Sheldon Axler's Precalculus: A Prelude to Calculus, 3rd Edition focuses only on topics that students actually need to succeed in calculus.  This book is geared towards courses with intermediate algebra prerequisites and it does not assume that students remember any trigonometry. It covers topics such as inverse functions, logarithms, half-life and exponential growth, area, e, the exponential function, the natural logarithm and trigonometry. 

Dr. Sheldon Axler is the dean of the College of Science and Engineering at San Francisco State University in California. He has received over a dozen awards, grants, and fellowships from different organizations including the M.I.T. Teaching Award, National Science Foundation ILI Grant, and the National Science Foundation Research Grants. He had published extensively in journals and has three other books to his name.