Worcester Polytechnic Institute

Syllabus for MA 1021-1024 using Edwards and Penney (6th ed., early transcendentals) published by Prentice-Hall

MA 1021 Differential Calculus

(Chapters 1, 2, 3, 4)

1.: Functions, operations on functions, transcendental functions (1.1-1.4)
2.: Limit Concepts (1.5-2.2)
3.: Limits of trig functions, rigorous definitions, infinite limits, etc. (2.3)
4.: Continuity (2.4)
5.: Introduction to the derivative (3.1, 3.2)
6.: Chain rule and Generalized Power Rule (3.3, 3.4)
7.: Optimization in one dimension, applications (3.5, 3.6)
8.: Derivatives of standard transcendental functions (3.7, 3.8)
9.: Implicit Differentiation, Related Rates (3.9)
10.: Newton's Method (3.10)
11.: Differentials and linear approximation (4.2)
12.: Mean Value Theorem (4.3)
13.: Extreme values, first and second derivative tests, concavity, curve sketching (4.4-4.7)

About 2 classes for Chapter 1, 4 classes for Chapter 2, 12 classes for Chapter 3 and 7 classes for Chapter 4.
Regarding Section 2.3, the rigorous definition of the limit will not be tested on the common final and so pages 83-85 are optional.
Some faculty may choose to cover sections in an order different from that suggested by the text.
Sections 4.8 and 4.9 are optional. But these will be covered in Calculus III.

(Chapters 5, 6, 7, 8)

1.: Antiderivatives (5.2)
2.: The definite integral (5.3-5.4)
3.: Fundamental theorem of calculus, properties of the definite integral, substitution (5.5-5.7)
4.: Areas of plane regions, numerical integration (5.8-5.9)
5.: Modelling with Riemann sums (6.1)
5.: Volumes (including the "washer method") (6.2)
6.: Force and work (6.5)
7.: The natural logarithm, inverse trig functions (6.7-6.8)
8.: Basic techniques of integration: substitution, integration by parts, trigonometric integrals (7.2-7.4)
9.: Exponential growth and decay (8.1)

Some faculty may choose to cover sections in an order different from that suggested by the text.
IMPORTANT: The large number of optional sections below does not permit the instructor to omit them all, but rather allows for a variety of styles. Each instructor should cover at least three of the sections listed below.
The following sections are optional: 6.3, 6.4, 6.6, 6.9, 7.5, 7.6, 7.7.
We suggest the instructor interpolate between the following two syllabi:
- Modeling Emphasis: 10 classes on Chapter 5, 10 classes on Chapter 6 (including sections 6.3, 6.4, 6.6), 4 classes on Chapter 7 and one class on Chapter 8.
- Techniques Emphasis: 10 classes on Chapter 5, 7 classes on Chapter 6, 7 classes on Chapter 7 (including sections 7.5-7.7) and one class on Chapter 8.

(Chapters 9, 10, 11, and parts of Chapters 4 and 7)

1.: Indeterminate forms (4.8, 4.9)
2.: Improper integrals (7.8)
3.: Polar Coordinates (9.2, 9.3)
4.: Parametric Curves (9.4, 9.5)
5.: Sequences (10.2)
6.: Series (10.3)
7.: Taylor series and Taylor polynomials (10.4)
8.: Convergence tests (10.5-10.7)
9.: Power Series (10.8, 10.9)
10.: Vectors and cross products (11.1-11.3)
11.: Lines and planes in space (11.4)
12.: Curves in space, motion, curvature, acceleration (11.5, 11.6)

About 3 classes on the sections from Chapters 4 and 7, 4 classes on Chapter 9, 11 on Chapter 10, and 6 on Chapter 11.
Some faculty may choose to cover sections in an order different from that suggested by the text. (For example, it may seem natural to cover Chapter 10 before Chapter 9.)
Sections 10.10 (series solutions to diff. eqns.) and 11.7 (cylinders and quadric surfaces) are optional.
Emphasis in Chapter 10 should be on geometric series, power series, and Taylor series, not on convergence tests.
Coverage of 11.4 through 11.6 will be a bit rushed, but students know much of this from physics.

(Chapters 12 and 13)

6.: Functions of several variables (12.2)
7.: Limits, continuity, partial derivatives (12.3, 12.4)
8.: Multivariable optimization (12.5)
8.: Linear approximation, differentials (12.6)
10.: Chain rule (12.7)
9.: Directional derivatives and the gradient (12.8)
12.: Critical points (12.10)
13.: Double integrals, iterated integrals, double integrals over non-rectangular regions (13.1-13.3)
14.: Double integrals in polar coordinates (13.4)
15.: Appplications of double integrals (13.5)
17.: Triple integrals (13.6)
18.: Integration in cylindrical and spherical coordinates (13.7)
16.: Surface area (13.8)
16.: Change of variables (13.9)

About 12 classes on Chapter 12, 13 on Chapter 13.
Sections 12.9 (Lagrange multipliers) and the early sections in Chapter 14 (14.1,14.2) are optional.

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Last Updated: August 5, 2005