MATH 100:701 Differential Calculus (Vantage College)


  • The final exam is comprehensive
    Here is a practice exam from last year, and its solution
    This year's final exam may differ significantly from last year's.
  • There is an additional office hour on Wednesday, December 11, 9-11 in MATH 228
  • All solutions are now available
  • Homework 10 and Solution 9 are online
  • The notes for Week 11, Homework 9 and Solution 8 are all available below
  • Solution 7 in online
  • Quiz 2 is taking place during the recitation on Friday, November 15
    The material for the quiz is differentiability, including the various rules of differentiation and implicit differentiation. The Mean Value Theorem and later topics are not covered
  • A short Homework 8 is posted
  • Homework 7 is online
  • Here is the solution of the midterm exam
  • Solution 6 is online
  • There will be no homework assignement appearing this week and due on November 1
    You are strongly encouraged to use the time read CLP-1 Sections 2.1-2.8
  • Solution 5 and Homework 6 are online
  • A practice midetrm can be downloaded here
  • The midterm on Wednesday, October 23, is taking place in class during the usual lecture time
    It covers all the material up to (and including) continuity
  • Solution 4 is available
  • Homework 5 is online
  • A detailed example of the bisection method can be found in Example 1.6.15 of CLP1
  • Homework 4 and Solution 3 are online
  • The midterm and the second quiz have been moved back by one week. The midterm will take place on October 23 and the second quiz on November 15
  • The solution key for Homework 2 is available below.
  • Quiz 1 is taking place during your recitation on Monday, September 30
    The material for the quiz is (a) limits of functions and (b) sequences. Series is not covered
  • Notes for Week 4 are posted below
  • Instructions to access the solution to Homework 1, linked below, can be found through Canvas -> Announcements
  • Homework 2 is available
  • The first homework assignment is available, see below. The online part accessible throught Canvas -> WebWork link opens on Friday at 9
  • You should now all be seeing the course in Canvas
  • Additional reading and many practice problems in the CLP textbooks
  • Welcome to the new term!

Basic Information

  • Full Syllabus
  • Lecture and discussions:
    • Lecture: W 11-12 in AERL 120
    • Discussions: MF 9-10 in ORCH 4018, V1B. MF 9-10 in GEOG 214, V1C. MF 2-3 in MATH 104, V1D. MF 2-3 in MATH 202
  • Instructor: Sven Bachmann
  • Contact:, office hours: Wednesdays 1:30pm-2:30pm
  • Graduate TAs: Lydia Chen, Sarai Hernandez Torres and Mingfeng Qiu, office hours: Mondays 5-6 in LSK 300
  • Undergraduate TAs: Fengpeng (Patrick) Huang, Ziyao Zhou, Ella Chan, Lingtong (Tony) Xu
  • To Canvas

Lecture notes

  • We will follow these and these online notes, up to some reordering.

Homework Assignments

Sheet Number Due Date Solution
Homework 1 September 20, 2019 Solution 1
Homework 2 September 27, 2019 Solution 2
Homework 3 October 04, 2019 Solution 3
Homework 4 October 11, 2019 Solution 4
Homework 5 October 18, 2019 Solution 5
Homework 6 October 25, 2019 Solution 6
Homework 7 November 8, 2019 Solution 7
Homework 8 November 15, 2019 Solution 8
Homework 9 November 22, 2019 Solution 9
Homework 10 November 29, 2019 Solution 10

Weekly lecture summaries
Week 13 Final comments on extrema. L'Hospital's rule. CLP-1, Sections 3.7 Notes
Week 12 Optimization and sketching functions. Critical points, singular points and inflection points. Increasing and decreasing functions; convex and concave functions. CLP-1, Sections 3.5, 3.6 Notes
Week 11 Local and global extrema. Critical points; Discussion; The second derivative criterion; Examples. CLP-1, Section 3.5. Notes
Week 10 More on implicit differentiation. The Mean Value Theorem and Rolle's Theorem. Discussion, elementary example and applications; Uniqueness of solutions. CLP-1, Section 2.13 Notes
Week 9 Recap of differentiation. The chain rule; Examples; Implicit differentiation; Derivatives of the logarithms and the exponentials. CLP-1, Sections 2.9-2.11. Notes
Week 8 Midterm exam and discussion of the solutions. The exponential function, the logarithm, trigonometric functions and their derivatives. CLP-1, Sections 2.7-2.8
Week 7 Differentiability. Definition and first examples; linearity, the product and the quotient rules. CLP-1, Section 2.1-2.6. Notes
Week 6 Continuity. Definition and discussion; rules; the intermediate value theorem; the bisection method. CLP-1, Section 1.6. Notes
Week 5 More on series. The limit comparison test, the ratio test and alternating series test; absolute and conditional convergence. CLP-2, Sections 3.3.3-3.3.6. (We have not convered the 'integral test') Notes
Week 4 Series. Motivation through decimal expansion; Definition; The divergence test; Geometric series, the harmonic series, the p-series; telescopic series; The comparison and limit comparison tests. CLP-2, Sections 3.2., 3.3.1, 3.3.3. Notes
Week 3 Limits at infinity. Definition; basic examples; Sequences and their limits; The bounded monotone convergence theorem. CLP-1, Section 1.5 and CLP-2, Section 3.1. Notes
Week 2 Limits of real-valued functions. Definition; basic examples; Arithmetics of limits; Left and right limits; Infinite limits; The squeeze theorem. CLP-1, Sections 1.1-1.4, 1.7. Notes
Week 1 Introduction. Basics of mathematical notations; Functions. CLP-1, Chapter 0