PREREQUISITE: MAT204, MAT205, 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 vocabulary of the topics of study such as limit, derivative, tangent, integral, differential, and extrema
2. Find the limit of a function graphically, numerically, analytically, and by using the formal definition of a limit
3. Determine the continuity of a function
4. Use the Intermediate Value Theorem to find zeros of a function
5. Use infinite limits to find asymptotes
6. Use the derivative to find the slope of the tangent line to a curve at a point
7. Write the equation of a tangent line to a curve at a point
8. Use the derivative to find rates of change
9. Differentiate various algebraic and trigonometric functions using the definition and using formulas
10. Differentiate using implicit differentiation
11. Locate relative and absolute extrema
12. Use Rolle’s Theorem
13. Use the Mean Value Theorem
14. Determine the intervals where a function is increasing or decreasing using the 1st derivative
15. Determine the intervals where a function is concave up or concave down using the 2nd derivative
16. Determine horizontal asymptotes of a function, when applicable
17. Find infinite limits at infinity
18. Use the derivative in various applications such as curve sketching and optimization problems
19. Apply the rules of integration to find the antiderivative of various algebraic and trigonometric functions
20. Find the general solution of a differential equation
21. Find a particular solution of a differential equation given an initial condition
22. Use sigma notation to write and evaluate a sum
23. Approximate area using upper and lower sums
24. Evaluate a definite integral using the Fundamental Theorem of Calculus
25. Evaluate integrals using u-substitution

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. Review of Precalculus (textbook chapter 1)- including graphs and models, linear models and rates of change, functions and their graphs, fitting models to data
2. Limits and their Properties (textbook chapter 2)- including finding limits numerically and graphically, evaluating limits analytically, continuity and one-sided limits, infinite limits
3. Differentiation (textbook chapter 3)- including the derivative and the tangent line problem, basic differentiation rules and rates of change, the product and quotient rules and higher-order derivatives, the Chain Rule, implicit differentiation, related rates
4. Applications of Differentiation (textbook chapter 4)- including extrema on an interval, Rolle’s Theorem and Mean Value Theorem, increasing and decreasing functions and the First Derivative Test, concavity and the Second Derivative Test, limits at infinity, a summary of curve sketching, optimization problems, Newton’s Method, differentials
5. Integration (textbook chapter 5)- including antiderivatives and indefinite integration, area, Riemann Sums and the definite integral, The Fundamental Theorem of Calculus, integration by substitution, numerical integration

The Math Department at CCC recommends that you review the following prerequisite topics to prepare for MAT224:

• Algebraic Expressions: adding, subtracting, multiplying, dividing, simplifying
• Functions and Their Properties: domain, range, symmetry, asymptotes
• Trigonometry: graphs, special triangles, unit circle, identities, radian measure
   

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 mini-lectures, practice problems, and helpful tips.

Solving Linear Equations
Graphing Linear Functions
Factoring Polynomials
Factoring Formulas
Solving Quadratic Equations
Quadratic Formula
Solving Quadratic Equations
Graphing Quadratic Functions
Simplifying Rational Expressions
Multiplying Rational Expressions
Adding & Subtracting Rational Expressions
Complex Fractions
Simplifying Expressions With Integer Exponents
Radicals and Rational Exponents
Exponents & Radicals
Functions
Function Transformations
Pythagorean Theorem
Right Triangle Trigonometry

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