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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 an assistant professor of Mathematics. It is intended for all students in the sciences, though the emphasis is on proofs and foundations over computations. Its sincere wish is to awaken in the student a love of mathematical argument, and to inspire her or him 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.