Course Info for MAT224 - CALCULUS I
This course is an introduction to the basic concepts of differential and integral calculus. Course topics include limits and continuity; differentiation and its applications including curve sketching; indefinite and definite integrals; the Fundamental Theorem of Calculus; derivatives and integrals of the trigonometric functions. The use of a graphing calculator is required for this course to further the exploration of these functions and their applications. Near the end of the course, students will complete a comprehensive, departmental final exam.
This course meets the SUNY General Education course requirements for the Mathematics Knowledge and Skill area.
PREREQUISITE: MAT204, MAT205, equivalent, or placement; placement into ENG101 and college-level reading, or completion of ENG101S and RDG095.
COREQUISITE: None
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:
- Understand and appropriately use the vocabulary of the topics of study such as limit, derivative, tangent, integral, differential, and extrema
- Find the limit of a function graphically, numerically, analytically, and by using the formal definition of a limit
- Determine the continuity of a function
- Use the Intermediate Value Theorem to find zeros of a function
- Use infinite limits to find asymptotes
- Use the derivative to find the slope of the tangent line to a curve at a point
- Write the equation of a tangent line to a curve at a point
- Use the derivative to find rates of change
- Differentiate various algebraic and trigonometric functions using the definition and using formulas
- Differentiate using implicit differentiation
- Locate relative and absolute extrema
- Use Rolle鈥檚 Theorem
- Use the Mean Value Theorem
- Determine the intervals where a function is increasing or decreasing using the 1st derivative
- Determine the intervals where a function is concave up or concave down using the 2nd derivative
- Determine horizontal asymptotes of a function, when applicable
- Find infinite limits at infinity
- Use the derivative in various applications such as curve sketching and optimization problems
- Apply the rules of integration to find the antiderivative of various algebraic and trigonometric functions
- Find the general solution of a differential equation
- Find a particular solution of a differential equation given an initial condition
- Use sigma notation to write and evaluate a sum
- Approximate area using upper and lower sums
- Evaluate a definite integral using the Fundamental Theorem of Calculus
- Evaluate integrals using u-substitution
SUNY GENERAL EDUCATION LEARNING OUTCOMES:
Students will demonstrate the ability to:
- interpret and draw inferences from mathematical models such as formulas, graphs, tables and schematics;
- represent mathematical information symbolically, visually, numerically and verbally;
- use arithmetical, algebraic, geometric and statistical methods to solve problems;
- estimate and check mathematical results for reasonableness; and
- recognize the limits of mathematical and statistical methods
GENERAL TOPICS OUTLINE:
- Review of Precalculus (textbook chapter 1)- including graphs and models, linear models and rates of change, functions and their graphs, fitting models to data
- Limits and their Properties (textbook chapter 2)- including finding limits numerically and graphically, evaluating limits analytically, continuity and one-sided limits, infinite limits
- 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
- Applications of Differentiation (textbook chapter 4)- including extrema on an interval, Rolle鈥檚 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鈥檚 Method, differentials
- 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
- 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.
Feel free to contact a member of the Math Department or the Math Department Chair.