• atoi (ascii to integer) and atof (ascii to double) functions from <stdlib.h>.
• Simple input with scanf function.
• Unix I/O redirection.
• Simple printf(...) or fprintf(stderr,...) debugging amounts to

  ...inserting printf commands that output more or less carefully chosen status information at key points in the program flow, observing that information and deducing what's wrong based on that information. ...Although often looked down on by users of modern debugging software, printf() debugging continues to prove itself indispensable.

  1. Switch on the necessary warnings (e.g. -Wall -Werror).
  2. Read carefully the error/warning messages from the compiler and act upon them. If a message seems cryptic, try the clang compiler (install it with sudo apt-get install clang). Clang largely takes the same options as GCC.
  3. Insert fprintf(stderr,...) command at the strategic points of the program and localize the source of the error.
  4. It is of advantage to define a TRACE macro (read the C preprocessor chapter) and use it instead of directly using fprintf function. The macro can then be simply disabled after debugging. For example:

     #ifndef NDEBUG
     #define TRACE fprintf
     #else
     #define TRACE(...)
     #endif
     

     or, more elegantly,

     #ifndef NDEBUG
     #define TRACE(...) fprintf(stderr,__VA_ARGS__)
     #else
     #define TRACE(...)
     #endif
     

• Make utility; Introduction go Makefiles in GNU make manual.
• C preprocessor → including files; macro definitions;

sudo apt-get --yes install gnuplot-x11
sudo apt-get --yes install pyxplot gv

Some of you might have managed to install a special version of gnuplot, called gnuplot-nox where 'nox' means 'no X-window'. This version, predictably, has no x-window terminal. If you plan to use gnuplot interactively, you have to install 'gnuplot', not 'gnuplot-nox'.

The two plotting utilities have very similar scripting languages but otherwise are somewhat different. Pyxplot uses LaTeX to render all text on the plot which is rather convenient. Gnuplot has more terminals. Look at their web-pages, gnuplot and pyxplot (specifically, the examples), and choose the one you like most (or both).

• The interface to the BLAS routines.
• The data type gsl_odeiv2_system with the fields function, jacobian, dimension, params to hold an Ordinary Differential Equations Initial Value System.
• The names of the available stepping algorithms: gsl_odeiv2_step_rk2, gsl_odeiv2_step_rk4, gsl_odeiv2_step_rk45, ... , gsl_odeiv2_step_bsimp. Note which of the algorithms require the Jacobian of the system.
• The driver functions "gsl_odeiv2_driver_alloc_y_new" and "gsl_odeiv2_driver_apply"

• gsl_function
• gsl_integration_qag
• gsl_integration_qags (singular integrand)
• gsl_integration_qagi (infinite interval)
• gsl_integration_qagiu (infinite upper interval)
• gsl_integration_qagil (infinite lower interval)
• gsl_integration_cquad

• gsl_multiroot_function
• gsl_multiroot_fsolver_alloc
• gsl_multiroot_fsolver_free
• gsl_multiroot_fsolver_set
• gsl_multiroot_fsolver_iterate
• gsl_multiroot_test_residual

• gsl_multimin_function
• gsl_multimin_fminimizer
• gsl_multimin_fminimizer_nmsimplex2
• gsl_multimin_fminimizer_alloc
• gsl_multimin_fminimizer_set
• gsl_multimin_fminimizer_iterate
• gsl_multimin_fminimizer_size
• gsl_multimin_fminimizer_test_size

1. The code is segmented into small methods/functions spanning no more than a screenful.
2. The names of functions, structures.members, and variables are meaningful and self-describing.
3. The logic of the code is easy to follow and easy to modify (by somebody else); only a small number of comments are needed in a good code.
4. Defensive programming: #include<assert.h> and use assertions plentifully: you can easily disable all assertions by simply recompiling the code with -DNDEBUG c-flag:

   CFLAGS += -DNDEBUG