課程概述 |
1. 1.Functions and its properties(Exponential functions, inverse functions, and logarithms)
2.The tangent and velocity problems, the limit of a function, calculating limits using the limits laws, the precise definition of a limit
3.Continuity, limits at infinity; horizontal asymptotes
4.Derivatives and rates of change, the derivative as a function, derivatives of polynomials and exponential functions, the product and quotient rules
5.Derivatives of trigonometric functions, the chain rule, Implicit differentiation
6.Derivatives of logarithmic functions, rates of change in the natural and social science, related rates
7. Linear approximations and differentials, hyperbolic functions
8.Maximum and minimum values,the mean value theorem, how derivatives affect the shape of a graph
9.Indeterminate forms and L’Hospital’s rule, summary of curve sketching, Graphing with calculus
10.Optimization problems, Newton’s method, antiderivatives
11.Areas and distances, the definite integral, the fundamental theorem of calculus
12.Indefinite integrals and the net change theorem, the substitution rule
13.Areas between curves, Volumes, Volumes by cylindrical shells
14.Work, average value of a function, Integration by parts
15.Trigonometric integrals, trigonometric substitution
16.Integration of rational functions by partial fractions, strategy for integration, integration using tables
17.Approximate integration, improper integrals |