1. Introduction. Review of basic concepts
of calculus
2. Definite and indefinite integrals. Table of basic
integrals. Properties of integrals, integration by reducing integrals
to tabular ones.
3. Properties of definite integrals and their application.
Integration of |f(x)|. Substitution rule and examples of its
application.
4. Substitutions in definite integral. Symmetry in definite
integrals. (Textbook, end of Chapter 5). Area between curves
(Textbook, Section 6.1).
Notes for lectures
1-3.5 .
5. Applications of integration. Areas and integrals.
Substitutions and a simple differential equation (supplementary).
Volumes by cross sections (Textbook, Section 6.2).
6. Volumes by cross-sections for solids of revolution or
"washers method" (Textbook, Section 6.2).
7. Volumes by cylindrical shells or "shells method" (Textbook,
Section 6.3).
Notes: Idea of
washers and
shells method
8. Volumes: choosing appropriate method.
9. Describing solid by integral. Beginning of new
topic -
Inverse functions (Chapter 7). One-to-one functions (Section 7.1).
10. How to make a differentiable function OTO? Inverse function,
cancelation identities.
11. Plot of inverse function., derivative of inverse function.
Notes for
volumes and inverse function
12. Exponential and logarithmic function (Sections 7.2, 7.3, 7.4)
13. Review of midterm content
14. Midterm 1
15. Exponential and logarithmic function (Sections 7.2, 7.3, 7.4)
16. Exponential and logarithmic function (Sections 7.2, 7.3, 7.4)
17. Logarithmic differentiation (Section 7.4). Separable
differential
equations, solving by reduction to integrals (Section 10.3).
18. Separable differential equations, exponential growth
(Sections 10.3, 10.4, 10.5).
19. Exponential and logistic
growth (Sections 10.3, 10.4, 10.5). Hyperbolic functions
(Section 7.6). (Feb. 23)
Notes for
exponential and logarithmic functions, differential equations, and
hyperbolic functions .
