Differentiation and integration of exponential and logarithmic functions, techniques of integration, applications of the definite integral, the calculus of transcendental functions, parametric equations, polar coordinates, indeterminate forms and L’Hopital’s Rule, improper integrals, sequences and series.

The student will:

- Use the concepts of definite integrals to solve problems involving area, volume, work, and other physical applications.
- Use substitution, integration by parts, trigonometric substitution, partial fractions, and tables of anti-derivatives to evaluate definite and indefinite integrals.
- Define an improper integral.
- Apply the concepts of limits, convergence, and divergence to evaluate some classes of improper integrals.
- Determine convergence or divergence of sequences and series.
- Use Taylor and MacLaurin series to represent functions.
- Use Taylor or MacLaurin series to integrate functions not integrable by conventional methods.
- Use the concept of parametric equations and polar coordinates to find areas, lengths of curves, and representations of conic sections.
- Apply L'hôpital's Rule to evaluate limits of indeterminate forms.

Credit Hours: 4

Lecture Hours: 4

Lab Hours: 1

External Hours: 0

Total Contact Hours: 80

MATH 2413;

College level readiness in reading and writing

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

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.

Students are expected to memorize the differentiation formulas on the last page inside the back cover of the text and integration formulas 1- 20 in the attached chart.

Chapter 6. Applications of Integration

6.1 Velocity and Net Change

6.2 Regions Between Curves

6.3 Volume by Slicing

6.4 Volume by Shells

6.5 Lengths of Curves

6.6 Surface Area

6.7 Physical Applications (*cover work and density and mass; all other topics optional*)

Chapter 7. Logarithmic, Exponential, and Hyperbolic Functions

7.1 Logarithmic and Exponential Functions Revisited

7.2 Exponential Models

7.3 Hyperbolic Functions

Chapter 8. Integration Techniques

8.1 Basic Approaches

8.2 Integration by Parts

8.3 Trigonometric Integrals

8.4 Trigonometric Substitutions

8.5 Partial Fractions

8.6 Integration Strategies

8.7 Other Methods of Integration

8.8 Numerical Integration

8.9 Improper Integrals

Chapter 9. Differential Equations

9.1 Basic Ideas

9.3 Separable Differential Equations

Chapter 10. Sequences and Infinite Series

10.1 An Overview

10.2 Sequences

10.3 Infinite Series

10.4 The Divergence and Integral Tests

10.5 Comparison Tests

10.6 Alternating Series

10.7 The Ratio and Root Tests

10.8 Choosing a Convergence Test

Chapter 11. Power Series

11.1 Approximating Functions with Polynomials

11.2 Properties of Power Series

11.3 Taylor Series

11.4 Working with Taylor Series

Chapter 12. Parametric and Polar Curves

12.1 Parametric Equations

12.2 Polar Coordinates

12.3 Calculus in Polar Coordinates

12.4 Conic Sections