Textbook & Practice Problems
Based on discussions we’ve had with students, many of you have not been able to gain access to the official course textbook. Below is a textbook tailored to MATH 101 that has been written by Joel Feldman and Andrew Rechnitzer (two math faculty members at UBC). The core material is the same, so this should be a good alternative. We’ve also posted the accompanying problem book started by the aforementioned professors and Elyse Yeager (another UBC math faculty member). We’ve also posted a free online textbook (by Community Calculus) that contains the multivariable calculus material we’ll cover. Practice problems are listed at the end of each section of this book.
Suggested readings and practice problems are posted below.
The CLP Textbook: UBC MATH 101 Textbook
The CLP Problem Book: UBC MATH 101 Problem Book
Whitman Book: Single and Multivariable Calculus
Suggested Readings:
Week #1:
- Chapter 1: 1.1, 1.1.2, 1.1.3, 1.1.5 (skip 1.1.1, 1.1.4, etc…)
- Chapter 11: 1.11, 1.11.1, Theorem 1.11.12 (pg. 181 — midpoint rule only!)
Week #2:
- Chapter 1: 1.2 (applications of Theorems 1.2.1 & 1.2.3 only), 1.3, 1.4, 1.8.1, 1.9, 1.10.1 & 1.10.2 (ignore the cases with repeated linear factors e.g.
), 1.7.
- Chapter 2: 2.4.
Week #3:
- Chapter 1: 1.12.1, 1.12.2.
- Probability handout
- Chapter 3: 3.1, 3.2.
Week #4
- Chapter 3: 3.3.1, 3.3.2, 3.3.3, 3.3.4, 3.3.5, 3.3.6, 3.4.1, 3.5.1, 3.5.2.
Week #5
- Chapter 3: 3.6, 3.6.2, 3.6.4.
- (Whitman Book) Chapter 12: 12.1, 12.2, 12.3.
- (Whitman Book) Chapter 14: 14.1, 14.3, 14.5, 14.6.
Week #6:
- (Whitman Book) Chapter 14: 14.7, 14.8.
Practice Problems:
Week #1:
- Chapter 1:
- §1.1: #1, 6, 7, 11, 12, 13, 15, 16, 17, 18.
- Chapter 11:
- §1.11: #2, 8, 9.
Week #2:
- Chapter 1:
- §1.2: #2, 3, 4, 5.
- §1.3: #1, 2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 27.
- §1.4: #1, 3, 4, 5, 6, 7, 8, 9, 10.
- §1.8: #1, 2, 3, 5. (Hint: Write
and
in terms of
and
).
- §1.9: #3, 4, 6, 10. (Many of the other problems require the use of inverse trig functions, which we won’t emphasize in this course, but could still be good practice.)
- §1.10: #3, 5, 6, 7, 8.
- §1.7: #1, 2, 3, 4, 9.
- §2.4: #1, 2, 3, 5, 6, 7, 8, 9, 10 11, 12, 14, 15, 16, 17, 18, 19, 20, 21.
Week #3:
- Chapter 1:
- §1.12: #2, 3, 4, 7.
- Circled problems from the probability handout.
- Chapter 3:
- §3.1: #1, 2, 3.
- §3.2: #1, 2, 3.
Week #4:
- Chapter 3:
- §3.2: #4, 5, 6, 10, 11, 12.
- §3.3: #1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11,12, 13, 14, 15, 16, 17, 18, 19, 21, 25, 28, 29, 31.
- §3.4: #2, 3, 4, 5, 6(a).
- §3.5: #1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11(a), 13, 14(a), 15.
Week #5:
- Chapter 3:
- §3.6: #1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15(a), 18, 19(a), 20(a), 21(a), 22(a), 23, 25, 28, 29(a).
- (Whitman Book) Chapter 12:
- §12.1: #1, 6.
- §12.2: #1, 2, 6, 7, 8, 9, 11.
- §12.3: #1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 16, 17, 18, 19.
- (Whitman Book) Chapter 14:
- §14.1: #6.
Other Midterm Practice Problems from the book:
- Chapter 1:
- §1.5: #5, 6, 8, 9, 11, 12, 13.
- §1.13: #1, 2, 3, 4, 5, 6(a) & (c), 7(a) & (c), 8(b) & (c), 9(a) & (c), 11(b) & (c), 12(a), 13(a), 14(a) & (b), 15(a) & (b).
Lecture Examples
Week #1:
Week #2:
- Examples: FTC, Substitution.
- Examples: Substitution, Trigonometric Integrals, Trigonometric Substitutions
- Examples: Partial Fractions (part 1), Partial Fractions (part 2 – Long Division).
- Examples: Integration by Parts
- Examples: Differential Equations
Week #3:
- Examples: Improper Integrals
- Examples: Probability, Expected Value, Variance, Standard Deviation
- Review Session Solutions
Week #4:
- Examples: Telescopic Series, Divergence Test, Comparison Test, Limit Comparison Test.
- Examples: Integral Test, Alternating Series, Absolute Convergence, Ratio Test
- Examples: Power Series
Week #5:
- Examples: Taylor and Maclaurin Series
- Examples: Taylor Applications
- Examples: Functions of two variables, vectors
- Examples: Level Curves, Partial Derivatives, Directional Derivatives, Gradients
Week #6