Calculus Notes - Summary

  • These notes serve as the foundation for the calculus portion of MATH1131 and MATH1141, but not all content is included in the syllabuses; refer to Moodle for a detailed syllabus.
  • University courses present material rapidly, requiring consistent effort from the beginning of the session.
  • Keep up with lectures and related problems.
  • The notes are a supplement, not a replacement, for lectures and tutorials, which expand on the content and aid understanding.
  • The lectures will clarify the relative importance of different topics in the notes.
  • Tutorials are for asking questions about both theory and problems covered in lectures.
  • Some material is marked with [H] for higher difficulty, or [X] for MATH1141 students.
  • Problems marked [V] have video solutions on Moodle.
  • It's essential to complete problems at the end of each chapter, attempting a representative selection if time is limited; Moodle provides advice on this.
  • Online Tutorials are available on Moodle.
  • Proficiency in Maple is expected for tests and the end-of-term examination, including understanding its syntax and output.
  • Robert Taggart and Peter Brown prepared this version of the Calculus Notes, building on the work of Tony Dooley and other members of the School of Mathematics and Statistics.
  • Copyright is held by The University of New South Wales, ©2020.
  • The calculus course for both MATH1131 and MATH1141 utilizes these Calculus Notes.
  • A detailed syllabus and lecture schedule will be available on Moodle.
  • The computer package Maple will be used; refer to the First Year Maple Notes for an introduction.
  • Calculus problems are at the end of each chapter and on Moodle.
  • Problems are marked [R] for routine, [H] for harder, and [X] for MATH1141 content.
  • Start with [R] problems, then attempt [H] problems, seeking help in tutorials if needed.
  • [V] problems come with video solutions on Moodle.
  • MATH1141 students should also complete [X] problems.
  • Practice is key to success: work through a wide range of problems to develop both problem-solving and clear mathematical writing skills.
  • Keep a workbook for practicing solutions to mathematical problems.
  • Calculus originated from the combination of algebra, geometry, and trigonometry with the limiting process, developed independently by Isaac Newton and Gottfried Leibniz.
  • Calculus has broad applications in engineering, physics, chemistry, biology, geology, surveying, sociology, economics, and statistics.
  • It includes differential calculus and integral calculus, linked by the fundamental theorem of calculus.
  • The concept of the limit is the underlying tool, applied to functions.
  • The chapter introduces functions, inequalities, and absolute values, and reviews sets of real numbers in preparation for discussing limits.