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 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: 3

Lab Hours: 2

External Hours: 0

Total Contact Hours: 80

Prerequisites

MATH 2412 OR placement by testing;

ENGL 0305 or ENGL 0365 OR higher level course (ENGL 1301), OR placement by testing

Corequisite

ENGL 0307

**Required Materials**

Textbook:

William Briggs, Lyle Cochran, Bernard Gillett**;*** Calculus for Scientists and Engineers, Early Transcendentals*; Pearson, 2013, ISBN Numbers:

Textbook Plus Maple Software and MyMathLab Portal Access: 9781269374965

Textbook Only: 9780321785374

MyMathLab Portal Access Only: 9780558357603

** Calculator:**Graphing Calculator required. TI 83, TI 84 or TI 86 series calculators recommended.

Calculators capable of symbolic manipulation will not be allowed on tests. Examples include, but are not limited to, TI 89, TI 92, and Nspire CAS models and HP 48 models.

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 Rules of Differentiation

3.3 The Product and Quotient Rules

3.4 Derivatives of Trigonometric Functions

3.5 Derivatives as Rates of Change

3.6 The Chain Rule

3.7 Implicit Differentiation

3.8 Derivatives of Logarithmic and Exponential Functions

3.9 Derivatives of Inverse Trigonometric Functions

3.10 Related Rates

**Chapter 4. Applications of the Derivative**

4.1 Maxima and Minima

4.2 What Derivatives Tell Us

4.3 Graphing Functions

4.4 Optimization Problems

4.5 Linear Approximation and Differentials

4.6 Mean Value Theorem

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