MATH 2413 - Calculus I - University of Houston
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MATH 2413 - Calculus I

*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 CourseWare (CASA) at . Students pay for access to CASA 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.

More information on the Cougar Textbook Access Program (CTAP):


Upon successful completion of this course, students will understand and be able to apply the ideas of differential and integral calculus to problems involving instantaneous rates of change,  properties of curves, areas bounded by curves, and motions of accelerated bodies.  They will develop proficiency in the rules and techniques of single-variable calculus, including derivatives of various combinations of functions, the chain rule, substitution, the mean value theorems, and the fundamental theorem of calculus.  Students will be able to use graphical information and symbolic expression simultaneously in solving mathematical problems.  They will be able to translate ordinary language descriptions of problems into mathematical expression, derive solutions by rigorous mathematical methods, interpret their results, and explain them.


Grading: Students will have access to the grading scale and assignments on the course syllabus. Please contact your instructor for additional questions.


Text:  The learning materials for Math 2413, including the textbook, are found online on the CourseWare site. Students are required to purchase an Access Code at the University Book Store to access the learning materials.


Calculus I Topics List:

Exam 1 covers pre-requisite material

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:

Academic Adjustments/Auxiliary Aids: The University of Houston System complies with Section 504 of the Rehabilitation Act of 1973 and the Americans with Disabilities Act of 1990, pertaining to the provision of reasonable academic adjustments/auxiliary aids for students who have a disability. In accordance with Section 504 and ADA guidelines, University of Houston strives to provide reasonable academic adjustments/auxiliary aids to students who request and require them. If you believe that you have a disability requiring an academic adjustments/auxiliary aid, please visit Justin Dart Jr. Student Accessibility Center website at for more information.

Accommodation Forms: Please visit: Details of this policy, and the corresponding responsibilities of the student are outlined in The Student Academic Adjustments/Auxiliary Aids Policy (01.D.09) . For more information please visit the Justin Dart Jr. Student Accessibility Center Policies page page.



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