MA103/MA110 Lecture Notes
Please note that the lecture notes linked to this page are skeletal only. They do not replace going to the lectures themselves.
The intention is for students to have access to these brief notes before the scheduled lectures in order to be better prepared for instruction on the relevant topics during class time. Further clarification and examples will be provided in the lecture. It is hoped that by having a copy of the notes contained here, students will spend less time copying from the board and have more time to really listen to what their instructor is saying, to further comprehend the material and to participate in any discussion.
Students should be aware that such things as the order of topics covered and notation may vary slightly depending on the preferences of their instructor.
Note: Some changes have been made in regards to the topics now taught in MA103/MA104. Thus, the following notes will not match the week-by-week schedule of the current lectures. But all topics are covered and should still be useful for both the current MA103 and MA110 classes.
These files are in pdf format, so a pdf reader is required to be able to view them. The latest version of Acrobat Reader can be downloaded for free; just click here. Note that the printed version of such files do not always look the way that we want them to look, so be careful of errors (especially in some of the special notation we use) seeming to appear on printed copies.
Week 1 - Notation; Basics of Functions; Exponential Functions; Logarithm Functions; Introduction to Limits; Continuity; Rates of Change; The Derivative
Week 2 - Differentiation Formulae including Derivatives of Exponential and Trigonometric Functions and the Chain Rule
Week 3 - Implicit Differentiation; Inverse Function Theorem; Inverse Trigonometric Functions; Higher Order Derivatives; Derivatives of Logarithm Functions
Week 4 - Linear Approximations and Differentials; Extreme Values; Mean Value Theorem
Week 5 - Curve Sketching; L'Hospital's Rule and Indeterminate Forms
Week 6 - Antiderivatives; Sigma Notation; Area
Week 7 - The Definite Integral and its Properties; The Fundamental Theorem of Calculus
Week 8 - Indefinite Integrals; Substitution; Area Between Curves; Volume (now covered in MA104); Integration by Parts
Week 9 - Partial Fractions; Approximate Integration (now covered in MA104)
Week 10 - Integration Strategies; Improper Integrals (now covered in MA104)
Week 11 - Functions of Several Variables and Partial Derivatives; Implicit Partial Differentiation; Higher Order Partial Derivatives
Week 12 - Chain Rule for Multivariate Functions; Multivariate Optimization