Course:MATH180/Archive/2011-2012/103/Syllabus

Here is the planned outline of the course. All the section number below refer to the textbook, except the course notes sections for Taylor polynomials.

This page will be updated twice a week all along the term so that it indicates exactly what have been covered in class. Moreover I will indicate here the reading assignments so be sure to check it regularly.

Week 1

• Tuesday 6th
  • No Class

• Thursday 8th
  • §2.1 The Tangent and Velocity Problems
  • §2.2 The Limit of a Function

Learning Objectives

1. Be able to explain the concept of a limit
2. Explain the relation between one-sided and two-sided limits

Week 2

• Tuesday 13th -- Read p. 99 & pp. 102-104
  • §2.3 Calculating Limits Using the Limit Laws

Learning Objectives

1. Compute limits using limit laws appropriately
2. Compute limits using the squeeze theorem
3. Understand the concept of continuity
4. Give examples of continuous functions

• Thursday 15th -- Read p.118 & pp. 120-123
  • §2.5 Continuity
  • §2.6 Limits at Infinity; Horizontal Asymptotes

Learning Objectives

1. Demonstrate whether or not a function is continuous
2. Explain and use the intermediate value theorem
3. Describe and compute horizontal asymptote

Week 3

• Tuesday 20th -- Read pp.143 - 145 & pp. 154 - 157
  • §2.7 Derivatives and Rates of Change
  • §2.8 The Derivative as a Function

Learning Objectives

1. Explain what the derivative of a function graphically means
2. Compute derivatives using the definition

• Thursday 22nd -- Read this article, pp.159-60 & Rules pp. 174-7
  • §3.1 Derivatives of Polynomials and Exponential Functions

Learning Objectives

1. Give examples of non-differentiable functions
2. Explain the relation between continuity and differentiability
3. Compute derivatives of polynomials and exponential functions
4. Compute equations of the tangent lines to such functions

Week 4

• Tuesday 27th -- Quiz -- Read pp. 179-81 & pp. 185-6
  • §3.2 The Product and Quotient Rules

Learning Objectives

1. Use correctly the product rule
2. Use correctly the quotient rule
3. Compute tangent lines using one of the above rules

• Thursday 29th -- Read Rules pp. 191 - 94 & Examples 1 to 4
  • §3.3 Derivatives of Trigonometric Functions
  • §3.4 The Chain Rule

Learning Objectives

1. Know and use the derivatives of trigonometric functions
2. Use the chain rule appropriately
3. Compute tangent lines using one of the above rules

Week 5

• Tuesday 4th October -- Read p. 61 & pp. 63-66
  • §1.6 Inverse Functions and Logarithms

Learning Objectives

1. Be able to compute an inverse function with correct domain and range
2. Know and use the inverse functions of ln x, log x, sin x, cos x, tan x with correct domain and range

• Thursday 6th -- Read pp. 209 - 211
  • §3.5 Implicit Differentiation
  • Review

Learning Objectives

1. Be able to compute implicit derivatives as the ones presented in the examples
2. Know and use the derivatives of arcsin x, arccos x and arctan x

Week 6

• Tuesday 11th
  • Midterm 1 (in class)

• Thursday 13th -- Read pp. 218 - 220
  • §3.6 Derivatives of Logarithmic Functions
  • §3.8 Exponential Growth and Decay - Part 1

Learning Objectives

1. Know and use the derivatives of the log functions
2. Use correctly the logarithmic differentiation technique

Week 7

• Tuesday 18th -- Read pp. 240 - 241
  • §3.8 Exponential Growth and Decay - Part 2

Learning Objectives

1. Know the differential equation defining exponential growth (or decay)
2. Know the function giving the solution of the above equation and use it solve such questions
3. Be able to solve Newton's Law of Cooling questions using the above

• Thursday 20th -- Read Examples 2 to 5 pp. 245 - 248
  • §3.9 Related Rates

Learning Objectives

Given such a question (eg. Speed camera question, etc.) you should be able to

1. Identify all the variables involved :
   • describe how they relate (using equations if relevant and/or writing a short paragraph)
   • make appropriate choices when a variable takes on constant values
2. draw a picture of the situation if needed
3. interpret rates in terms of derivatives with the appropriate variables
4. derive an equation which describes how the relevant rates are related and solve in that equation for the desired target rate

Week 8

• Tuesday 25th -- Read pp. 250 - 252
  • §3.10 Linear Approximations and Differentials
  • Course Notes §1 Taylor Polynomials - Part 1

Learning Objectives

1. Explain what a linear approximation is and graphically represent it
2. Compute the linear approximation of a function at a given point and use it to approximate functions
3. Explain what the Taylor polynomial of a function is

• Thursday 27th -- Read from bottom p. 3 to p. 5 in the course notes
  • Course Notes §1 Taylor Polynomials - Part 2
  • Course Notes §2 Taylor’s Formula with Remainder

Week 9

• Tuesday 1st November - Quiz
  • Course Notes §2 Taylor’s Formula with Remainder

Learning Objectives

1. Be able to compute new Taylor polynomials using a substitution in the ones we already know
2. Compute the maximal error of a given Taylor polynomial

• Thursday 3rd
  • §4.1 Maximum and Minimum Values

Learning Objectives

1. Describe the conditions for a function to attain its min/max
2. Give examples of functions not attaining their min/max
3. Compute the min/max of a given function (if it exists!)

Week 10

• Tuesday 8th
  • Midterm 2 (in class)

• Thursday 10th -- Read pp. 284 - 287
  • §4.2 The Mean Value Theorem
  • §4.3 How Derivatives Affect the Shape of a Graph (First and Second Derivative Tests) Part 1

Week 11

• Tuesday 15th -- Read pp. 311 - 315
  • §4.3 How Derivatives Affect the Shape of a Graph (First and Second Derivative Tests) Part 2
  • §4.5 Summary of Curve Sketching

• Thursday 17th
  • §4.7 Optimization Problems

Week 12

• Tuesday 22nd - Quiz -- Read pp. 338 - 340
  • §4.8 Newton’s Method

• Thursday 24th -- Read Examples 2 - 6 on pages 345 - 347
  • §4.9 Antiderivatives

Week 13

• Tuesday 29th
  • Review

• Thursday 1st December
  • Review