18.T Exponential and logarithmic functions and their derivatives
Reference:
Stewart 6.2, 6.3, 6.4 (or review the
quick treatment from last semester
and then read 6.2*, 6.3*, 6.4* for a different approach)
Keywords: Exponential functions, logarithms, logarithmic
functions, natural logarithms, the base of natural logarithms,
e,
logarithmic differentiation
Learning Objectives: The student will be able to:
- Compute the derivatives of the functions
f(x) = ex
and f(x) = eu,
where u is a function of x
- Compute the derivatives of the functions
f(x) = ln x,
f(x) = loga x, and
f(x) = ln u, where u is a function of x
- Evaluate simple integrals involving these functions,
and the integral of x-1
- Use logarithmic differentiation
18.R Exponential growth and decay
problems;
Inverse trigonometric functions (<--READ ME)
Reference: Stewart 6.5, 6.6
Keywords: Exponential growth, exponential decay, half-life,
Newton's law of cooling, continuous compounding of interest, first-order
chemical reaction, inverse trig functions, arcsin, arccos, arctan, derivatives
of these functions
Learning Objectives: The student will be able to:
- Solve the differential equation dy/dt = ky, and interpret the
solution in terms of exponential growth (k > 0) or
exponential decay (k < 0)
- Recognize and solve common problems of the form dy/dt = ky,
such as
radioactive decay, bacterial growth, Newton's law of cooling, continuously
compounded interest, and first-order chemical reactions
- Define and sketch the graphs of the the inverse trig functions arcsin,
arccos, arctan
- Compute the derivatives of the above functions
- Use inverse trig functions in applications
- Recognize and evaluate integrals that involve inverse trig functions