Single Variable Calculus

Lecture 1: Derivatives, slope, velocity, rate of change

Lecture 2: Limits, continuity Trigonometric limits

Lecture 3: Derivatives of products, quotients, sine, cosine

Lecture 4: Chain rule Higher derivatives

Lecture 5: Implicit differentiation, inverses

Lecture 6: Exponential and log Logarithmic differentiation; hyperbolic functions
Note: More on “exponents continued” in lecture 7

Lecture 7: Hyperbolic functions (cont.) and exam 1 review
Note: the review for the exam in lecture 7 is not comprehensive because the students already have practice exams available to them. Lecture 8 is Exam 1, so no video was recorded.

Lecture 9:​ Linear and quadratic approximations

Lecture 10: Approximations (cont.); curve sketching

Lecture 11: Max-min problems

Lecture 12: Related rates

Lecture 13: Newton’s method and other applications

Lecture 14: Mean value theorem; Inequalities

Lecture 15: Differentials, antiderivatives

Lecture 16: Continuation: Differential equations, separation of variables
Note: Lecture 17 is Exam 2, so no video was recorded

Lecture 18: Definite integrals

Lecture 19: First fundamental theorem of calculus

Lecture 20: Second fundamental theorem

Lecture 21: Applications to logarithms and geometry

Lecture 22: Volumes by disks and shells

Lecture 23: Work, average value, probability

Lecture 24: Numerical integration

Lecture 25: Exam 3 review

Lecture 27: Trigonometric integrals and substitution

Lecture 28: Integration by inverse substitution; completing the square

Lecture 29: Partial fractions

Lecture 30: Integration by parts, reduction formulae

Lecture 31: Parametric equations, arclength, surface area

Lecture 32: Polar coordinates; area in polar coordinates

Lecture 33: Exam 4 review

Lecture 35: Indeterminate forms – L’Hospital’s rule

Lecture 36: Improper integrals

Lecture 37: Infinite series and convergence tests

Lecture 38: Taylor’s series

Lecture 39: Final review


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