# 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 21A: Calculus: Differential Calculus

**Approved:**2007-04-01 (revised 2013-01-01, J. DeLoera)

**ATTENTION:**

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

**Prerequisites:**

**Suggested Schedule:**

Lecture(s) |
Sections |
Comments/Topics |

1 |
1.1 – 1.6 |
Review chapter one. Cover definitions of exponential functions, inverse functions, and logarithms. Okay to skip and refer to as needed. |

1 |
2.1 |
Rates of change and tangents to curves |

1 |
2.2 |
Limit of a function and limit laws |

1 |
2.3 |
Precise definition of limit |

1 |
2.4 |
One-sided limits |

1.5 |
2.5 |
Continuity |

1.5 |
2.6 |
Limits involving infinity; asymptotes of graphs |

0.5 |
3.1 |
Tangents and the derivative at a point |

1 |
3.2 |
The derivative as a function |

1.5 |
3.3 |
Differentiation rules |

1 |
3.4 |
The derivative as a rate of change |

0.5 |
3.5 |
Derivatives of trigonometric functions |

1.5 |
3.6 |
The Chain Rule |

1 |
3.7 |
Implicit differentiation |

1 |
3.8 |
Derivative of inverse functions and logarithms |

1 |
3.9 |
Inverse trigonometric functions |

1 |
3.10 |
Related rates |

1 |
3.11 |
Linearization and differentials |

1 |
4.1 |
Extreme values of functions |

1 |
4.2 |
The Mean Value Theorem |

1 |
4.3 |
Monotonic functions and the first derivative test |

1 |
4.4 |
Concavity and curve sketching |

1 |
4.5 |
Indeterminate forms and L’Hopital’s Rule (omit proof) |

1 |
4.6 |
Applied optimization |

1 |
4.7 |
Newton’s method |

**Additional Notes:**

**Learning Goals:**

Students will learn the fundaments of differential calculus. At its most rudimentary level, this is the study of rates of change and motion which enables computations of how systems evolve based on simple laws. Calculus therefore forms the foundations of modern science. In this course student not only learn the basic techniques of calculus, but also how to distill the mathematical essence of real world systems in terms of well posed problems for the important variables of the problem.

This course is an entry point to advance mathematics. Mastery of this course enhances analytic and problem solving skills of students. At the same time the course supports the ability to design mathematical models in a wide range of applied fields.

**Assessment:**