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.
• Apply L’Hôpital’s Rule to evaluate limits of indeterminate forms.

Contact Hour Information

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

Prerequisites

MATH 2412 (Precalculus) or placement by testing;
College level readiness in reading and writing

Required Materials

Textbook:

Willliam Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz; Calculus, Early Transcendentals, 3rd ed. (digital update); Pearson
Required: 
ISBN for hard copies of access codes: 9780135904183

*Please inform students that access to MyMathLab (MML) must be purchased through the bookstore website.

For students participating in the STAR Bundle, access will be automatically purchased and provided to them.

Students who are not participating in the STAR Bundle will encounter a paywall when attempting to access MyMathLab and will need to complete the purchase on their own.

Calculator:

Calculators may be required for some assignments/assessments at the discretion of the instructor. Refer to class syllabus for details.
Cell phones and other internet-connected devices may not 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