# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

## MAT 21B: Calculus: Integral Calculus

**Approved:**2007-04-01 (revised 2021-12-08, J.Challenor and UPC)

**ATTENTION:**

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

**Prerequisites:**

**Suggested Schedule:**

Lecture(s) |
Sections |
Comments/Topics |

1 |
4.8 |
Antiderivatives |

1 |
5.1 |
Area and estimating with finite sums |

1 |
5.2 |
Sigma notation and limits of finite sums |

1 |
5.3 |
The definite integral |

1.5 |
5.4 |
The Fundamental Theorem of Calculus |

1 |
5.5 |
Indefinite integrals and the substitution method |

1 |
5.6 |
Definite Integral Substitutions and the area between curves |

1 |
6.1 |
Volumes using cross sections |

1 |
6.2 |
Volumes using cylindrical shells |

1 |
6.3 |
Arc length |

1 |
6.4 |
Areas of surfaces of revolution |

1 |
7.1 |
The Lorgarithm Defined as an integral |

0.5 |
8.1 |
Using basic integration formulas |

1 |
8.2 |
Integration by Parts |

1 |
8.3 |
Trigonometric Integrals |

1 |
8.4 |
Trigonometric Substitutions |

1 |
8.5 |
Integration of rational functions by partial fractions |

1 |
8.7 |
Numerical integration |

2 |
8.8 |
Improper integrals |

0.5 |
11.1 |
Parametrization of plane curves |

1 |
11.2 |
Calculus with plane curves |

0.5 |
11.3 |
Polar coordinates |

1 |
11.4 |
Graphing Polar Coordinate Equations |

**Additional Notes:**

- 7.2 Exponential Change and Separable Differential Equations
- 8.6 Integral Tables and Computer Algebra Systems
- 9.2 First-Order Linear Differential Equations
- 11.5 Areas and Lengths in Polar Coordinates

Instructors may want to consider the following adjustments to the schedule as stated above:

- Instructors may want to cover antiderivatives (section 4.8) after introducing Riemann sums and right before the Fundamental Theorem of Calculus (section 5.4). They may also want to wait to introduce indefinite integral notation until section 5.5.
- Instructors may find that they can discuss a wider variety of applications of integrals if the integration techniques in chapter 8 are covered before the applications in chapter 6.
- Instructors may consider adding an additional half-lecture on numerical integration error analysis in section 8.7.
- Covering section 11.5 (areas and lengths in polar coordinates) immediately after section 11.4 is a particularly appropriate way to conclude the class as it revisits the idea of a Riemann sum in the context of polar functions.

**Learning Goals:**

**Assessment:**