MATH 2414 - Calculus II - University of Houston

# MATH 2414 - Calculus II

***This is a course guideline. Students should contact instructor for the updated information on current course syllabus, textbooks, and course content***

*This course was previously MATH 1432*

Section number: This information applies to all sections.

Delivery format: face-to-face lecture or online.

Prerequisites: C- or higher in Math 2413.

Course Description: Techniques and applications of integration, sequences, series, polar coordinates and parametric equations.

Core Category: Math/Reasoning (90)

Textbook & Access Code: The textbook,online quizzes, and additional help materials will be made available by logging into CASA Campus Services (CCS) at https://ccs.casa.uh.edu/ . Students pay for access to CCS as part of their fee bill via CTAP. If one opts out of the CTAP, they can purchase an access code for this course at UH Bookstore. In this case, if the code is not entered by the deadline specified on CASA, students will lose access to CASA. No make ups will be given for assignments missed during the no-access period.

Upon successful completion of this course, students will:

• Use the concepts of definite integrals to solve problems involving area, volume, work, and other physical applications.
• Use substitution, integration by parts, trigonometric substitution, partial fractions, and tables of anti-derivatives to evaluate definite and indefinite integrals.
• Define an improper integral.
• Apply the concepts of limits, convergence, and divergence to evaluate some classes of improper integrals.
• Determine convergence or divergence of sequences and series.
• Use Taylor and MacLaurin series to represent functions.

[Additional course curriculum details: Differentiation and integration of transcendental functions; parametric equations and polar coordinates; techniques of integration; sequences and series; improper integrals.]

Assignments:

• Regular Exams
• Final Exam
• Online Quizzes
• Written Quizzes
• Homework
• Poppers  – in-class quizzes

### Calculus II Topic List

Chapter 7. Applications of Integration

Section 7.1. Integration Review
Section 7.2. The Mean Value Theorem for Integrals
Section 7.3. Area
Section 7.4. Volume
Section 7.5. Arc Length, Centroids and Surface Area
Section 7.6. Differential Equations and Exponential Growth/Decay

Chapter 8. Techniques of Integration

Section 8.1. Integration by Parts
Section 8.2. Powers of Trigonometric Functions
Section 8.3. Trigonometric Substitutions
Section 8.4. Integrating Rational Functions
Section 8.5. Improper Integrals
Section 8.6. Numerical Integration

Chapter 9. Sequences and Series

Section 9.1. Bounded Sets and Sequences
Section 9.2. Convergence of Sequences
Section 9.3. Numerical Series and Convergence
Section 9.4. Integral Test, Comparision Tests
Section 9.5. The Ratio Test and the Root Test
Section 9.6. Alternating Series and Absolute Convergence
Section 9.7. The Power Series
Section 9.8. The Taylor Series

Chapter 10. Polar Coordinates and Parametric Equations

Section 10.1. Polar Coordinates
Section 10.2. Graphing in Polar Coordinates
Section 10.3. Area in Polar Coordinates
Section 10.4. Curves Given Parametrically
Section 10.5. Tangents to Curves Given Parametrically
Section 10.6. Arc Length and Surface Area for Curves Given Parametrically

Justin Dart Jr. Center Accommodations: