Math 1700 is the first of a two-semester sequence in differential and intgral calculus, and part of a four-semester sequence of core mathematics courses required by most engineering and science programs. Math 1700 is also suitable for some mathematics majors. Topics include: vectors, their operations and applications, functions, limits, continuity, techniques and applications of differentiation and integration and fundamental theorem of calculus. This is roughly corresponding to Chapters 1-6 of the text. Students are responsible for all material in the text and all material presented in class. This includes any material not in the text and all material in the text that was not presented in class.

** Course
Prerequisites:** A passing grade (C or
better) in Math 1180 or a satisfactory score on an appropriate
placement exam (ACT, SAT, WMU math placement exam). There will be an
advisory algebra exam on prerequisite skills for this course.

__Objectives:__

1. Understanding how vectors and their operations related to
real world models, in particular, to goemetrical and physical models.

2. Understanding the concept of limit and how it relates average and
instantaneous quantities.

3. Understanding the concept of derivative, interpreting it
geometrically, physically and using it in optimization and linear
approximation.

4. Understanding integration and its relationship with differentiation
and applying integration in goemetrical and physical problems.

5. Learning the proper use of mathematical notation.

6. Developing sufficient computational skills in vector, differential
and integral operations for subsequent calculus courses and for
applications in other areas.

7. Developing abilities to tackle multi-step problems and to explain
the process.

8. Understanding the possibilities of modern computer algebra
systems in assisting the analysis of problems in
calculus and the visualization of their solutions.

9. Developing skills in mathematical reasoning.

10. Developing a broad perspective of how various different topics in
this course fit together.

__Calculator:__

A graphing
calculator is required for this class. A TI-89 or equivalent is
required. Extra capabilities of these calculators will be used. The
following website by Professor Pence** **contains
a nice tutorial of how to use these graphing calculators: http://homepages.wmich.edu/~pence/MATH170-171.htm

Section | Topic | Time (50 min. periods) |

1.1 | ${\mathbb{R}}^{n}$ | 1 |

1.2 | Graphs in ${\mathbb{R}}^{2}$and ${\mathbb{R}}^{3}$ | 1 |

1.3 | Algebra in ${\mathbb{R}}^{n}$ | 1 |

1.4 | The dot product | 1 |

1.5 | Determinants, areas, and volume | 1 1/2 |

1.6 | Equations of lines and planes | 1 |

2.1 | Functions | 1 |

2.2 | Functions and graphing technology. Lightly | 1 |

2.3 | Functions from $\mathbb{R}$to ${\mathbb{R}}^{n}$ | 1 |

2.4 | The wrapping function and other functions | 1 |

2.5 | Sketching parametrized curves. Quickly, some students have not seen this before. | 1 |

2.6 | Composition of functions | 1 1/2 |

2.7 | Building new functions, Lightly, this appear again in Math 272. | 1 |

3.1 | Average velocity and average rate of change | 1 |

3.2 | Limits: an intuitive approach | 1 |

3.3 | Instantaneous rate of change: the derivative | 1 |

3.4 | Linear approximations of functions | 1 1/2 |

3.5 | More on limits | 1 |

3.6 | Limits: a formal approach | 1 |

4.1 | Sum and product rule, higher order derivatives | 1 (+1/2) |

4.2 | The quotient rule | 1 |

4.3 | The chain rule | 1 |

Supp. | Derivatives of ln and exp functions | 1 |

4.4 | Implicit differentiation | 1 1/2 |

4.5 | Higher order Taylor polynomials Skip if you do not have time. | 1 1/2 |

5.1 | Asymptotes | 1 |

5.2 | Increasing and decreasing functions | 1 |

5.3 | Increasing and decreasing curves | 1 |

5.4 | Concavity | 1 |

5.7 | Applications of maxima and minima | 1 1/2 |

5.8 | The remainder theorem for Taylor polynomials Skip if you do not have time. | 1 1/2 |

6.1 | Antiderivatives and the integral | 1 |

6.2 | The chain rule in reverse (Substitution) | 1 1/2 |

6.3 | Acceleration, velocity, and position | 1/2 |

6.4 | Antiderivatives and Area | 1 |

6.5 | Area and Riemann Sums | 1 |

6.6 | The Definite Integral | 1 |

6.8 | Fundametal Theorem of Calculus | 1 |

Approved by the Department Curriculum Committee 4/08