vcc.ca
MATH 1200: Calculus 2
Effective date
September 2015
Department
UT Math
School
Arts and Sciences
Description
This course is designed to provide students with a fundamental knowledge of integral calculus. Topics include antidifferentiation; the definite integral; the fundamental theorem of calculus, areas and volumes; integration techniques; improper integrals; applications of the integral; slope fields; numerical approximations; linear differential equations and applications; polynomial approximations; Taylor series, power series and calculus with parametric curves and polar coordinates.
Credits
3.0
Year of study
1st Year Post-secondary
Prerequisites
MATH 1100 with a minimum 'C-' grade.
Corequisites
None
Course Learning Outcomes
Upon successful completion of this course, students will be able to:
- Evaluate integrals using Riemann sums, the Fundamental Theorem of Calculus and numerical techniques
- Compute areas and volumes using integration
- Use various techniques of integration
- Solve applied problems using integrals
- Compute approximations and corresponding errors of integrals
- Solve applied problems involving first-order linear differential equations
- Determine Taylor and Maclaurin series of functions
- Determine convergence of series using various covergence tests
- Determine the radius and interval of convergence of power series
- Use power series to approximate integral values and evaluate limits
Prior Learning Assessment & Recognition (PLAR)
Math 1200 Challenge Exam with a C (not accepted for the UT Engineering Certificate or the UT Computer Science and Software Systems Certificate).
Hours
Lecture, Online, Seminar, Tutorial: 60
Total Hours: 60
Total Hours: 60
Instructional Strategies
Lectures coupled with computer lab exercises
Grading System
Letter Grade (A-F)
Passing grade
D
Evaluation Plan
|
Type |
Percentage |
Assessment activity |
|
Assignments |
30 |
|
|
Midterm Exam |
35 |
Written, MC, SA, problems |
|
Final Exam |
35 |
Written, MC, SA, problems |
Course topics
- The Integral: elementary area computations; Riemann sums and the integral; evaluation of integrals; the Fundamental Theorem of Calculus; integration by substitution; areas of plane regions; numerical integration
- Applications of the Integral: Riemann sum approximations; volumes by cross sections; volumes by cylindrical shells; arc length and surface area of revolution; force and work; average value of a function, centroids of plane regions and curves
- Techniques of Integration: integral tables and simple substitutions; integration by parts; trigonometric integrals; rational functions and partial fractions; trigonometric substitution; improper integrals
- Differential Equations: separable equations and applications; linear equations and applications
- Sequences and Series: infinite sequences; infinite series and convergence; the integral test; comparison tests for positive-term series; alternating series and absolute convergence; Taylor series and Taylor polynomials; radius and interval of convergence of power series; power series applications
Notes:
- Course contents and descriptions, offerings and schedules are subject to change without notice.
- Students are required to follow all College policies including ones that govern their educational experience at VCC. Policies are available on the VCC website at:
https://www.vcc.ca/about/governance--policies/policies/. - To find out if there are existing transfer agreements for this course, visit the BC Transfer Guide at https://www.bctransferguide.ca.