MTH132: Calculus with Analytic Geometry II
4.1 Indefinite Integrals
4.3 Definite Integrals and Accumulation of Change
Unit 5 - Applications of Integration
Unit 6 - Infinite Series**
6.1 Power Series
6.2 Taylor Series and Taylor's Theorem
I will send you Google Calendar invites for live lessons.
You only have to attend the live lessons that you want.
You can watch the record lessons that are linked.
Live Lesson 4.3 - https://youtu.be/-gyVkS8JLlg
covers definite integration, improper integrations, and area of a polar region
Live Lesson 5.1
Live Lesson 6.1
Live Lesson 6.2
Live Lesson 6.3
There will be six quizzes throughout the semester. The dates for these are in the syllabus.
You will be expected to attend class for all of the quizzes.
The last meeting we have will be the final exam.
MTH132 Course Objectives
Calculate derivatives of parametric functions. (2.3.2)
Calculate derivatives of functions written in polar coordinates. (2.3.4)
Determine antiderivatives of functions and indefinite integrals, using knowledge of derivatives. (4.1.1, 4.1.2)
For integrands requiring substitution or rearrangements into equivalent forms: determine indefinite integrals and evaluate definite integrals. (4.1.3)
For integrands requiring integration by parts: determine indefinite integrals and evaluate definite integrals. (4.1.4)
For integrands requiring integration by linear partial fractions: determine indefinite integrals and evaluate definite integrals. (4.1.5)
Evaluate definite integrals analytically using the Fundamental Theorem of Calculus. (4.3.3)
Evaluate an improper integral or determine that the integral diverges. (4.3.4)
Calculate areas of regions defined by polar curves using definite integrals. (4.3.5)
Calculate areas in the plane using the definite integral. (5.1.1)
Determine the average value of a function using definite integrals. (5.1.2)
Calculate volumes of solids with known cross sections using definite integrals. (5.1.3)
Calculate volumes of solids of revolution using definite integrals. (5.1.3)
Determine the length of a curve in the plane defined by a function, using a definite integral. (5.1.4)
Determine whether a series converges or diverges. (6.1.1, 6.1.2, 6.3)
Represent a given function as a power series. (6.1.3)
Represent a function as a Taylor series or a Maclaurin series. (6.2.1, 6.2.2)
Interpret Taylor series and Maclaurin series. (6.2.1)
Represent a function at a point as a Taylor polynomial. (6.2.1)
Approximate function values using a Taylor polynomial. (6.2)
Determine the error bound associated with a Taylor polynomial approximation. (6.2.2)
Approximate the sum of a series. (6.3.7)
Determine the radius of convergence and interval of convergence for a power series. (6.3.9)