MATH 2413 - Calculus I - University of Houston

# MATH 2413 - Calculus I

***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 1431*

Section number: This information applies to all sections.

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

Prerequisites: MATH 2312 or a satisfactory score on a placement examination.

Course DescriptionCalculus of single variable functions, limits, continuity, derivatives, mean value theorem, applications of the derivative,  motion problems, optimization, antiderivatives, the definite integral,  fundamental theorem of calculus, and numerical integration.

Core Category: Mathematics (20 and 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:

• Develop solutions for tangent and area problems using the concepts of limits, derivatives, and integrals.
• Draw graphs of algebraic and transcendental functions considering limits, continuity, and differentiability at a point.
• Determine whether a function is continuous and/or differentiable at a point using limits.
• Use differentiation rules to differentiate algebraic and transcendental functions.
• Identify appropriate calculus concepts and techniques to provide mathematical models of real-world situations and determine solutions to applied problems.
• Evaluate definite integrals using the Fundamental Theorem of Calculus.
• Articulate the relationship

[Additional course curriculum details: Limits and continuity; the Fundamental Theorem of Calculus; definition of the derivative of a function and techniques of differentiation; applications of the derivative to maximizing or minimizing a function; the chain rule, mean value theorem, and rate of change problems; curve sketching; definite and indefinite integration of algebraic, trigonometric, and transcendental functions, with an application to calculation of areas.]

Calculus I Topics List:

Chapter 1 - Limits and Continuity
1.1     A Review of Functions
1.2     An Intuitive Introduction to Limits
1.3     Definition of Limit and Arithmetic Rules
1.4     Continuity
1.5     The Intermediate Value Theorem
1.6     Limits of Trigonometric Functions and the Pinching Theorem

Chapter 2 - Differentiation
2.1     The Definition of the Derivative
2.2     Derivatives of Polynomials and Trigonometric Functions
2.3     Differentiation Rules
2.4     Implicit Differentiation

Chapter 3 - Applications of the Derivative
3.1     Related Rates
3.2     The Mean-Value Theorem
3.3     Intervals of Increase and Decrease

3.4     Extreme Values
3.5     Concavity and Points of Inflection
3.6     Curve Sketching

Chapter 4 - The Transcendental Functions
4.1     Inverse Functions
4.2     The Exponential Function
4.3     Natural Logarithm Function
4.4     Inverse Trigonometric Functions
4.5     Hyperbolic Functions

Chapter 5 - Further Applications of the Derivative
5.1     Optimization
5.2     Differentials
5.3     L’Hospital’s Rule

Chapter 6 - Integration
6.1     The Definite Integral
6.2     The Fundamental Theorem of Calculus
6.3     Basic Integration Rules
6.4     Integration by Substitution

Justin Dart Jr. Center Accommodations: