## 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):