PREREQUISITE: MAT224 Calculus I or equivalent, or placement; placement into ENG101 and college-level reading, or completion of ENG101S and RDG095.

COREQUISITE: None 

REQUIRED TEXTBOOK:

MyMathLab Access Code Calculus, 3/E; Briggs, Cochran, Gillett; Pearson.

ISBN #9780134856889

The MyMathLab (MML) kit provides you access to the MML online learning system, which includes an e-text and online homework assignments. A hardcopy of the textbook is not required for this course.

REQUIRED MATERIALS:

A graphing calculator (the TI-83, TI-83 Plus, or TI-84 Plus)

COURSE OBJECTIVES:

As the result of instructional activities, students will be able to:

1. Understand and appropriately use the technical vocabulary of the topics covered such as inverse, solid of revolution, surface of revolution, fluid pressure, arc length, partial fraction, improper integral, sequence, series, convergence, divergence, conic section, hyperbola, and polar coordinates
2. Find the derivative and integral of various logarithmic, exponential, and trigonometric functions
3. Find the inverse of a function
4. Use exponential functions to model growth and decay in applied problems
5. Use initial conditions to find particular solutions of differential equations
6. Find the area between two curves
7. Find the volume of a solid of revolution using the disc, washer, and shell methods.
8. Find arc length of a smooth curve
9. Find the area of surface of revolution
10. Find the volume of a solid of revolution using the Theorem of Pappus
11. Calculate work done by constant and variable forces
12. Find the center of mass in one and two-dimensions
13. Integrate using techniques such as integration by parts, trigonometric substitution, and methods of partial fractions
14. Apply L’Hopital’s Rule to evaluate a limit
15. Evaluate improper integrals
16. List terms in a sequence
17. Determine the convergence or divergence of a sequence
18. Use series tests such as nth term, geometric, telescoping, integral, p-series, alternating, direct comparison, limit comparison, ratio, and root to determine the convergence or divergence of a series
19. Determine the endpoint convergence of a power series
20. Differentiate and integrate a power series
21. Find the Taylor and Maclaurin polynomial approximations of elementary functions
22. Write equations of parabolas, ellipses, and hyperbolas using their properties
23. Sketch the graph of a curve given by a set of parametric equations
24. Find the slope of a tangent line to a curve given by a set of parametric equations
25. Rewrite rectangular equations in polar form and vice versa
26. Sketch the graph of an equation given in polar form

SUNY GENERAL EDUCATION LEARNING OUTCOMES:

Students will demonstrate the ability to:

1. interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics;
2. represent mathematical information symbolically, visually, numerically and verbally;
3. use arithmetical, algebraic, geometric and statistical methods to solve problems;
4. estimate and check mathematical results for reasonableness; and
5. recognize the limits of mathematical and statistical methods

GENERAL TOPICS OUTLINE:

1. Applications of Integration (textbook chapter 6)- including area of a region between two curves, volume using the disc method and the shell method, work, arc length and surfaces of revolution
2. Logarithmic, Exponential, and Other Transcendental Functions (textbook chapter 7)- including the natural logarithmic function and differentiation, the natural logarithmic function and integration, inverse functions, exponential functions and differentiation, exponential functions and integration, bases other than e and applications
3. Integration Techniques, L’Hopital’s Rule, and Improper Integrals (textbook chapter 8)- including basic integration formulas, integration by parts, trigonometric integrals, trigonometric substitution, partial fractions, summary and integration by tables, numerical integration, indeterminate forms and L'Hopital's Rule, improper integrals
4. Infinite Series (textbook chapters 9 and 10)- including Taylor Polynomials and approximations, sequences, series and convergence, the integral test and p-series, comparisons of series, alternating series, the ratio and root tests, power series, representation of functions by power series, Taylor and Maclaurin Series
5. Conics (textbook chapter 11)- including parabolas, ellipses, hyperbola, rotation and the general second-degree equations

The Math Department at CCC recommends that you review the following prerequisite topics to prepare for MAT225:

• Algebraic Expressions: adding, subtracting, multiplying, dividing, simplifying
• Logarithmic Functions: graphs, properties, inverses
• Trigonometry: graphs, identities, derivatives, integrals, inverses
• Limits: analytical, numerical, one-sided, properties of, infinite
• Derivative Rules: power, constant, sum/difference, product, quotient, trig
• Integrals: indefinite, definite, integration by substitution

You can do this from home by selecting any of the aforementioned topics on the math-tutorial websites listed below; there you will find links to math tutorial websites that provide practice problems and helpful tips, which reviews precalculus topics.

Quizzes for Limits, Derivative, and Integrals
Review of Calculus Topics
Calculus Videos

Feel free to contact a member of the Math Department or the Math Department Chair.