Course Schedule

Below is the complete schedule for our 7-week summer course (June 29 - August 14).

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Week 1 (June 29 - July 4)

Day Date Topics Notes link
1 Sunday, June 29 Program orientation (no class)
2 Monday, June 30 Course overview. Probability introduction (meaning of probability), events, sample space, and basic counting rules. lecture 1
3 Tuesday, July 1 Dependent vs independent events and their formal definition. Independence as conditional probability. Venn diagrams. lecture 2
4 Wednesday, July 2 Descriptive statistics: mean, median, variance, and standard deviation. Applications in real life. lecture 3
5 Thursday, July 3 Lab 1: Toy probability experiment / expectation lab. lab 1
- Friday, July 4 No Class

Week 2 (July 5 - July 11)

Day Date Topics Notes link
6 Saturday, July 5 Formal definition of a function, simple examples of functions (linear, quadratic), how to draw them and how to figure out their domain and range.
7 Sunday, July 6 Polynomial functions, their graphs, their domain and range, and their infinity behavior.
8 Monday, July 7 Root and rational functions, their graphs, their domain and range, points of discontinuity, and their infinity behavior.
9 Tuesday, July 8 Exponential and log functions, their graphs, their domain and range, points of discontinuity, and their infinity behavior.
10 Wednesday, July 9 Operations on functions. Transformations: shifting, squeezing, reflecting, and composing functions.
11 Thursday, July 10 Lab 2: Function plotting lab (Desmos/Geogebra).
- Friday, July 11 No Class

Week 3 (July 12 - July 18)

Day Date Topic Notes link
12 Saturday, July 12 Operations on functions (continued). Inverse functions and implicit vs. explicit functions.
13 Sunday, July 13 Review Quiz Session 1 (Probability and Functions)
14 Monday, July 14 Introduction of discontinuities, discontinuities in graphs. Desmos exercises.
15 Tuesday, July 15 Formal definition of discontinuities, removable vs essential discontinuities, and various functions behaviors.
16 Wednesday, July 16 Introduction to limits, limits on graphs, and limits of infinity.
17 Thursday, July 17 Introductory limits problems and exercises.
- Friday, July 18 No Class

Week 4 (July 19 - July 25)

Day Date Topic Notes link
18 Saturday, July 19 Formal definition of limits, laws of limits (addition/multiplication), and examples on previous functions (could also add step function).
19 Sunday, July 20 Laws of limits continued. More examples and problems.
20 Monday, July 21 Existence of limits, one sided limits, and infinity limits.
21 Tuesday, July 22 Squeeze Theorem. Intermediate Value Theorem. Examples and Applications.
22 Wednesday, July 23 Lab 3: Limits lab. Case study of sin⁡(1x)\sin(\frac{1}{x}), and guided exploration of ϵ−δ\epsilon-\delta definition of limits.
23 Thursday, July 24 Review Quiz Session 2 (Limits and Continuity)
- Friday, July 25 No Class

Week 5 (July 26 - August 1)

Day Date Topic Notes link
24 Saturday, July 26 Derivatives Introduction 1: Derivatives as rate of change, connections to real-life examples.
25 Sunday, July 27 Derivatives Introduction 2: Derivatives as slopes of functions, connections to real-life examples.
26 Monday, July 28 Derivatives Introduction 3: Formal algebraic definition of derivatives. Calculate derivatives of simple functions (linear/quadratic).
27 Tuesday, July 29 Lab 4: Derivatives Lab 1. Guided examples of various important derivatives (e.g. xn,1xn,ex,ln⁡(x)x^n, \frac{1}{x^n},e^x,\ln(x)).
28 Wednesday, July 30 Derivatives rules 1: addition, multiplication, constant multiple, power rule, and many examples.
29 Thursday, July 31 Derivatives rules 2: division, show it as another form of multiplication and many examples involving polynomials, rational, and root functions.
- Friday, August 1 No Class

Week 6 (August 2 - August 8)

Day Date Topic Notes link
30 Saturday, August 2 Derivatives rules 3: chain rule, examples and problems.
31 Sunday, August 3 Derivatives in real life. Derivatives role in optimization problems. Fence perimeter/area and factory production problems.
32 Monday, August 4 Lab 5: Derivates Lab 2. Guided example of an elaborate optimization problem.
33 Tuesday, August 5 Derivatives and graphs of functions. Derivatives use to understand behavior of functions. First and second derivative tests.
34 Wednesday, August 6 Trigonometric functions derivatives. Geometrical proof of ddxsin⁡(x)\frac{d}{dx} \sin(x). problems and examples.
35 Thursday, July 31 Review Quiz Session 3 (Derivatives)
- Friday, August 8 No Class

Week 7 (August 9 - August 15)

Day Date Topic Notes link
36 Saturday, August 9 L'hopital's rule, Mean Value Theorem, and applications.
37 Sunday, August 10 Implicit differentiation, differentiability vs. continuity.
38 Monday, August 11 Lab 6: Derivates Lab 3. Related-rates problem.
39 Tuesday, August 12 Inverse of derivatives. Brief introduction to integrals.
40 Wednesday, August 13 Review of graph sketching.
41 Thursday, August 14 Review of calculus concepts.
- Friday, August 15 No Class