Math 126 syllabus
This course is a continuation of MA 125 with emphasis on
integral calculus. Topics include techniques of integration; applications of the
definite integral to geometry, natural sciences, engineering, and economics;
improper integrals; infinite sequences and series; Taylor polynomials and Taylor
series; parametric equations and polar coordinates.
Prerequisites: C or better in MA 125
Textbook: Joel Hass, Maurice D. Weir, and George B. Thomas, Jr.: University
Calculus – Early Transcendentals, Pearson, 3rd edition, 2014
Upon the successful completion of the course a student
will be able to:
- Define, compute, and interpret a definite integral.
- State, explain, and apply the fundamental theorem of calculus.
- Perform techniques of integration, including u-substitution, integration by
parts, decomposition into partial fractions, and trigonometric substitution.
- Recognize and compute improper integrals.
- Apply integrals to concepts such as area, volume, arc length, mass, work,
- Manipulate infinite sequences and series.
- Apply tests of convergence and divergence.
- Find the interval of convergence for power series, manipulate power series
within their intervals of convergence, and represent analytic functions as a Taylor series.
- Describe plane curves in terms of parametric equations and polar
Topics & Time Distribution:
By assuming the total of 13 weeks, the instructor
is given an extra week and a half to use for tests, emphasis on certain topics, etc.
Chapter 5 - Integration (1 week)
Chapter 6 - Applications of Definite Integrals (2 weeks)
Chapter 7 - Integrals and Transcendental Functions (1 week)
Chapter 8 - Techniques of Integration (3 weeks)
Chapter 9 - Infinite Sequences and Series (4 weeks)
Chapter 10 - Parametric Equations and Polar Coordinates (2 weeks)
Below are the essential sections which should be covered by all instructors.
Chapter 5: 5.5, 5.6
Chapter 6: 6.1 – 6.5
Chapter 7: 7.1, 7.3 (only the hyperbolic functions without their inverses)
Chapter 8: 8.1 – 8.4, 8.7
Chapter 9: 9.1 – 9.9
Chapter 10: 10.1 – 10.3, 10.5
Last updated: January 31, 2014