48 Hours of Honors Calculus

This textbook is ideal for a year-long sequence of Honors Calculus at the undergraduate level, or for self-study; it is based on an Honors Calculus course the author has taught at Clark University, where he is a professor of Mathematics. It is intended for all students in the sciences, though the emphasis is on proofs and foundations over computations. Its wish is to awaken in the student a love of mathematical argument, and to inspire them to major in mathematics.One novelty of the book is that it includes a substantial amount of ordinary differential equations (ODEs) and multivariable calculus, topics usually not covered in an Honors Calculus course. Applications are also discussed: compound interest and continuous compounding in finance; Hamiltonian systems and ODEs inspired from physics and population dynamics; and an introduction to gradient descent and neural networks. There are over 100 exercises.This text is a natural precursor to more advanced undergraduate texts in real analysis, such as Understanding Analysis by Stephen Abbott or Principles of Mathematical Analysis by Walter Rudin. Read more