# MATH 1431 - Calculus I

**Section number**: This information applies to all sections.

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

**Prerequisites**: MATH 1330 or a satisfactory score on a placement examination.

**Course Description**: Calculus 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. **Note: TCCNS Equivalent: MATH 2413*

** Core Category:** Mathematics (20 and Math/Reasoning (90)

**Textbook**: Single Variable Calculus, copyright University of Houston Mathematics Department. Available in electronic form (PDF) through CASA for all enrolled students via an **Access Code**. ***Note: If you misplace/lose your code, you will need to purchase another. There is no exception to this.**

**The information contained in this class outline is an abbreviated description of the course. Additional important information is contained at your instructor’s personal webpage. You are responsible for knowing all of this information.**

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 1431, 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

**2.1 The Definition of the Derivative**

Chapter 2 - Differentiation

Chapter 2 - Differentiation

2.2 Derivatives of Polynomials and Trigonometric Functions

2.3 Differentiation Rules

2.4 Implicit Differentiation

**3.1 Related Rates**

Chapter 3 - Applications of the Derivative

Chapter 3 - Applications of the Derivative

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

**6.1 The Definite Integral**

Chapter 6 - Integration

Chapter 6 - Integration

6.2 The Fundamental Theorem of Calculus

6.3 Basic Integration Rules

6.4 Integration by Substitution

**FINAL EXAM**

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