# 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 16C: Short Calculus

Approved: 2000-09-01 (revised 2013-12-01, D.A. Kouba)
ATTENTION:
This course is part of the inclusive access program, in which your textbook and other course resources will be made available online. Please consult your instructor on the FIRST DAY of instruction.
Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Calculus: An Applied Approach, 9th Edition, by Larson/Edwards; Cengage Learning.
Search by ISBN on Amazon: 9781133115007
Prerequisites:
Completion of courses MAT 16B, 17B or 21B.
Suggested Schedule:
 Lecture(s) Sections Comments/Topics 0.5 C.1 Introduction to differential equations 1 C.2 Separation of variables (Show how to derive the exponential growth and decay formula). 1.5 C.3 First order linear DE’s (Give students practice solving a mixture of separable and linear De’s). 1.5 C.4 Applications of DE’s (You may want to cover logistic growth on page 410; Notice the error in the Study Tip) 0.5 7.1 3-dimensional coordinates 1.5 7.2 Planes and quadric surfaces 0.5 7.3 Functions of several variables, level curves. 1.5 7.4 Partial derivatives 2 7.5 Relative extrema for functions of two variables. 1.5 7.6 Lagrange multipliers 1.5 7.8 Double integrals 1.5 7.9 Applications of double integrals: volume and average value (You may want to show how to find the volumes of solids bounded by 2 surfaces). 1 10.1 Sequences 1.5 10.2 Definition of infinite series, Divergence test, geometric series. 2 10.3 P-series, Ratio test (You may want to introduce the Comparison Test). 2 10.4 Power series, Taylor’s Theorem. 0.5 10.4 Maclaurin series for sine and cosine, binomial series (Assign problems to estimate function values and definite integrals using these series) 1 10.5 Taylor polynomials (Taylor’s Theorem with Remainder, page 694, is optional). 1 10.6 Newton’s Method
Learning Goals:
This course, the third in our short calculus sequence, is designed to give students exposure to several topics in mathematics with important applications. One main topic covered in the course is differential equations, with an introduction to separable and linear first-order differential equations in particular. Students are also presented with examples of applications of differential equations, and are expected to develop the ability to set up and solve differential equations for simple applications. The next major topic in the course is functions of two variables, including topics such as partial derivatives, relative extrema for functions of two variables, and double integrals. Students also see how to find volumes using double integrals, and they also learn how to use Lagrange multipliers to solve constrained optimization problems. The other main part of the course is devoted to sequences and infinite series, including power series representations of functions. In this part of the course, students develop practice in logical reasoning and see how to estimate function values and definite integrals using series. They also learn how to estimate roots of equations using Newton's method.
Assessment:
Students' progress in the course is typically assessed by 2-3 tests during the quarter as well as a comprehensive final examination, and in some cases by homework problems and quizzes in addition.