Study Guide for Calculus (I) Chap 5-8
Chapter 5: Integration (5.1-5.6)
- Definition of Riemann Sum.
- Meaning of the limit " || P || -> 0".
- (Impotent) Be able to express a definite integral as
a limit of Riemann sum.
- (More impotent) Be able to express the limit of
a Riemann sum as a definite integral and evaluate
the limit.
- (Most Important) The statement and applications
of `Fundamental Theorems of Calculus' Part 1 and 2.
- How to take derivatives with respect to the upper and
lower limits of integration? (page 304)
- The meaning of indefinite integrals.
- How to solve Initial Value Problems using
definite or indefinite integrals?
- How to use the chain rule in integration?
Chapter 6: Transcendental Functions
(6.4, 6.9, 6.10, 6.11, Integration part only)
- Be able to handle integration of elementary functions
such as polynomials, trigonometric functions, exponential
functions and logarithms.
what you learned in high school. Focus your reading
on 3.4-3.8.
- Integrations related to inverse trigonometric and
inverse hyperbolic functions.
In particular, be able to memorize
the formulas for arcsin, arctan, sinh, cosh, tanh,
arcsinh and arccosh.
- How to integrate `Separable Ordinary Differential Equations'?
- How to integrate
`Linear First Order Ordinary Differential Equations'?
Lecture notes (manual):