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 16B: Short Calculus
Approved: 1999-09-01 (revised 2005-09-01, 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.
Search by ISBN on Amazon: 9781133115007

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1.5

4.1 – 4.3

Exponential functions and their derivatives.

Note: You may want to skip the “proof” on page 273 that the exponential function is its own derivative, and justify this after you show in section 4.5 how to differentiate y = ln x, using the def. of the derivative).

1

4.4

Logarithmic functions

1.5

4.5

Derivatives of logarithmic functions

Note: Show how to differentiate functions of the form

y = [f(x)] ^ [g(x)]

1

4.6

Exponential growth and decay

Note: notice that the proof on page 299 is incomplete.

1

5.1

Antiderivatives and indefinite integrals

1

5.2

The General Power Rule

Note: Use this section as a simple introduction to substitution, rather than emphasizing the general power rule itself.

0.5

8.5

Simple trig integrals

Note: Introduce the integration rules on page 588. Point out that the substitution u = x in example one is never needed.

1

5.3

Exponential and logarithmic integrals

1.5

5.4

Definite integrals and the Fundamental Theorem of Calculus

Note: Mention that a more standard approach to definite integrals is presented in Appendix A.

1

5.5

Area of a region

Note: Present some examples of regions bounded by graphs of functions of y, since these are not included in the examples.

1.5

5.7

Volumes of solids of revolution (disc/washer method).

Note: You may want to show how to find the volume when a region is revolved around a general vertical or horizontal line.

1

6.1

Integration by substitution

1.5

6.2

Integration by parts

Note: you may want to introduce tabular integration (vertical integration by parts).

1

8.5

Trigonometric integrals

Note: Introduce the integrals on page 592. Mention that there are two common ways to write the anti-derivative of the tangent function.

1

6.3

Partial fractions

Note: Make it clear when division is necessary.

1.5

6.6

Improper integrals

1

9.1

Discrete probability

Note: This section is meant to motivate the ideas in the next two sections.

1

9.2

Continuous random variables

1.5

9.3

Mean and median; variance and standard deviation; uniform, normal, and exponential probability density functions.

0.5

5.6

The midpoint rule

Note: Point out that any integrals cannot be evaluated using the Fundamental Theorem of Calculus.

1

6.5

The trapezoidal rule and Simpson’s rule.

Note: do not require memorization of the error formulas on page 431.

0.5

6.4

Integration tables and completing the square.

Note: Make it clear that the formulas on pages 417-419 do not have to be memorized.

Additional Notes:

You might prefer to cover Section 5.6 immediately before Section 5.7 to motivate the formulas given in that section.