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 (1.1-1.6)
- 2. Limit Concepts (2.1, 2.2)
- 3. Rigorous definitions, one-sided limits (2.3, 2.4)
- 4. Continuity (2.5)
- 5. Limits involving infinity (2.6)
- 6. Introduction to the derivative (3.1-3.4)
- 7. Derivatives of trig functions (3.5)
- 8. Chain rule (3.6)
- 9. Implicit Differentiation (3.7)
- 10. Derivatives of inverse functions: logs and inverse trig functions (3.8, 3.9)
- 11. Related rates (3.10)
- 12. Differentials and linear approximation (3.11)
- 13. Extreme values (4.1)
- 14. Mean value theorem (4.2)
- 15. First and second derivative tests, concavity, curve sketching (4.3-4.4)
- 16. Applied optimization (4.6)
- 17. Newton's Method (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.
- Some faculty may choose to cover sections in an order different from that suggested by the text.
- Section 4.5 is optional, but will be covered in Calculus III.

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- 1. Antiderivatives (4.8)
- 2. The definite integral (5.1-5.3)
- 3. Fundamental theorem of calculus, substitution for indefinite integrals (5.4, 5.5)
- 4. Areas of plane regions, substitution in definite integrals (5.6)
- 5. Volumes (including the "washer method") (6.1)
- 6. Arc length, surfaces of revolution (6.3 and 6.4)
- 7. Moments and centers of mass (6.6)
- 8. The natural logarithm as an integral (7.1)
- 9. Exponential growth and decay (7.2)
- 10. Basic techniques of integration: substitution, integration by parts, trigonometric integrals (8.1-8.3)
- 11. Additional techniques of integration: partial fractions (8.5)
- 12. Numerical integration (8.7)

- About 10 classes for Chapter 5 (including sec. 4.8), 6 classes for Chapter 6, 2 classes for Chapter 7, and 7 classes 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: 6.2, 6.5, 7.3, 7.4, and 8.4. The instructor should cover at least one of the optional sections.

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- 1. Indeterminate forms (4.5)
- 2. Improper integrals (8.8)
- 3. Sequences (10.1)
- 4. Series (10.2)
- 5. Integral test (10.3)
- 6. Power Series (10.7)
- 7. Taylor polynomials, Taylor series, applications (10.8-10.10)
- 8. Parametric Curves (11.1, 11.2)
- 9. Polar Coordinates (11.3-11.5)
- 10. Vectors, dot product, and cross product (12.1-12.4)
- 11. Lines and planes in space (12.5)
- 12. Curves in space, motion, curvature, acceleration (13.1-13.5)

- About 3 classes on the sections from Chapters 4 and 8, 10 classes on Chapter 10, 5 on Chapter 11, 3 on Chapter 12, and 4 on Chapter 13.
- Some faculty may choose to cover sections in an order different from that suggested by the text.
- Sections 10.4 (comparison tests) 10.5 (absolute convergence), and 10.6 (alternating series) are optional, but should be part of the syllabus for freshmen in A term and B term.
- Note that if sections 10.4 (comparison tests) and 10.6 (alternating series) are not covered, convergence of power series at the endpoints of the interval of convergence should be omitted as well.
- Emphasis in Chapter 10 should be on geometric series, power series, and Taylor series, not on convergence tests.
- Coverage of 13.1 through 13.5 will be a bit rushed, but students know much of this from physics.

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- 1. Functions of several variables (14.1)
- 2. Limits, continuity, partial derivatives (14.2, 14.3)
- 3. Chain rule (14.4)
- 4. Directional derivatives and the gradient (14.5)
- 5. Linear approximation, differentials (14.6)
- 6. Multivariable optimization (14.7)
- 7. Double integrals, iterated integrals, double integrals over non-rectangular regions (15.1-15.2)
- 8. Area by double integrals (15.3)
- 9. Double integrals in polar coordinates (15.4)
- 10. Triple integrals (15.5)
- 11. Moments and centers of mass (15.6)
- 12. Integration in cylindrical and spherical coordinates (15.7)
- 13. Change of variables (15.8)

- About 11 classes on Chapter 14, 14 on Chapter 15.
- Sections 14.8 (Lagrange multipliers) and the early sections in Chapter 16 (16.1,16.2) are optional.

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Last Updated: April 22, 2014