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Learning Goals

Week 12:

• Ch 9.1 Taylor polynomials
• Ch 3.10 Derivatives of Inverse trigonometric functions
• Practice problems:
  Section 9.1: 1, 2, 6, 9, 11, 17, 21, 31, 39, 42, 43, 73.
  Section 3.10: 7-12, 22, 26

Week 11:

• Ch 4.5 Linear approximation
• Ch 9.1 Taylor polynomials
• Practice problems:
  Section 4.5: Quick Checks: 1-4; Exercises: 2, 3, 4, 15, 16, 18, 24, 26, 30, 37, 38, 47, 51, 57, 61, 63.
  Section 9.1: 1, 2, 6, 9, 11, 17, 21, 31, 39, 42, 43, 73.

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Week 9/10:

• Ch 4.4 Optimization
• Ch 4.5 Linear approximation
• Practice problems:
  Section 4.4: 2, 3, 4, 6, 15, 17, 21, 22, 26, 29, 31, 37, 39, 54, 61, 63.
  Section 4.5: Quick Checks: 1-4; Exercises: 2, 3, 4, 15, 16, 18, 24, 26, 30, 37, 38, 47, 51, 57, 61, 63.

Week 8:

• Ch 4.1 (Maxima and minima), Ch 4.2 (What derivatives tell us), Ch 4.3 (Graphing functions)
• Ch 2.4, 2.5 (Material on asymptotes)
• Practice problems:
  Section 4.1: 1, 4, 5, 7, 8, 10, 13, 14, 20, 24, 30, 31, 33, 52, 54, 58, 61, 62, 66, 79.
  Section 4.2: 1, 2, 3, 12, 16, 22, 34, 40, 46, 47, 50, 60, 64, 68, 70, 79, 80, 97, 98, 100.
  Section 2.4: 9, 11, 17, 19, 21.
  Section 2.5: 28, 32, 52, 53, 57, 68.
  Section 4.3: 2, 3, 8, 13, 19, 25, 30, 35, 36, 48, 49, 70.

Week 7:

• Chapters 3.11: Related rates
• Chapter 4.1: Maxima and minima
• Practice problems:
  Section 3.11: 3, 10, 15, 19, 22, 24, 29, 46.
  Section 4.1: 1, 4, 5, 7, 8, 10, 13, 14, 20, 24, 30, 31, 33, 52, 54, 58, 61, 62, 66, 79. Related rates in business problems

Week 6:

• Chapters 3.9: Derivative of Logarithms
• Chapter 6.8: Exponential models (to the end of Example 3)
  This chapter is not included in your textbook, so download it here. Also see notes on compound interest.
• Elasticity of demand
• Practice problems:
  Section 3.9: 1, 2, 6, 12, 16, 19, 54, 57, 60, 65, 68, 97, 105.
  Section 6.8: 1, 10, 11, 13, 16, 25, 30, 38
  Problems on Elasticity and compound interest

Week 5:

• Chapters 3.8 Implicit differentiation
• Practice problems:
  Section 3.8: 2, 3, 10, 12, 18, 24, 27, 28, 51, 54, 56, 60, 61, 75

Week 4:

• Chapters 3.6 Rates of Change (Midterm 1 up to and including this)
• Chapter 3.7 Chain rule (not on Midterm 1)
• Practice problems:
  Section 3.6: 7, 10, 11, 12, 20, 21, 35, 41, 42, 46, 47.
  Section 3.7: 2, 4, 5, 6, 35, 36, 38, 50, 51, 52, 79, 81, 82, 88, 93, 99, 100.

Week 3:

• Chapters 3.3, 3.4 Rules of differentiation; Product/quotient rules
• Chapter 3.5 Derivatives of Trig functions (Theorem 3.13 only)
• Practice problems:
  Section 3.3: 19-24, 28, 33, 36, 38, 41, 54, 62, 72, 79.
  Section 3.4: 7-14, 15, 31, 34, 51, 54, 59, 60, 72, 85, 87.
  Section 3.5: 6, 17-28, 46, 62, 66.

Week 2:

• Chapters 2.6, 3.1, 3.2 (Continuity, Intro to derivative, Working with derivatives)
• Practice problems:
  Section 2.6: 8, 10, 18, 23, 39, 58, 65, 84, 85. Section 3.1: 2, 10, 23, 56, 63. Section 3.2: 9, 10, 15, 19.

Week 1:

• Chapters 2.1, 2.2, 2.3 (Limits)
• Practice problems:
  Section 2.1: 3, 5, 7, 11, 15, 29. Section 2.2: 2, 5, 10, 11, 21, 23, 27, 29, 43. Section 2.3: 5, 10, 26, 29, 33, 34, 37, 40, 41, 46, 47, 51, 68.

Week 0:

• Chapter 1.3 (Exponential/logarithmic functions, inverse functions)
• Practice problems:
  Section 1.3: 3, 5, 11, 15, 17, 19, 25, 27, 29, 41, 43, 45, 53, 55, 70, 71, 72, 73, 79, 81, 91.

Lecture Notes

• Nov 28 (Week 12): Review and problem session
• Nov 26 (Week 12): Taylor polynomials (Ch 9.1) and Derivatives of Inverse Trig (Ch 3.10)
  A worked example that will be helpful for HW9 Q2, approximating roots of functions.
• Nov 24 (Week 12): Error estimate (Ch 9.1) class activity
  
• Nov 21 (Week 11): Error estimate for linear approximation (Ch 9.1) Lecture notes
  
• Nov 19 (Week 11): Quadratic Approximation (Ch 9.1) Lecture notes, class activity
  
• Nov 17 (Week 11): Linear Approximation (Ch 4.5) Lecture notes, class activity
  
• Nov 14 (Week 10): Optimization (Ch 4.4) Business example + Elvis the dog Lecture notes
  
• Nov 10/12 (Week 10): Optimization (Ch 4.4) Formulating and Solving optimization problems
  
• Nov 7 (Week 9): Limits at infinity (Ch 2.4/2.5) Asymptotic behaviour of functions Lecture notes
  
• Nov 5 (Week 9): Curve sketching (Ch 4.3) Lecture notes
  Guest lecture notes: Section 101 and Section 102
• Nov 3 (Week 9):Second derivative and $f(x) = e^{-\frac{1}{2}x^2}$ example. Lecture notes
  
• Oct 31/Nov 3 (Week 8): What derivatives tell us (Ch 4.2) Lecture notes
  
• Oct 29 (Week 8): Maxima & minima (Ch 4.1) Lecture notes
  
• Oct 27 (Week 8): Related rates (Ch 3.11) More examples! Lecture notes
  
• Oct 24 (Week 7): Related rates (Ch 3.11) with 4-step strategy Lecture notes
  
• Oct 22 (Week 7): Related rates (Ch 3.11) Lecture notes
  The elasticity example we covered today is included in Oct 20th's notes.
• Oct 20 (Week 7): Compound interest/Interest rate models Lecture notes
  Elasticity Lecture notes
  
• Oct 17 (Week 6): Exponential models (Ch 6.8) Lecture notes
  
• Oct 15 (Week 6): Logarithmic differentiation (Ch 3.9), Exponential models (Ch 6.8) Lecture notes
  
• Oct 10 (Week 5): Derivatives of Logarithmic functions (Ch 3.9) Lecture notes
  
• Oct 8 (Week 5): Implicit differentiation (Ch 3.8) Lecture notes
  
• Oct 6 (Week 5): Chain Rule (Ch 3.7) -- Combining derivatives rules Lecture notes
  
• Oct 3 (Week 4): Chain Rule (Ch 3.7) Lecture notes
  
• Oct 1 (Week 4): Business problem Lecture notes
  
• Sep 29 (Week 4): Rates of Change (Ch 3.6) -- Rate of change, business problem Lecture notes
  (Example with equation of tangent line is in Sep 26 notes.)
• Sep 26 (Week 3): Derivative rules (Ch 3.5) -- Trigonometric derivative rules, example with equation of tangent line Lecture notes
  
• Sep 24 (Week 3): Derivative rules (Ch 3.3, 3.4) -- Power, Exponential, Sum, Product, Quotient rules Lecture notes
  Summary sheet of derivative rules.
• Sep 22 (Week 3): Working with derivatives (Ch 3.2) -- Sketching graph of derivative Lecture notes
  Continuation of $f(x)=\sqrt{x}$ example, finding eqn of tangent line Notes
• Sep 19 (Week 2): Intro to derivatives (Ch 3.1) -- Definition of derivatives, tangent lines Lecture notes
• Sep 17 (Week 2): Continuity (Ch 2.6) -- Composite functions, Intermediate Value Theorem Lecture notes
• Sep 15 (Week 2): Continuity (Ch 2.6) -- Definition, continuity on interval, continuity rules. Lecture notes
• Sep 12 (Week 1): Computing limits (Ch 2.3) -- Limit laws. Lecture notes
• Sep 10 (Week 1): Idea of limits, Definition of limits (Ch 2.1, 2.2) Lecture notes
• Sep 8 (Week 1): A business problem. Lecture notes
• Sep 5 (Week 0): Inverse, exp/log Lecture notes
• Sep 3 (Week 0): Lecture notes
• Sep 3 (Week 0): Introduction & logistics Slides

Supplementary Notes

• A business problem. Notes
• Shrinking circle problem on WebWork 1: Solution.
• Summary sheet of derivative rules: Derivative rules.
• Sample Midterm 1 with solutions
• Implicit differentiation example
• Combining derivative rules worksheet with answers
• Chapter 6.8.
• Notes on compound interest.
• Notes on Elasticity of demand
• Problems on Elasticity and compound interest
• Related rates in business problems
• Answers to Ch 6.8 practice problems
• Solutions to selected problems in WebWork 9

Quiz/Assignment Solutions

• HW9 Solutions
• HW8 Solutions
• Quiz 8 Solutions
• HW7 Solutions
• HW6 Solutions
• HW5 Solutions
• Quiz 7 Solutions
• Solutions for retracted Quiz 7
• Quiz 6 Solutions
• Quiz 5 Solutions
• HW4 Solutions
• HW3
• Quiz 3 Solutions
• HW2 Solutions
• Quiz 1 & 2 solutions
• HW1 Solutions