The main objective of Calculus II is for students to continue learning the basics of the calculus of functions of one variable. They will study both the concepts and techniques of integration, parametric equations and infinite sequences and series, culminating with Taylor series. They will also apply these ideas to a wide range of problems that include area between curves, volume, work, arc length and surface area. They will study approximate integration, a topic that will involve an introduction to a computer algebra system. The students should be able to interpret the concepts of Calculus algebraically, graphically and verbally. More generally, the students will improve their ability to think critically, to analyze a problem and solve it using a wide array of tools. These skills will be invaluable to them in whatever path they choose to follow, be it as a mathematics major or in pursuit of a career in one of the other sciences. Upon successful completion of the course, students should be able to:
- Evaluate definite, indefinite and improper integrals exactly using basic integration techniques such as substitution, integration by parts and partial fractions.
- Apply integration to problems such as volume, arc length, surface area, and work or hydrostatic force.
- Approximate definite integrals numerically including error analysis.
- Use Mathematica to solve basic calculus problems.
- Correctly apply convergence tests to infinite series and determine the interval of convergence of a power series.
- Approximate functions by Taylor polynomials and provide error estimates.
- Sketch graphs and calculate areas in polar coordinates.
Evaluation of Students
Students will be evaluated on their ability to devise, organize and present complete solutions to problems. While instructors may design their own methods of evaluating student performance, these methods must include in-class examinations, frequent homework assignments and a final exam.
|Topics||Number of Weeks||Sections in Text|
|Applications of Definite Integrals||2||6.3 - 6.5, 6.6*, 6.7|
|Exponential Growth and Decay||1||6.8 - 6.9|
|Techniques of Integration||3||7.1, 7.2, 7.5 - 7.8|
|Infinite Sequences and Series||4||8.1 - 8.6, 9.1 - 9.4|
|Polar Coordinates, Polar Graphs and Areas||2||10.1 - 10.3|
Textbooks & Software
Calculus Early Transcendentals Second Edition by Briggs, Cochran and Gillet
Mathematica by Wolfram Reasearch
Date: August 2017