**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):**

- mathematical symbols or the compressed version
- Week 2: Chapter 2 or the compressed version
- Week 3: Chapter 3, Part 1 or the compressed version
- Week 4: Chapter 3, Part 2, Chapter 3, Part 3 or the compressed version
- Week 5: Chapter 3, Part 4 or the compressed version. Chapter 4, Part 1 or the compressed version.