These are some recommended readings and problems from the free online textbook accessible
here:
https://lyryx.com/wp-content/uploads/2017/06/Guichard-Calculus-EarlyTranscendentals2017A.pdf
Review (Upcoming tutorial material and general background):
Textbook Section 1.1 (1.1.1 through 1.1.6)
Recommended Problems:
Examples 1.7, 1.8, 1.10, 1.11, 1.12, 1.13, 1.14, 1.16-1.20
Exercises 1.1.1 - 1.1.7
(Not sure if you need to go through these? Try Exercises 1.1.4, 1.1.5(c), and 1.1.7(d) )
Textbook Section 1.2 (1.2.1, 1.2.3 (don’t spend much time on hyperbolas)
Recommended Problems:
Examples 1.25, 1.31
Exercises 1.2.1, 1.2.2(e), 1.2.3, 1.2.5, 1.2.9
(Not sure if you need to go through these? Try Exercises 1.2.1(d), 1.2.2(e), and 1.2.5)
Additional Exercises
Exercises 1.4.1, 1.4.2(a, c, e), 1.4.3, 1.4.4, 1.4.5, 1.4.16
Lecture 2: Functions
Textbook Section: 2.1
Recommended Problems:
Example 2.5
Exercises 2.1.1(b, c, d, e, g, j, l), 2.1.2
Lecture 3: Combining Functions
Textbook Section 2.2.2
Recommended Problems:
Examples 2.8, 2.9
Exercises 2.2.3, 2.8.1, 2.8.2, 2.8.3, 2.8.4
Lecture 4: Inverses
Textbook Section 2.4
Recommended Problems:
Examples 2.16, 2.17
Exercise 2.4.3
Lecture 5: Modelling with Functions
Textbook Section 2.2.1
Recommended Problems:
Examples 2.3, 2.6, 2.7
Exercises 2.1.2, 2.1.3, 2.1.4
Lecture 6: Exponential Functions
Textbook Section 2.3
Recommended Problems:
Example 2.12
Exercises 2.3.1, 2.3.2, 2.3.3, 2.3.4, 2.8.12
Lecture 7: Logarithmic Functions
Textbook Section 2.5
Recommended Problems:
Examples 2.20, 2.21
Exercises 2.5.4, 2.5.5, 2.5.6, 2.8.8, 2.8.9
Lecture 8: Trigonometric Functions
Textbook Section 1.3
Recommended Problems:
Examples 1.36, 1.37
Exercises 1.3.1, 1.3.2, 1.3.3, 1.3.4, 1.3.10, 1.3.11*tricky!
Lecture 9: Trigonometric Functions Part II
Textbook Sections 1.3.5, 2.6
Recommended Problems:
Examples 2.25, 2.26, 2.27, 2.28
Exercises 2.6.1, 2.6.2, 2.6.3, 2.8.10, 2.8.13
Lecture 10: Limits
Textbook Section 3.5
Recommended Problems:
Examples 3.17, 3.18, 3.20, 3.21, 3.22
Exercises 3.5.1(a, d, e, f, g, j, o)
Lecture 11, Instantaneous Velocity, is covered after the derivative in this textbook.
Lecture 12: Limits of Function (incl. at a point)
Textbook Section 3.1, 3.3, 3.4, 3.5.1, 3.5.2
Recommended Problems:
Examples 3.9, 3.10, 3.13, 3.14, 3.17, 3.18, 3.20
Exercises 3.3.1, 3.4.1, 3.5.2, 3.5.4, 3.5.6(abc)
Lecture 13: Continuity
Textbook Section 3.7
Recommended Problems:
Examples 3.44, 3.50, 3.52, 3.55, 3.56, 3.57
Exercises 3.7.1-3.7.3, 3.7.4
Lecture 14: The Derivative
Textbook Sections 4.1, 4.2
Recommended Problems:
Examples 4.4, 4.5, 4.10
Exercises 4.1.4, 4.1.6, 4.2.1(b,c), 4.2.4, 4.2.5
Lecture 15: Differentiation Rules
Textbook Sections 4.3, 4.4
Recommended Problems:
Examples 4.24, 4.26, 4.29,
Exercises 4.3.1, 4.3.2, 4.3.3, 4.3.4, 4.4.1, 4.4.2
Lecture 16: Chain Rule
Textbook Sections 4.5, 4.6
Recommended Problems:
Examples 4.30, 4.31, 4.32, 4.34, 4.35, 4.36,
Exercises 4.5.all, 4.6.all (lots of good practice!)
Lecture 17: Implicit Differentiation
Textbook Sections 4.7, 4.8
Recommended Problems:
Examples 4.39, 4.40, 4.41, 4.43, 4.44, 4.46, 4.49, 4.50, 4.51
Exercises 4.7.1, 4.8.6, 4.8.7, 4.9.5, 4.9.6(a,c)
Lectures 18 & 19: Modelling with Derivatives and Exponential Processes
These subjects are covered later in the textbook (and assume knowledge of the integral). See
note after lecture 31.
Lecture 20: Linearization
Textbook Sections 5.4.1, 5.4.2
Recommended Problems:
Examples 5.27, 5.28
Exercises 5.4.1-5.4.7
Lecture 21: Newton’s Method
Textbook Section 5.4.4
Recommended Problems:
Example 5.32
Exercise 5.4.14
Lecture 22: Indeterminate Forms
Textbook Section 5.5
Recommended Problems:
Examples 5.35, 5.36, 5.38
Exercises 5.5.1-5.5.20
Lecture 23: Extreme Values
Textbook Section 5.2
Recommended Problems:
Examples 5.9, 5.10, 5.11, 5.17, 5.18
Exercises 5.2.1-5.2.9, 5.2.16-5.2.22
Lecture 24: Shapes of Graphs
Textbook Section 5.6
Recommended Problems:
Example 5.42, 5.45, 5.46
Exercises 5.6.1-5.6.7, 5.6.17-5.6.23, 5.6.35-5.6.41, 5.6.56-5.6.57, 5.6.65, 5.6.60, 5.6.77
Lecture 25: Optimization
Textbook Section 5.7
Recommended Problems:
Examples 5.48, 5.49, 5.50, 5.51, 5.52,
Exercises 5.7.1-5.7.14, 5.7.23-5.7.25
Lecture 26: Antiderivatives
Textbook Section 6.1
Recommended Problems:
Examples 6.1, 6.2
Exercises 6.1.1, 6.1.2
Lecture 27: Sigma Notation
Textbook Section 6.1 (page 225), 9.2
Recommended Problems:
Examples 6.4, 6.6
Lecture 28: Riemann Sums
Textbook Section 6.1.1
Recommended Problems:
Examples 6.3, 6.7
Lecture 29: Definite Integrals
Textbook Section 8.1
Recommended Problems:
Examples 8.2,
Exercises 8.1.1-8.1.5
Lecture 30: The Fundamental Theorem of Calculus
Textbook Section 6.2
Recommended Problems:
Examples 6.15
Exercises 6.2.1-6.2.6
Lecture 31: Indefinite Integrals
Textbook Section 6.3
Recommended Problems:
Examples 6.21, 6.22, 6.23, 6.24, 6.25,
Exercises 6.3.1-6.3.9
At this point, it may be helpful to read Textbook Section 10.1. This chapter covers the same
material we covered in “modelling with derivatives (Lecture 18)”, but does so assuming the
concept of the integral is known.
Lecture 32: Integration by Substitution
Textbook Section 7.1
Recommended Problems:
Examples 7.4, 7.5, 7.6, 7.7*,
Exercises 7.1.1-7.1.15
Lecture 33: Integration by Parts
Textbook Section: 7.4
Recommended Problems:
Example 7.28, 7.29, 7.31
Exercises 7.4.1-7.4.11