,
with the actual change in y, 
.TRI-COUNTY TECHNICAL COLLEGE
COURSE SYLLABUS
Course Prefix & Number: MAT 140
Course Title: Analytic Geometry and Calculus I
Class Hours Lab Hours Credits
Per week: 4.0 Per Week: 0 Awarded: 4
Catalog Description:
This course includes the following topics: derivatives and integrals of polynomials, rational, logarithmic, exponential, trigonometric, and inverse trigonometric functions, curve sketching, maxima and minima of functions, related rates, work, and analytic geometry.
Entry Level Skills: College Algebra and College Trigonometry
Pre-requisites: MAT 111 with a grade of C or better.
Co-requisites: None
Additional Information: Most colleges and universities do not award credit for both MAT 140 and MAT 130, so students should take care to enroll in the appropriate course.
Text(s)/Required Materials: Calculus: Early Transcendental Function, Fourth Edition, by Ron Larson, Robert Hostetler, Bruce H. Edwards, published by Houghton Mifflin Company, 2007
Equipment: A graphing calculator is required. A model with a computer algebra system (such as the TI-89 or TI-92 Plus) is recommended
Course Competencies and Objectives / Major Course Topics:
Unit 1: Limits and Continuity
Upon completion of this unit (Sections 2.1 – 2.5) the successful student should be able to:
1. understand what calculus is and tangent line problems are basic to calculus;
2. evaluate limits numerically and graphically recognize where limits don’t exist, and examining left- and right-hand limits;
3. evaluate limits of transcendental functions;
4. compute limits using algebraic manipulation, and using the limit rules;
5. use graphical and mathematical definitions of continuity to explain why a function is continuous or discontinuous;
6. understand and use the Intermediate Value Theorem to verify that a function has a zero in a given interval;
7. determine infinite limits from the left and from the right and identify horizontal, slant, and vertical asymptotes of a function;
8. compute limits involving infinity.
Unit 2: Differentiation
Upon completion of this unit (Sections 3.1 – 3.8) the successful student should be able to:
1. interpret the derivative as the slope of a tangent or as a rate of change, using appropriate units;
2. find the derivative of a function using the limit definition;
3. recognize the relationship between differentiability and continuity;
4. find derivatives using basic rules: power rule, product and quotient rules;
5. compute higher derivatives of function;
6. find the derivative of the sine, cosine, exponential, and logarithmic functions;
7. use the chain rule to compute derivatives;
8. use the technique of implicit differentiation to find dy/dx;
9. find the derivative of inverse function;
10. use derivatives to solve related rates problems;
11. use Newton’s method to approximate roots of equations.
Unit 3: Applications of Differentiation
Upon completion of this unit (Sections 4.1 – 4.8) the successful student should be able to:
1. find critical numbers and identify local extrema of a given function;
2. understand and use Rolle’s Theorem;
3. understand and use Mean Value Theorem;
4. use the first derivative to determine whether a function is increasing or decreasing, and find relative extrema;
5. use the second derivative to determine concavity, points of inflection, and relative exrrema;
6. find the limit of a function at infinity;
7. analyze and sketch curves by identifying and making use of domain, intercepts, symmetry, asymptotes, intervals of increase or decrease, local maximum and minimum values, concavity and points of inflection;
8. produce a graph with the use of a graphing calculator and use calculus to make sure all important aspects of the curve are revealed;
9. use derivative to solve applied minimum and maximum problems;
10. interpret the tangent line as the linear approximation of a function;
11.
compare the value of differential,
with the actual change in y, .
Unit 4: Integration
Upon completion of this unit (Sections 5.1 – 5.7) the successful student should be able to:
1. evaluate integrals using substitution to simplify the integral;
2. use sigma notation to write and evaluate a sum;
3. estimate area under a curve using a sum of areas of rectangles;
4. understand the definition of Riemann sums;
5. Evaluate a definite integral using limits and properties of definite integrals;
6. use the first Fundamental Theorem of Calculus to evaluate definite integrals and areas;
7. find the average value of a function on a given interval;
8. use the second Fundamental Theorem of Calculus to find the derivative of a function defined by a definite integral;
9. evaluate integrals using substitution and changing variable;
10. approximate definite integrals using numerical techniques;
11. use Log Rule for Integration to integrate a rational function;
12. integrate trigonometric functions.
Unit 5: Applications of the Definite Integral
Upon completion of this unit (Sections 7.1 – 7.7) the successful student should be able to:
1. use integration to determine the area between graphs of functions, including curves that cross each other;
2. find the volume of solid of revolution by disk and washer methods;
3. find the volume of solids with known cross sections;
4. find the volume of solids using shell method and compare it with disk method;
5. find the arc length of a smooth curve, approximating the integral numerically as necessary;
6. find the area of a surface of revolution, approximating the integral numerically as necessary;
7. use integration to determine the work done by a constant as well as a variable force;
8. find the center of mass in a one and two – dimensional systems;
9. determine the center of mass of a planar lamina;
10. use the Pappus to find the volume of a solid of revolution;
11. use integration to find fluid pressure and fluid force on a vertical surface.
Grade Calculation Method: Unit 1 = 16%
Unit 2 = 16%
Unit 3 = 16%
Unit 4 = 16%
Unit 5 = 16%
Final Exam = 20%
________
100%
Prepared by Mohammad Ghobadi Date written or revised: July 10, 2006