San Antonio College Library

This book covers the main topics concerned with interpolation and approximation by polynomials. This subject can be traced back to the precalculus era but has enjoyed most of its growth and development since the end of the nineteenth century and is still a lively and flourishing part of mathematics. In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical...

The linear approximation of a function at a point is just the equation of the tangent line there. Since the value of the tangent line is very close to the value of the function near the point of tangency, we can use the linear approximation to estimate the function's value near that point.

You can write an expanded sum in collapsed summation notation by identifying the pattern among the terms in the expanded sum.

Trapezoidal rule, like Riemann sums and Simpson's rule, is a method you can use to approximate the area under the curve. Trapezoidal rule can be more accurate than the other methods, because it uses trapezoids to get close to the curve, instead of rectangles.

"Is there always a prime number between N and 2N? Where, approximately, is the millionth prime? And just what does calculus have to do with answering either of these questions? It turns out that calculus has a lot to do with these questions, as this book can show you. The theme of the book is approximations. Calculus is a powerful tool because it allows us to aproximate complicated functions with simpler ones. Indeed, replacing a function locally...

When you use a Riemann sum to approximate the area under the curve, you're just sketching rectangles under the curve, taking the area of each rectangle, and then adding the areas together. When you use midpoints, it means that you draw the rectangles such that the midpoints of their top edges touch the curve.