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 16A: Short Calculus
Approved: 2005-09-01 (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.

This course requires the Math Placement Exam. Read More.

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:

Two years of High School algebra, plane geometry, plane trigonometry, and satisfying the Mathematics Placement Exam.

Suggested Schedule:

Lecture(s)

Sections

Comments/Topics

1

1.1 – 1.3

Cartesian plane, distance formula, midpoint formula, graphs, intercepts, circles, and lines (Review the definition of absolute value on page O-8).

1.5

1.4

Functions, composition of functions, and inverse.

1.5

1.5

Limits

1

3.6

Vertical asymptotes and finite limits; horizontal asymptotes and limits of infinity.

1

1.6

Continuity

2

2.1

Slope of the tangent line, definition of the derivative, differentiability and continuity.

1

8.1 – 8.3

Trigonometry review

0.5

2..2

Constant rule, power rule, constant multiple rule, sum and differences rules.

1

2.3

Average rate change, instantaneous rate of change, velocity, marginals in economics.

1

2.4

Product and quotient rules.

1

8.4

Derivatives or trig functions.

1

2.5

Chain rule, general power rule (Include relevant problems from section 8.4).

0.5

2.6

Higher order derivatives, acceleration.

1

2.7

Implicit differentiation (Include relevant problems from Section 8.4).

1.5

2.8

Related rates.

1

3.1

Increasing and decreasing functions, critical numbers.

1.5

3.2

Relative extrema, the first-derivative test, absolute extrema (Include relevant problems from section 8.4 and page 612).

1

3.3

Concavity, points of inflection, the second-derivative test.

2

3.4

Optimization problems (You may want to assign some problems from section 3.5).

2

3.7

Sketching graphs (You may want to assign some problems from section 3.6).

1

3.8

Differentials (Explain estimating function values using differentials).

Additional Notes:

Students will briefly review some critical pre-calculus concepts, including trigonometry and analytic geometry, before learning the basic concepts of differential calculus. After discussing continuity and limits, the course introduces the derivative of a function defined as the slopes of its tangent lines. When applied to examples in economics, physics, chemistry, etc. the derivative is viewed as a rate of change, which allows for a deeper qualitative discussion and analysis of graphs, extrema, and inflection points.

This course is a pre-requisite for integral and mult-variable calculus. Mastery of this course will be reflected in improved reading and logical thinking skills, as well as enhanced algebraic, analytic, and general problem-solving skills, especially in the context of related rates and maximum-minimum word problems.

Assessment:

Mastery of this course is usually assessed by periodic quizzes, homework problems, hour exams, short papers, and a comprehensive final exam.