# Math 1700          Calculus I Science and Engineering

Text: Calculus with Early Vectors by Zenor, Slaminka and Thaxton, Prentice-Hall, 1999
Course Description:

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

Schedule:   The following suggested schedule covers 38 sections in 42.5 unit of 50 minute classes (about 11 weeks). Leave about 2-2.5 weeks for expanding, testing and additional materials.

 Section Topic Time (50 min. periods) 1.1 ${ℝ}^{n}$ 1 1.2 Graphs in ${ℝ}^{2}$and ${ℝ}^{3}$ 1 1.3 Algebra in ${ℝ}^{n}$ 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  $ℝ$to  ${ℝ}^{n}$ 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