# Math 2413 Calculus I Information

## LSC-CyFair Math Department

### Course Description

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 the calculation of areas.

### Course Learning Outcomes

The student 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 between derivatives and integrals using the Fundamental Theorem of Calculus.
• Use implicit differentiation to solve related rates problems.

### Contact Hour Information

Credit Hours:  4
Lecture Hours:  4
Lab Hours:  1
External Hours:  0
Total Contact Hours:  80

### Prerequisites

MATH 2412 OR placement by testing;

## Required Materials

### Textbook:

Willliam Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz; Calculus, Early Transcendentals, 3rd ed.; Pearson
Required: Students must buy an access code to MyMathLab, an online course management system which includes a complete eBook; students will first need a Course ID provided by the instructor in order to register; online purchase of MyMathLab access at www.mymathlab.com;
ISBN for hard copies of access codes: 9780134856926
Hardbound text (optional), ISBN: 9780134995991
Loose Leaf text + free MyMathLab access, ISBN: 9780134996684

### Calculator:

Calculators may be required for some assignments/assessments at the discrection of the Instructor.  Refer to class syllabus for details.
Neither cell phones nor PDA’s can be used as calculators.  Calculators may be cleared before tests.

### Textbook Sections

Chapter 2.  Limits

2.1  The Idea of Limits

2.2  Definition of Limits

2.3  Techniques for Computing Limits

2.4  Infinite Limits

2.5  Limits at Infinity

2.6  Continuity

2.7  Precise Definition of Limits

Chapter 3.  Derivatives

3.1  Introducing the Derivative

3.2  The Derivative as a Function

3.3  Rules of Differentiation

3.4  The Product and Quotient Rules

3.5  Derivatives of Trignometric Functions

3.6  Derivatives as Rates of Change

3.7  The Chain Rule

3.8  Implicit Differentiation

3.9  Derivatives of Logarithmic and Exponential Functions

3.10  Derivatives of Inverse Trigonometric Functions

3.11  Related Rates

Chapter 4.  Applications of the Derivative

4.1  Maxima and Minima

4.2  Mean Value Theorem

4.3  What Derivatives Tell Us

4.4  Graphing Functions

4.5  Optimization Problems

4.6  Linear Approximation and Differentials

4.7  L'Hopital's Rule

4.8  Newton's Method (optional)

4.9  Antiderivatives

Chapter 5.  Integration

5.1  Approximating Area Under Curves

5.2  Definite Integrals

5.3  Fundamental Theorem of Calculus

5.4  Working with Integrals

5.5  Substitution Rule