The summer quarter is brief and intense, making it impossible to cover all important topics of calculus in depth. The following reading materials, though optional, are highly recommended.
Left/Right Limits: (OpenStax Vol 1 p144) Left/right limit theory provides us with a useful tool to analyze the existence of limits.
Infinite Limits: (OpenStax Vol 1 p146) Some limits, for example, f(x) = 1/x as x goes to 0, have a convergent nature in some sense but are identified as divergent in our current limit model. The infinite limit theory is such an extension by allowing those functions 'converge to infinity'.
The Squeeze Theorem: (OpenStax Vol 1 p146) A powerful technique which should be covered in any calculus course. (Unfortunately, we won't.)
Types of Discontinuity: (OpenStax Vol 1 p184) They are actually covered in the lecture without introducing the terminologies.
The Intermediate Value Theorem: (OpenStax Vol 1 p188) Continuous functions won't break connectedness.
The Epsilon-Delta Model*: (OpenStax Vol 1 Section 2.5) A rigorous formalization of the limit theory.
Differentials: (OpenStax Vol 1 p358) An intrinsic formalization of differentiation. It has the advantage of being conceptual and coordinate-free compared with derivatives. As an analog, 'differential vs derivative' in calculus is like 'linear transformation vs matrix' in linear algebra.
Lecture 1: preview of calculus*, functions, lines on the plane, trigonometric functions
Lecture 2: graph shifting, quadratic functions, exp & log, the tangent problem
Lecture 3: limit, limit laws, continuity
Lecture 4: tangent lines, derivatives, differentiation rules
Lecture 5: derivatives of trig. functions, the chain rule
Lecture 6: the chain rule(continued), inverse functions and their derivatives*, midterm review
Lecture 7: derivatives of exp. & log., implicit differentiation
Lecture 8: linear approximation, max. & min., the mean value theorem
Lecture 9: the shape of a graph, limits at infinity, indeterminate forms
Lecture 10: optimization problems, final review
Wolfram|Alpha: A 'computational knowledge engine' developed by Wolfram Research.
Numberphile: Videos about various math topics.
3Blue1Brown: You can find videos themed around visualizing math.
Wikipedia Math Portal: It could be fun to pick a random article, explore related entries, and see where they lead you.
Khan Academy: An online educational platform providing a great many basic math lessons.