Class 1:
Introduction and basics
Class 2:
1.5 Inverse functions 2.4 The precise definition of a limit (shortly)
Class 3:
3.5 Implicit differentiation 3.10 Linear approximation and Differentials
Class 4:
3.11 Hyperbolic functions 4.1 Maximum and minimum values 4.2 Mean value theorem
Class 5:
4.4 Indeterminate form and l’Hospital’s rule 4.7 Optimization problems 4.8 Newton’s theorem
Class 6:
5.2 Definite integral 5.3 Fundamental theorem of calculus 5.5 Substitution rule
Class 7:
6.2 Volumes 6.3 Volumes by cylindrical shells 6.5 Average value of a function
Class 8:
Midterm Exam
Class 9:
7.1 Integration by parts 7.2 Trigonometric integrals 7.3 Trigonometric substitution 7.4 Integration of rational functions by partial fractions
Class 10:
7.8 Improper integrals 8.1 Arc length 8.2 Area of a surface of revolution
Class 11:
10.2 Calculus with parametric curves 10.3 Polar coordinates 10.4 Calculus in polar coordinates
Class 12:
11.1 Sequences 11.2 Series 11.3 Integral test 11.4 Comparison test
Class 13:
11.5 Alternating series and absolute convergence 11.6 Ratio and root tests 11.8 Power series
Class 14:
11.9 Representation of functions as power series 11.10 Taylor and Maclaurin series 11.11 Applications of Taylor polynomials
Class 15:
Final exam