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.
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.