Worcester Polytechnic Institute

MA 1021 - Differential Calculus

MA 1022 - Integral Calculus

MA 1023 - Approximation, Series, polar coordinates, and vectors

MA 1024 - Multivariable Calculus

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- 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.

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- 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)
- 6. Volumes (including the "washer method") (6.2)
- 7. Arc length, Centroids (6.4 and 6.6)
- 8. The natural logarithm, inverse trig functions (6.7-6.8)
- 9. Basic techniques of integration: substitution, integration by parts, trigonometric integrals (7.2-7.4)
- 10. Additional techniques of integration: partial fractions (7.5)
- 11. Exponential growth and decay (8.1)

- About 10 classes for Chapter 5, 7 classes for Chapter 6, 7 classes for Chapter 7, and one class for Chapter 8.
- Some faculty may choose to cover sections in an order different from that suggested by the text.
- The following sections are optional: 6.3, 6.5, 6.9, 7.6, and 7.7. The instructor should cover at least one of the optional sections.

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- 1. Indeterminate forms (4.8-4.9)
- 2. Improper integrals (7.8)
- 3. Sequences (10.2)
- 4. Series (10.3)
- 5. Taylor polynomials and Taylor series (10.4)
- 6. Integral test (10.5)
- 7. Power Series (10.8-10.9)
- 8. Polar Coordinates (9.2-9.3)
- 9. Parametric Curves (9.4-9.5)
- 10. Vectors, dot product, and cross product (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, 5 classes on Chapter 9, 10 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. The order above seems natural because it keeps the focus on limits and convergence without interruption in the first half of the course. The second half then focuses on calculus for parametric curves, with polar coordinates a natural introduction.
- Sections 10.6 (comparison tests) and 10.7 (absolute convergence) are optional, but should be part of the syllabus for freshmen in A term and B term.
- Note that if sections 10.6 (comparison tests) and 10.7 (absolute convergence) are not covered, convergence of power series at the endpoints of the interval of convergence should be omitted as well.
- 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.

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- 1. Functions of several variables (12.2)
- 2. Limits, continuity, partial derivatives (12.3, 12.4)
- 3. Multivariable optimization (12.5)
- 4. Linear approximation, differentials (12.6)
- 5. Chain rule (12.7)
- 6. Directional derivatives and the gradient (12.8)
- 7. Critical points (12.10)
- 8. Double integrals, iterated integrals, double integrals over non-rectangular regions (13.1-13.3)
- 9. Double integrals in polar coordinates (13.4)
- 10. Appplications of double integrals (13.5)
- 11. Triple integrals (13.6)
- 12. Integration in cylindrical and spherical coordinates (13.7)
- 13. Surface area (13.8)
- 14. 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: April 28, 2010