# Math115, T2, Winter 2004

CAB 239, Monday, Wednesday, Friday 12:00 - 12:50

## General information

Instructor : Alex Potapov   e-mail :

Office : CAB 551 (CAB, 5 floor, North side),

Office hours :
Usually by appointment. For emergency questions you may try to come any time without appointment, though there is no guarantee that I'm available.

Lectures
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 .
20.  Inverse trigonometric functions (Section 7.5) (Feb. 25). Lecture transparencies .
21.  Indeterminate forms (Section 7.7) (Feb. 27). Lecture transparencies
22.  Indeterminate forms (Section 7.7). Integration by parts (Section 8.1) (Mar. 3). Lecture transparencies .
23.  Integration by parts. Trigonometric integrals. (Sections 8.1, 8.2) (Mar. 5)
24.  Solving problems (Mar. 8)
25.  Midterm 2  (Mar. 10)
26.  Trigonometric integrals (Sect. 8.2) (Mar. 12) Lecture transparencies .
27.  Trigonometric substitution (Sect. 8.3) (Mar. 15) Lecture transparencies .
28.  Trigonometric substitution: examples. Integration of rational functions (Sect. 8.4) (Mar. 17)
29.  Integration of rational functions. Partial fractions. (Mar. 19) Lecture transparencies .
30.  Rationalizing substitution (Sect. 8.4). (Mar. 22).
31.  Strategy for integration (Sect. 8.5) Lecture transparency .  Improper integrals (Sect. 8.8). (Mar. 24).
32.  Improper integrals. Lecture transparencies .  (Mar. 26)
33.  Arc length (Sect. 9.1). (Mar. 29)
34.  Surface of solids of revolution. (Sect. 9.2) Course evaluation (Mar. 31)
35.  Numerical integration (Sect. 8.7). Lecture transparencies .  (Apr. 2)
36.  Review. Example final problems   (Apr. 5)
37.  Review. Example final problems   (Apr. 7)

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