MATH 114: Analytic Geometry and Calculus II

MATH 114-K01: Analytic Geom and Calc II
(Fall 2024)

02:00 PM to 03:50 PM MW

Mason Korea (119 Songdomunhwa-ro, Yeonsu-gu, Incheon, Korea) G204

Section Information for Fall 2024

MATH 114 - K01: Analytic Geom and Calc II

To develop concepts in calculus and apply them to problems using analytic and software techniques. To develop elementary skills for proving mathematical statements.

A review of the topics in Calculus 1 with a viewpoint of mathematical analysis, i.e. in more depth: proof of facts in limits and continuity, differentiation, integration.
Integration techniques: simple substitutions, integration by parts, rational functions and partial fractions, trigonometric substitutions.
Polar coordinates, equations of simple curves and integration.
L’Hopital’s rule.
Improper integrals. Sequences, convergence of sequences.
Infinite series, convergence tests for series, Maclaurin and Taylor series.
Calculus in two and three variables: limits and continuity, partial differentiation, illustration of multivariable optimization problems.
Proofs of most theorems involved in the above topics.

Topics Sections
1 Review of integration, areas between curves. 
2 Volumes 
3 Integration by parts. 
4 Trigonometric integrals. 
5 Trigonometric substitution. 
6 Integration of rational functions. 
7 Improper integrals. 
8 Review, strategy for integration. 
9 Test 1. 
10 Differential equations. 
11 Separable equations. 
12 Linear equations. 
13 Parametrized curves. 
14 Polar coordinates, area length in polar coordinates. 
15 Review. 
16 Test 2. 
17 Sequences. 
18 Series and the integral test. 
19 Comparison tests. 
20 Alternating Series, absolute convergence, ratio and root tests. §11.5, 11.6
21 Strategy for testing series. 
22 Power series, representations of functions as power series. §11.8, 11.9
23 Taylor and Maclaurin series. 
24 Applications of Taylor polynomials. 
25 Review.

Course Information from the University Catalog

Credits: 4

Methods of integration, conic sections, parametric equations, infinite series, and power series. Offered by Mathematics. Limited to three attempts. Equivalent to MATH 116.
Registration Restrictions:

Required Prerequisites: ((MATH 113C, 113XS or U113) or ((MATH 123C or 123XS) and (MATH 124C or 124XS) or MATH 115C)).
C Requires minimum grade of C.
XS Requires minimum grade of XS.

Schedule Type: Lecture, Recitation
Grading:
This course is graded on the Undergraduate Regular scale.

The University Catalog is the authoritative source for information on courses. The Schedule of Classes is the authoritative source for information on classes scheduled for this semester. See the Schedule for the most up-to-date information and see Patriot web to register for classes.