Working with applied math, this book allows students to solve most second-order differential equations; however, answers you get in numerical analysis are only in numeric approximations. Life of Fred Calculus is recommended as a prerequisite because students are learning how to integrate tons of functions. Students write fairly simple computer programs in this course. Complete solutions are included. 
 
Solving every equation that is in the form f(x) = 0. 
Bisection method. 
Solving f(x) = 5. 
Solve x to the x power equals 5.
Solving f(x) = g(x). 
Finding the value of cos(cos(cos(cos(cos(cos(cos(cos(cos(cos(cos(cos(x)))))))))))). 
Secant method. 
Newton method. 
Finding the polynomial to interpolate five points. 
The Lagrange polynomial. 
Dealing with 900 points and no given f(x). 
Splines. 
Piecewise polynomial approximations. 
Numerical integration. 
Why Simpson's rule is true. 
Numerical differentiation. 
Monte Carlo methods. 
First-order ordinary differential equations starting with y' = g(x). 
Starting with y' = g(x, y). 
Euler's method. 
Runge-Kutta method. 
Second-order differential equations. 
Second-order boundary problems. 
Second-order initial value problems. 
Parabolic partial differential equations. 
Elliptic partial differential equations. 
Hyperbolic partial differential equations.