TRI-COUNTY TECHNICAL COLLEGE
COURSE SYLLABUS
Course Prefix & Number: MAT 141
Course Title: Analytic Geometry and Calculus II
Class Hours Lab Hours Credits
Per week: 4.0 Per Week: 0 Awarded: 4
Catalog Description:
This course includes the following topics: continuation of calculus of one variable including analytic geometry; techniques of integration; volumes by integration, and other applications; infinite series, including Taylor series; improper integrals.
Entry Level Skills: One semester of calculus
Pre-requisites: MAT 140, Analytical Geometry and Calculus I
Co-requisites: None
Text(s)/Required Materials: Calculus: Early Transcendental Functions, 4th 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: Calculus of Inverse Trigonometric Functions, Hyperbolic Functions, and Applications of integrals,
Upon completion of this unit (Sections 5.8-5.9 and 7.5-7.7) the successful student should be able to:
1. find derivatives of inverse trigonometric functions;
2. integrate functions whose anti – derivatives involve inverse trigonometric function;
3. review the basic integration rules involving elementary functions;
4. find derivatives and integrals of hyperbolic functions;
5. find derivatives and integrals of inverse hyperbolic functions;
6. use integration to determine the work done by a constant as well as a variable force;
7. find the center of mass in a one and two – dimensional systems;
8. determine the center of mass of a planar lamina;
9. use the Pappus to find the volume of a solid of revolution;
10. use integration to find fluid pressure and fluid force on a vertical surface.
Unit 2: Integration Techniques, L’Hopital’s Rule, and Improper Integrals
Upon completion of this unit (Sections 8.1-8.8) the successful student should be able to:
1. review procedures for fitting an integrand to one of the basic integration rules;
2. use integration by parts, including repeated integration by parts, to evaluate integrals;
3. use trigonometric identities to integrate powers and products of sine and cosine functions;
4. use trigonometric identities to integrate powers and products of tangent and secant functions;
5. use trigonometric substitutions to evaluate integrals;
6. use the method of partial fractions to integrate rational functions;
7. use tables and computer algebra systems to integrate functions;
8. use L’Hopital’s Rule to evaluate limits of indeterminate forms;
9. recognize and evaluate improper integrals;
10. determine whether improper integrals are convergent or divergent.
Unit 3: Infinite Sequences and Series
Upon completion of this unit (Sections 9.1 – 9.6) the successful student should be able to:
1. list the terms of a sequence, and determine whether a sequence converges or diverges;
2. write a formula for nth term of a sequence;
3. understand the definition of a convergent and divergent infinite series;
4. use properties of infinite geometric series, p-series and harmonic series;
5. use the nth term test for divergence of an infinite series;
6. use the integral test to determine whether an infinite series converges or diverges;
7. use the direct comparison test to determine whether a series converges or divergs;
8. use the limit comparison test to determine whether a series converges or diverges;
9. use the alternating series test to determine whether a series converges or diverges;
10. use the alternating series remainder to approximate the sum of an alternating series;
11. classify a convergent series as absolutely or conditionally convergent;
12. use the ratio test to determine whether a series converges or diverges;
13. use the root test to determine whether a series converges or diverges.
Unit 4: More Infinite Sequences and Series
Upon completion of this unit (Sections 9.7 – 9.10) the successful student should be able to:
1. find Taylor and Maclaurin polynomial approximations of elementary functions;
2. find the remainder of a Taylor polynomial;
3. find the center, radius and interval of convergence of a power series;
4. determine the endpoint convergence of a power series;
5. differentiate and integrate a power series;
6. find a geometric power series that represents a function;
7. find a Taylor or Maclaurin series for a function;
8. find a binomial series;
9. use a basic list of Taylor series to find other Taylor series;
10. use power series to approximate some functional values and integrals.
Unit 5: Parametric Equations and Polar Coordinates
Upon completion of this unit (Chapter 10) the successful student should be able to:
1. describe the general shape and characteristics of each conic section;
2. analyze and write equations of parabolas, ellipses, and hyperbolas;
3. sketch the graph of a curve given by a set of parametric equations;
4. eliminate the parameter in a set of parametric equations;
5. find first and second derivatives, and the arc length of a curve given by a set of parametric equation;
6. find the area enclosed within a parametric curve, or several such curves, and the area of surface of revolution (parametric form);
7. convert polar coordinates and equations to Cartesian and vice versa;
8. sketch polar curves by hand and with graphing devices;
9. find tangent lines to polar curves, and identify several types of special polar graphs;
10. find the intersection points and the area of a region bounded by polar graphs;
11. find the arc length and the area of a surface of revolution of an equation in polar form;
12. analyze and write polar equations of conics.
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: November 2006