WPI Mathematical Sciences Department Worcester Polytechnic Institute


Syllabus for MA 1021-1024 using Thomas, Hass, Heil, Weir (14th ed., early transcendentals) published by Pearson



MA 1021 - Differential Calculus
MA 1022 - Integral Calculus
MA 1023 - Approximation, Series, polar coordinates, and vectors
MA 1024 - Multivariable Calculus



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MA 1021 Differential Calculus

(Chapters 1, 2, 3, 4)

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)

Remarks



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MA 1022 Integral Calculus

(Chapters 5, 6, 7, 8)

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)

Remarks



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MA 1023 Series, approximations, polar coordinates, and vectors

(Chapters 10, 11, 12, 13 and parts of Chapters 4 and 8)

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)

Remarks



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MA 1024 Multivariable Calculus

(Chapters 14 and 15)

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)

Remarks


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Last Updated: April 22, 2014