Instructor: Robert McOwen, 505 LAKE; phone ext. 5635; e-mail: mcowen@neu.edu

Schedule & Room: MTTh 4:05 - 5:10 pm in 103 RY

Office Hours: Mondays 10:30-11:30 am, Tuesdays 2:00-4:00 pm.

Textbook: Calculus, Early Transcendentals by Finney, Weir, and Giordano (10th Ed.).

Calculator (Required): Scientific graphing (TI83 or higher).

Prerequisites: Good command of algebra and Cartesian geometry, and basic knowledge of functions and their inverses. (The course begins with a review of exponential, logarithmic, and trigonometric functions, but some familiarity is expected.)

This course has one all-encompassing goal, namely to understand the concept of the derivative and be able to display that understanding through a variety of applications. Specific, measurable manifestations of your understanding that will be tested during the quarter include your ability to:

• Parameterize curves in the plane and motion along a straight line;
• Describe velocities, and more general rates of change, analytically, graphically and numerically;
• Apply the definition of the derivative to algebraically/analytically realize instantaneous rates of change as limits of average rates of change;
• Visualize and interpret derivatives via slopes of tangent lines to graphs;
• Derive, memorize, and apply the rules for differentiation to calculate derivatives of given functions, including polynomials, exponential and logarithmic functions, trig.\ and inverse-trigonometric functions, and combinations of such functions by using the product rule, the quotient rule, and the chain rule;
• Sketch graphs of functions by analyzing the first and second derivatives;
• Model, by using derivatives, physical problems involving rates of change, including velocity/acceleration problems, exponential growth and decay, and simple oscillations;
• Solve, via derivatives, optimization problems (maximum-minimum problems) which arise in a wide variety of situations involving physics, engineering, economics, etc;
• Calculate the linearization of a function;
• Approximate changes using differentials;
• Estimate roots of equations using Newton's method.

Homework: Assignments will generally be due on Mondays and Thursdays; they will be discussed and sometimes collected. The first assignment is due Monday, January 7: P.3 Exponential Functions: #1-14, 21, 28, 29, 31, 35, 39, 40.

Quizzes: There will generally be weekly quizzes, given on Tuesdays. The lowest quiz score will be dropped.

Exams: In addition to the final exam, there will be one midterm exam, probably to be held Tuesday, February 5.

Grading: Your course grade will be determined as follows

• Homework/Quizzes 30%
• Midterm Exam 30%
• Final Exam 40%

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  Homework Problems for MTH 1740, Winter 2002

  Instructor: Robert McOwen

  Preliminaries

  P.3 Exponential Functions: #1-14, 21, 28, 29, 31, 35, 39, 40.

  P.4 Inverse Funct'ns & Logs: #1-8, 11-13, 17, 20, 31-33, 37, 38, 39(a), 41, 43, 57.

  P.5 Trig Functions & Inverses: #1, 2, 5, 7, 8, 10, 13, 19, 21-24, 27, 39, 43, 44.

  P.6 Parametric Equations: #1-3, 7, 8, 10, 17, 19 21-23.

  Chapter 1

  1.1 Rates of Change and Limits: #1, 2, 5, 7, 9, 11, 13, 14, 17, 19, 23, 41.

  1.2 Finding limits and one-sided limits : #1, 2, 6.

  1.3 Limits involving infinity: #1, 2, 7, 8, 11, 21, 25, 26, 33, 63.

  1.4 Continuity: #1-5, 26, 28(a).

  1.5 Tangent lines: #1, 3, 5-7, 13, 15, 19, 21, 23, 24, 29, 30, 33(a-b), 35, 42.

  Chapter 2

  2.1 The Derivative as a Function: #1-3, 6-8, 13, 15-18, 24-26, 33, 34.

  2.2 The derivative as a rate of change: #1-7, 13, 18, 22, 23, 25.

  2.3 Derivatives of Products, Quotients, and Negative Powers: #1-5, 7, 11-13, 19, 21, 29.

  2.4 Derivatives of Trigonometric Functions: #1-5, 8, 13, 14, 27, 31, 37, 39.

  2.5 The Chain Rule and Parametric Equations: #1, 3, 6, 9, 11-13, 16, 21, 22, 26, 27, 33, 37, 39, 41, 44, 45, 51, 59, 65.

  2.6 Implicit Differentiation: #1, 2, 7, 13, 19, 20, 27, 37, 39, 61.

  2.7 Related Rates: #1-3, 5, 10, 11, 13, 15, 30, 31, 33, 35

  2.8 Derivatives of Inverse Trigonometric Functions: #1, 3, 5, 8, 11, 18-20, 22, 31, 32

  2.9 Derivatives of Exponential and Logarithmic Functions: #1-3, 7, 11, 15-21 odd, 22, 29, 31-33, 39, 41, 43, 47, 49.

  Chapter 3

  3.1 Extreme Values of Functions: #1-6, 10-14, 16, 17, 21, 24, 25, 47, 53, 54.

  3.2 The MVT and Differential Equations: #9, 12-14, 17, 19, 20, 22, 23, 25, 29.

  3.3 The Shape of a Graph: #6-8, 13-19 odd, 20, 23, 27, 43, 45, 47, 59.

  3.1 Extreme Values of Functions (again): #31, 33, 36, 37, 39.

  3.5 Modeling and Optimization: #1, 7, 14-16, 22, 32, 33.

  3.6 Linearization and Differentials: #1, 2, 3, 6, 7, 15, 17, 21, 25, 26, 33, 36.

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  Last modified January 2, 2002. Comments to:  mcowen@neu.edu