## Math 110 - Course Content

The main topics covered in the course are Limits and Derivatives of elementary functions, Related Rates problems, Optimization, Graphing, and Approximations. We also review some key precalculus concepts, such as functions, points and lines, basic trigonometry, exponentials and logarithms, etc.

This is a detailed list of Learning goals for the course.

Below is a weekly schedule of the topics covered in each term. Note a “Week” represents approximately a week's worth of lecture time, not necessarily a calendar week. Unless otherwise stated, the section numbers listed in the Notes column refer to the textbook Contemporary Calculus by Dale Hoffman. Some sections of the textbook include material that is not part of the course, a list of these topics is given at the bottom of this page.

Note that the schedule below may change as the term progresses.

Term 1

 Week Topics Notes 1.1 Introduction Sect. 0.2 1.2 Lines in the Plane; Functions Sect. 0.2-0.4 1.3 Tangent Lines, Velocities, Growth Sect. 1.0 1.4 Evaluating limits Sect. 1.1, 1.2 1.5 Continuity and the Intermediate Value Theorem Sect. 1.3 1.6 The definition of derivative Sect. 2.0, 2.1 1.7 Derivatives: properties and formulae Sect. 2.2 1.8 Exponentials; more differentiation rules Sect. TBA 1.9 Trigonometry Sect. TBA 1.10 The chain rule Sect. 2.4 1.11 More on the chain rule; Review of logarithms Sect. 2.0 1.12 Exponential growth and decay Sect. TBA 1.13 The second derivative Sect. TBA

Term 2

 Week Topics Notes 2.1 Implicit differentiation Sect. 2.9 2.2 Related Rates problems Sect 2.6 2.3 more on related rates problems Sect 2.6 2.4 Extrema and the Mean Value Theorem Sect, 3.1, 3.2 2.5 The first derivative test Sect. 3.3 2.6 Concavity Sect. 3.3, 3.4 2.7 Asymptotic behaviour Sect. 3.6, 3.7 2.8 Curve sketching 2.9 Optimization Sect. 3.5 2.10 more on Optimization Sect. 3.5 2.11 Approximations TBA 2.12 more on Approximations TBA 2.13 Antiderivatives TBA

Note: You are not responsible for the content of the following sections of the textbook: section 0.1: all (although I recommend you read this introductory section for your own interest); section 0.2: Angles between Lines, Angle Formed by Intersecting Lines; section 0.4: Iteration of Functions, the Greatest Integer Function, A Really "Holey" Function; section 0.5: all; section 1.2: Comparing the limits of functions; List method for showing that a limit does not exist; section 1.3: Bisection Algortihm for approximating roots; section 1.4: all; section 2.3: A Really "Bent" function; section 2.5: Parametric equations; section 2.7: all; section 2.8: Relative error and percentage error, the differential of f.

Additional topics covered in the course that are not included in the textbook are: a review of trigonometric, exponential and logarithmic functions, Taylor polynomials, antiderivatives.