# Math 1710       Calculus II Science and Engineering

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

Math 1710 is the second 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 1710 is also suitable for some mathematics majors. Topics include: further techniques and applications of integration, more on trignometric functions, differential equations and their applications, sequences and series, indeterminate forms and improper integrals. This is roughly corresponding to Chapters 7-11 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 1700 or equivalent.

Calculus II Skill Exam:

A Skills Exam focusing on basic skills of differentiation and integration will be given in the first week of the class. Students will have a second opportunity to makeup the skills test. Failing both will result in a half letter grade reduction the course grade. Additional information about the skills exam and some sample problems can be found on website http://www.wmich.edu/math/coursepages/math123/index.html

Objectives:

1. Retention and strengthening prerequisite knowledge base.
2. Evaluating definite, indefinite and improper integrals using a variety of integration techniques.
3. Using numerical techniques to estimate integrals and assess error involved..
4. Understanding the concept of convergence of a infinite series and mastering methods for determining the convergence of a variety of infinite series.
5. Learning the proper use of mathematical notation.
6. Strenthening abilities to tackle multi-step problems and to explain the process.
8. Applying 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 and Maple:

A graphing calculator is required for this class. A TI-89 or equivalent is required. We will use many of the extra capabilities of these calculators. 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 28 sections in 40 unit of 50 minute classes (about 10 weeks). Leave about 3.5-4 weeks for expanding, testing and optional materials.

 Section Topic Time (50 Min. Periods) 7.1 Antiderivatives revisited 1 7.2 Numerical methods 1 7.3 The ln function  (A more formal definition than is in the supplement.) 1 7.4 The function ${e}^{x}$  (A more formal definition than is in the supplement.) 1/2 7.5 Skip 0 7.6 Euler's formula 1 7.7 Inverse trigonometric functions 1 1/2 7.8 Derivatives of inverse trigonometric functions 1 1/2 7.9 Tables of integrals  (This can be done with the calculator.) 1 10.1 Integration by parts 1 1/2 10.2 Trigonometric substitutions  (Yes, these do show up in 2720 and 3740.) 1 1/2 10.3 Rational functions  (These show up in 3740.) 2 10.4 Integration factors  (Lightly.) 1 6.7 Volumes   (We need problems using  ln and exp.) 2 11.1 Work 1 1/2 11.2 The work-energy theorem 1 5.5 Tangent and normal components of acceleration 1 1/2 5.6 Circular motion and curvature 1 1/2 8.1 Separation of variables and exponential growth 1 8.2 Equations of the form $y\text{'}=\mathrm{ky}+b$ 1 8.3 The logistic equation 1 1/2 9.1 L'Hopital's Rule 2 9.2 Improper integrals 1 1/2 9.3 Series 2 9.4 Alternating series and absolute convergence 2 9.5 The ratio test and power series 2 9.6 Power series of functions 2 9.7 Radius of convergence for rational functions 2 11.4 Line integrals of Type I and arc length  (Optional) 11.5 Center of mass and moment of inertia  (Optional) 11.6 Vector fields  (Optional) 11.7 Line integrals of type II and work  (Optional)

Approved by the Department Curriculum Committee 4/08